Chronological and Astronomical Treatises of Ancient Writers, edited by Denis Pétau

GEMINI INTRODUCTION TO THE PHENOMENA

GEMINI ELEMENTS OF ASTRONOMY

CAPUT I.

^A The circle of the zodiac is divided into twelve parts, and each of these segments is generally called a *dodecatemorion*, that is, a twelfth part; but specifically it is called a sign: and it receives this name from the stars which it contains, and by which each of these signs is also delineated. Now these twelve signs are the following: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces.

The term "sign" is used in two ways: in one way, as the twelfth part of the zodiac, which is a certain local interval determined either by stars or by points; in another way, as that which is fashioned from stars according to the likeness and the position of the stars as a constellation.

The dodecatemoria, therefore, are equal to one another in size, for the reason that the zodiac is divided into twelve equal parts; but the signs which are composed of fixed stars are not equal in size, nor are they composed of an equal number of stars; nor do they all fill up the proper regions of the dodecatemoria. Rather, some fall short of this completion, as for instance Cancer, ^B which occupies only a small portion of its own proper place, while others extend beyond their proper places, and occupy parts of the preceding and following signs, as does Leo.

^C (1) The term "sign" is twofold, which pertains to our undertaking: one is in the *primum mobile*, which does not change its position—that is, it forever retains the same intersections of its ecliptic with the equinoctial—and it is devoid of figures; the other is in the starry sphere, which, in progressing, continually makes its intersections with the equinoctial at different points. To this belong the signs, or the asterisms of the dodecatemoria. Hipparchus, by comparing the observations of the ancients with his own, was the first to suspect that the eighth sphere moves in the order of the signs, and that consequently there is a double zodiac. But because the observations of his predecessors were not sufficiently long-standing, he did not treat it as a settled fact. Ptolemy, however, clearly defined the matter. These things had to be stated lest anyone wonder why they were passed over by Geminus, who, as in most other matters, follows Eudoxus rather than Hipparchus. Nor does he pursue the question, for there was no necessity to do so while writing the first elements of this art. For this reason, he speaks of the zodiac as if it were a single sphere and never changed its position. The dodecatemoria of the true zodiac, which is in the *primum mobile*, received their names at that time from the asterisms when they contained them: thus, for instance, Aries was called the first dodecatemorion because at that time the asterism of the eighth sphere—to which this name was given—was in it, which occurred accurately in the ages of Meton, Eudoxus, and Ptolemy. In our own time, however, the asterisms have progressed much further toward the rear, and they consist almost entirely outside of those segments. Because of this, for most stars, the latitudes from the true ecliptic and the declinations have been changed, so that those which were southern became northern, and vice versa. ^D (2) *Nor do they all fill up...* See Hipparchus, Book II, near the beginning.

^A Furthermore, certain of the twelve signs are not even entirely laid out within the zodiacal circle; but some are further to the north of it, as is Leo, and others further to the south, as is Scorpio.

Again, each of the dodecatemoria is divided into thirty parts, and the one segment is called a degree. Thus, the whole circle of the zodiac contains twelve signs and three hundred and sixty degrees.

The sun traverses the zodiacal circle in a year (3). For the annual time is that in which the sun travels around the zodiacal circle and returns from the same point to the same point. This time is of three hundred and sixty-five and one-quarter days. For in such a quantity of days the sun passes through the three hundred and sixty degrees; so that the sun moves almost one degree in one day.

However, a degree is one thing, and a day is another. For a degree is a certain interval, existing as a part of the sign; but a day is a time, which is approximately the thirtieth part of the monthly time. And the degree is the three hundred and sixtieth part of the zodiacal circle, but the day is the three hundred and sixty-five and one-quarter part of the annual time, approximately. And while the signs are always of thirty parts, they are not always of thirty days.

The annual time is divided into four parts: spring, summer, autumn, and winter. The vernal equinox (4) occurs about the height of the blossoms, in the first degree of Aries; but the summer solstice occurs about the intensity of the heat, in the first degree of Cancer, where the sun describes the most northern circle and performs the longest day of all those in the year, and the shortest night. Yet the longest day is equal to the longest night, and the shortest day is equal to the shortest night. And the longest day, according to the climate of Rhodes, is 14 1/4 equinoctial hours. The autumnal equinox ^B is when the sun, moving from the north toward the south, again arrives at the equinoctial circle and makes the day equal to the night. But the winter solstice is when the sun has become as distant as possible from our habitable region, and is at its lowest position locally with respect to the horizon (5), and describes the most southern circle, and makes the longest night of all those in the year, and the shortest day. And the longest night, according to the climate of Rhodes, is 14 1/2 equinoctial hours.

The times, therefore, that are between the solstices and the equinoxes in the same [year]. ^{C D}

are divided in this way: from the vernal equinox to the summer solstice there are 94 1/2 days; for in that many days the sun travels through Aries, Taurus, and Gemini, and, arriving at the first part of Cancer, it creates the summer solstice. From the summer solstice to the autumnal equinox there are 92 1/2 days; for in that many days the sun travels through Cancer, Leo, and Virgo, and, arriving at the first part of Libra, it creates the autumnal equinox. From the autumnal equinox to the winter solstice there are 88 1/8 days; for in that many days the sun travels through Libra, Scorpio, and Sagittarius, and, arriving at the first part of Capricorn, the sun creates the winter solstice. From the winter solstice to the vernal equinox there are 90 1/8 days; for in that many days the sun travels through the remaining three signs, Capricorn, Aquarius, and Pisces. All the days of these four seasons, when added together, make 365 1/4, which is the number of days in the year. ^B

It is asked, therefore, in these matters, how it is that, while the four quadrants of the zodiac arc equal, and the sun always moves at an equal speed, it traverses the equal arcs of these quadrants in unequal times; for throughout all of astronomy it is presupposed that both the sun and the moon, and the five planets, move equally, circularly, and contrary to the motion of the world. For the Pythagoreans, being the first to approach such investigations, assumed circular and uniform motions for the sun, the moon, and the wandering stars. For they did not accept such an irregularity in these divine and eternal bodies, such that they would move sometimes faster, sometimes slower, and sometimes stand still—which they indeed call "stations" in the case of the five wandering stars. For no one would admit such an irregularity of motion in the steps of a well-composed and orderly man; for the needs of life often become for men the causes of slowness and speed. But in the incorruptible nature of the stars, no cause for speed or slowness can be brought forward. For which reason the Pythagoreans proposed this question: How could the appearances be saved by circular and uniform motions? ^C

Therefore, we shall explain the cause regarding the other planets in other writings; but now we shall demonstrate the cause regarding the sun, why, although it moves uniformly, it traverses the equal arcs of the zodiac in unequal times. For the supreme sphere of all is that which is called the [sphere] of the fixed stars, which contains in itself the configuration of all the fixed constellations, or signs. However, one should not think that all the stars are placed under the same surface, but that some are higher and others are lower. For since our vision extends to an equal length from the earth into the sky, the difference in altitude becomes imperceptible. ^D

Beneath the sphere of the ^A fixed stars lies the star named Phainon, or Saturn. This star traverses the zodiacal circle in approximately thirty years, and a single sign in two years and six months. Beneath Phainon is carried the lower star, Phaethon, which is called the star of Zeus (Jupiter). This star traverses the zodiacal circle in twelve years, and a single sign in one year. Beneath this is placed Pyroeis, the star of Ares (Mars). This star passes through the zodiacal circle in two years and six months, and a single sign in two months and a half. The adjacent region is held by the Sun, which traverses the zodiacal circle in a year, and a single sign in approximately one month. Lower than this lies Phosphoros, the star of Aphrodite (Venus). This moves with approximately equal velocity to the Sun ^B. Beneath this is placed the star of Hermes (Mercury); it too moves with velocity equal to the Sun. Lower than all is carried the Moon, which traverses the zodiacal circle in twenty-seven and a third days; and a single sign in two days and approximately the fourth part of one day.

If, therefore, the Sun moved upon the constellations of the zodiac, the times between the solstices and the equinoxes would necessarily be equal to one another. For, moving with equal velocity over equal arcs, it would accomplish them in equal times. Likewise, if the Sun were carried below the zodiacal circle, but moved around the same center as the zodiacal circle, in this case too the times between the solstices and the equinoxes ^C would be equal. For all circles described about the same center are divided in like manner by their diameters. Thus, since the zodiacal circle is divided into four equal parts by the diameters connecting the tropical and equinoctial points, it is necessary that the solar circle also be divided into four equal parts by the same diameters. Moving with equal velocity upon its own circumference, the Sun would therefore complete the times of the quadrants in equal intervals. But in fact the Sun is carried lower, and moves upon an eccentric circle, as has been described below. For the center of the solar circle and that of the zodiac are not the same; ^D rather, the sphere of the Sun is drawn aside toward one part. Because of such a position, the solar path is divided into four unequal parts; and the greatest arc becomes that which falls under the quadrant of the zodiac circle, that from the first degree of Aries to the thirtieth of Gemini, while the least arc is the one lying under the quadrant from the first degree of Libra to the thirtieth degree of Sagittarius.

^A Hence, the sun, moving with an even speed along its own circle, reasonably traverses unequal arcs in unequal times; and it travels through the greatest arc in the greatest time, and the least arc in the least time. But when it traverses the greatest arc on its own circle, it then passes through that quadrant of the zodiac which lies between the vernal equinox and the summer solstice; and when it moves along the least arc on its own circle, it then travels through that quadrant of the zodiac which lies between the autumnal equinox and the winter solstice. Since, therefore, unequal arcs of the solar circle fall under equal arcs of the zodiacal circle, it is necessary that the times between the solstitial and equinoctial points be unequal, and that the greatest time be that from the vernal equinoctial point to the summer solstitial point, and the least be that from the autumnal equinoctial point to the winter solstitial point ^B. The sun, therefore, is perpetually moving at a steady pace. But because of the eccentricity of the solar sphere, it traverses the quadrants of the zodiac in unequal times. For the same reason, the sun also traverses equal signs of the zodiac in unequal times. For if we draw straight lines from the extremities of the dodecatemoria to the center of the zodiacal circle, as the underlying figure shows, the zodiac will be divided into twelve equal parts, but the circle of the sun, because of the eccentricity, will be divided into twelve unequal parts; and the greatest arc on the solar circle will be that which lies under Gemini, and the least will be that which lies under Sagittarius. ^C

[Diagram of the Zodiac]

^D For which reason the sun traverses Gemini in the greatest time, and Sagittarius in the least time, though the sun itself is always moving with an even speed. But since, because of the eccentricity, the solar circle is cut into unequal parts, it happens that the times of the signs of the zodiac are unequal.

Gemini Elementa Astronomiae

There are four differences in the order and position of the ^A twelve signs of the zodiac relative to one another. For some are said to be diametrically opposite, others triangular, others quadrangular, and others in conjunction, which some also call opposite combination.

Now, those signs are diametrically opposite which are situated along the same diameter. These are as follows: Aries, Libra, Taurus, Scorpius, Gemini, Sagittarius, Cancer, Capricornus, Leo, Aquarius, ^B Virgo, Pisces. It happens with these that when the one rises, the one diametrically opposite to it sets, and vice versa. This principle applies to the dodecatemoria (the twelve signs), not to the starry signs themselves. For when Aries rises, Libra sets; when Taurus rises, Scorpius sets. The same ratio applies to the rest of the diametrically opposite signs. These diametrically opposite signs are also taken by the Chaldeans regarding mutual sympathies in nativities. For they seem to be in sympathy with those born in opposite signs, and, as one might say, to be opposed to one ^C another. And the positions of the stars in diametrically opposite signs, at the same time, both assist and harm nativities according to the transmitted powers of the stars.

The triangular signs are Aries, Leo, Sagittarius; Taurus, Virgo, Capricornus; Gemini, Libra, Aquarius; Cancer, Scorpius, Pisces. All four triangles are equilateral. The side of the triangle subtends four signs, or 120 degrees. The first triangle, starting from Aries, is called the northern triangle. For if, when the moon is in one of these three signs, a north wind blows, the same condition remains for many days. Hence, ^D starting from this observation, astrologers predict northern conditions. For if, while the moon is in another sign, a northern condition arises, the north wind is easily dissolved; but if a north wind blows while the moon is in one of those signs contained within the northern triangle, they predict that the same constitution will remain for many days. The next triangle, which starts from Taurus, is called southern. For if, again, when the moon is in one of these three signs...

^A a south wind blows, the same state remains for many days. The next triangle, which begins from the Twins, is called zephyric for the same reason; and the last triangle, which begins from the Crab, is called subsolan for the same reason.

These triangles are also used for finding the sympathies which are observed in nativities. For those who are born according to the same triangle seem to sympathize with one another, and the configurations of the stars which are in the same triangles simultaneously aid or harm the nativities. For sympathies occur in three ways: by diameter, by triangle, and by square. By another interval, no sympathy occurs. And yet it was reasonable that sympathy should occur from the most closely situated signs. For the bearing and flow [flux], which is carried from the proper power ^B of each of the stars, ought especially to be blended and mixed with the neighboring signs. For just as triangles and squares are inscribed in the circle, so too are the hexagon, and the octagon, and the dodecagon. But according to the inscriptions of these, no sympathy occurs; it occurs only according to the aforementioned ways, because of a certain natural sympathy existing in such intervals.

^A According to the square, the signs are these: Aries, Cancer, Libra, Capricorn; Taurus, Leo, Scorpio, Aquarius; Gemini, Virgo, Sagittarius, Pisces. All the squares are three in number. The side of the square subtends three signs, that is, 90 degrees. The first square is called the square beginning from Aries, in which the hours or the four parts of the year begin—spring, summer, autumn, winter; the second square is called the square beginning from Taurus, in which the hours have the middle time of spring, summer, autumn, and winter; the third square is called the square beginning from Gemini, in which the hours end according to the seasons. This same square is also employed, as has been said, for discovering the sympathies which are observed in nativities.

^B Furthermore, the doctrine of the squares is accepted by some for another certain use. For they assumed that when one of those signs which are in the same square is setting, the next one holds the mid-heaven in the upper hemisphere; for example, when Capricorn is setting, Aries holds the mid-heaven, Cancer is rising, and Libra holds the lower mid-heaven. The same principle applies to the remaining squares. This precept, when it is stated in its entirety, since it only fits in the one square that contains the solstitial and equinoctial points, will agree with what appears; but if this whole square is considered precisely, it disagrees. For when the first degree of Capricorn is setting, the first degree of Aries will hold the mid-heaven; Cancer will rise by its first degree; and Libra will hold the lower mid-heaven by its first degree. For then the circle through the middle of the signs [the ecliptic] is divided into four equal parts by the colure circles, so that the interval of the zodiac from the mid-heaven to the east is equal to the interval of the zodiac from the mid-heaven to the west; for each of these contains three signs. ^C But in the remaining positions of this square and of the others, it does not happen that the zodiacal circle is divided into four equal parts. For this reason, the interval from the mid-heaven to the east is not always equal to the interval to the west when the intervals are taken upon the zodiacal circle.

For according to a parallel circle, the interval from the mid-heaven to the east and the interval to the west is always equal. Whence it also happens for the sun, being carried each day upon parallel circles, that the course from the sunrise to the mid-heaven is equal to that course which is from the mid-heaven until the sunset. But when these intervals are taken on the zodiacal circle, it happens that the interval which is from the mid-heaven to the east is unequal to the interval which is from the mid-heaven to the west, on account of the obliquity of the zodiac. ^D And it is sometimes the case that, of the six signs which are always above the horizon, three and a half are intercepted from the mid-heaven toward the east, and two and a half toward the west.

Furthermore, ^A due to the differences of the climates, the zodiac is divided into even more unequal parts by the meridian circle. And it is sometimes the case that, of the 180 degrees which are always above the horizon, 120 degrees are intercepted from the mid-heaven toward the east, and 60 toward the west, and vice versa. There being, therefore, such a variation in the division of the zodiacal circle, the error becomes entirely manifest. For when Aquarius is rising, Taurus does not occupy the mid-heaven, but it will be removed from the mid-heaven by a whole sign, and sometimes even more. Nor will Scorpio occupy the imum coeli, but it will be distant from the meridian by a whole sign, and sometimes even more. Thus, the doctrine of the squares, according to some, is entirely false.

Regarding "combination," those signs are said to be such which rise from the same place and set in the same place. These, however, are the ones that are situated between the same parallel circles. The ancients, indeed, used to explain the combinations of the signs in this manner: they taught that Cancer has no combination with any other sign; but that it rises ^B at the furthest northern point and sets at the furthest northern point, resting their case on such a probable argument. For since the summer solstices occur in Cancer, and at the summer solstices the sun is at its most northern point, for this reason they supposed that Cancer rises at its most northern point, and similarly sets there. The same reasoning applies also to Capricorn. For they supposed that it rises at its most southern point, and has a combination with no other sign. For since the winter solstices occur in

Capricorn, and the sun is most southern at the winter solstices: on this account they thought that Capricorn rises at its most southern point, and that no other sign rises from the same place nor sets in the same place as Capricorn. They set out the remaining combinations thus: Leo with Gemini, Virgo with Taurus, Libra with Aries, Scorpio with Pisces, and Sagittarius with Aquarius. ^A But it turns out that such an exposition is entirely erroneous. For the solstices do not occur in the whole of Cancer, but there is one certain point, perceptible by reason, upon which the sun, when it is present, causes the solstice. For the solstices occur in an instantaneous moment of time. The whole dodecatemorion of Cancer is situated similarly to Gemini, and each of them is equidistant from the summer solstice point. For which reason also the magnitudes of the days and nights are equal in Gemini and in Cancer; and in the horological instruments the lines traced by the gnomons are equidistant from the summer solstice point, both in Cancer and in Gemini. For the two dodecatemoria are situated equally with respect to the summer point. ^B Whence also they are encompassed by the same parallel circles, and on this account Gemini and Cancer rise from the same place and likewise set in the same place.

The same reasoning applies also to Capricorn. For it is not the most southern, but there is one certain point, perceptible by reason, which is common to the end of Sagittarius and the beginning of Capricorn. For which reason it is situated equally with Sagittarius and has the same distance from the winter solstice point. Whence also the magnitudes of the days and nights are the same in Sagittarius and in Capricorn, and the extremity of the gnomon in the horological instruments traces the same lines, and these two ^C dodecatemoria, both of Sagittarius and of Capricorn, are contained between the same parallel circles; and on this account Sagittarius and Capricorn rise from the same place and set in the same place.

Likewise it turns out that the other combinations are erroneous. But the error becomes most manifest concerning the combination of Aries. For they declare Aries and Libra to be in combination, as if these signs rise from the same place and set in the same place. But Aries rises and sets in the north, for it is situated from the equinoctial circle towards the north; whereas Libra rises and sets in the south, ^D for it is situated from the equinoctial circle towards the south. How therefore can Aries have a combination with Libra? For they rise from different places, and likewise they set in different places. And these signs cannot be comprehended by the same parallels. Likewise neither do the other combinations agree. They have therefore been ignorant regarding the matters touching the first parts having occurred to the signs in combination, setting them forth for the whole signs. For they ought by much more to have [attributed] the things to the whole dodecatemoria.

There are in truth six combinations: Gemini with Cancer, Taurus with Leo, Aries with Virgo, Pisces with Libra, Aquarius with Scorpio, Sagittarius with Capricorn. For these both rise from the same place and set in the same place; they are contained by the same parallel circles and have a similar position with respect to the solstitial points. For in these, the magnitudes of the days and nights are equal, and the extremities of the gnomons on the horary instruments describe the same lines.

CHAPTER II. On the signs that are distinguished by stars, or on the constellations.

The constellations are divided into three parts. For some of them are situated on the zodiacal circle, some are called northern, and some are termed southern.

Therefore, those that are placed on the zodiac are the twelve signs, whose names we have mentioned before. But in the twelve signs, certain stars are considered worthy of their own names on account of the significance they possess. For the six stars situated on the back of Taurus are called the Pleiades.

The five stars situated on the forehead of Taurus are named the Hyades; the star which precedes the feet of the Gemini is called the Propus; those in Cancer, which resemble a nebulous gathering of stars, are called the Manger (Praesepe); two stars near the Manger are called the Asses; the brilliant star which is situated in the heart of Leo, sharing the name of the place in which it is situated, is called the Heart of Leo, and by some it is named the Basilisk, or Regulus, because those who are born around this place appear to have a royal nativity.

And the brilliant star which is placed in the left hand of Virgo is called the Spica (Ear of Corn); but that little star which is placed near the right wing of Virgo is called the Vindemiator (Grape-gatherer); the four stars which are situated in the extreme right hand of Aquarius are named the Urn.

The stars which are situated in a line from the extreme parts of the Pisces are called the Lines. There are, indeed, nine stars in the southern line, and five stars in the northern line; the brilliant star, however, which is placed at the end of the line, is called the Knot (Nodus).

The northern signs, indeed, are those which are situated outside the zodiacal circle toward the Bears. And they are these: the great Bear...

the small Bear, the Dragon extended through the Bears, Arctophylax, Corona, in the knees, Serpentarius, Serpens, Lyra, Avis, Sagitta, Aquila, Delphinus, the forepart of a horse, or according to Hipparchus, the Horse, Cepheus, Cassiopeia, Andromeda, Perseus, Auriga, Deltoton, and that which was later related among the stars by Callimachus, the Coma Berenices.

^A Furthermore, in these northern signs, certain stars have their own specific appellations on account of the significations they possess in various ways. For the notable star which is situated in the middle of the legs of Arctophylax is named Arcturus. The splendid star which is placed near Lyra is called by the name of its entire asterism, Lyra. The stars which are situated in the extreme left hand of Perseus are called the stars of the Gorgons; ^B while the dense and small starlets which are located in the extreme right hand of Perseus form the constellation of the Sickle; the splendid star which is placed on the left shoulder of Auriga is called the Goat (Capra), and the two starlets which are situated in the extreme part of the same hand are called the Kids (Hædi).

Southern signs are those which decline from the zodiac circle toward the south. They are these: Orion, Canis major, Procyon, Lepus, Argo, Hydra, Crater, Corvus, Centaurus, Fera, the spear which the Centaurus holds, and the thyrso-bearer (according to Hipparchus, the Altar), the southern fish, Cetus, the water coming from Aquarius, the river coming from Orion, the southern crown, which is called by some Uraniscus, that is, the little heaven, but according to Hipparchus, the Caduceus.

^C Furthermore, in these southern signs, certain stars have their own specific appellations. For the splendid star which is in the Lesser Dog is called Procyon; the splendid star which is in the mouth of the Greater Dog, and which is thought to cause the intensity of the heat, is called by the same name as the entire sign, Canis; but the notable star which is situated in the highest part of the rudder of the ship Argo is called Canobus. This star is difficult to see in Rhodes, or it appears only in places that are clearly elevated; but at Alexandria it can be seen completely. For it appears elevated almost a fourth part of a sign from the horizon.

CHAPTER III.

Since the world has a spherical figure, its diameter, around which the world rotates, is called the axis. The extremities of the axis are called the poles of the world: one of the poles is called northern, that is, arctic; the other is called southern, that is, antarctic. The northern one always appears, as far as our habitation is concerned, whereas the southern one is always...

invisible. ^A However, there are some places on the earth where it happens that the pole which is always visible to us is invisible to them, and that the one which is invisible to us is visible to them; and again, there is a place on the earth where these two poles lie similarly upon the horizon.

CHAPTER IV.

Concerning the circles of the sphere.

Of the circles of the sphere, some are parallel, some oblique, and some are drawn through the poles: they are parallel which have the same poles as the world. There are five parallel circles: the arctic, the summer tropic, the equinoctial, the winter tropic, and the antarctic.

The arctic circle, therefore, ^B is the greatest of the circles that are always visible, touching the horizon at one point, and being entirely contained above the earth, in which the stars situated find neither setting nor rising, but are seen moving around the pole throughout the whole night. This circle, in our inhabited world, is described by the front foot of the greater bear.

The summer tropic circle is the most northerly of the circles described by the sun according to the rotation of the world; upon this, the sun arriving makes the summer solstice, in which the day becomes the longest of all in the year, and the night the shortest. But after the summer solstice, the sun is no longer seen advancing toward the bears, but turns toward the other parts of the world; ^C for which reason it is called a tropic, that is, a turning circle.

The equinoctial is the greatest circle of the five parallel circles, which is cut equally by the horizon, so that a semicircle of it is taken above the earth, and the other semicircle below the horizon; upon this, the sun arriving produces the equinoxes, both the vernal and the autumnal.

The winter tropic circle is the most southerly of those circles described by the sun according to the daily rotation of the world; upon this, the sun arriving makes the winter solstice, in which the night, being the greatest of all in the year, is completed, and the day is the shortest. However, after the winter solstice, the sun is no longer seen advancing toward the south ^D

^A but turns again to the opposite parts of the world; for which reason this is also called the tropic.

The antarctic circle is equal and parallel to the arctic circle, and it touches the horizon at a single point, being entirely contained beneath the earth; in it, the stars situated there are always invisible to us.

Of the aforementioned five circles, the greatest is the equator; next in size are the tropics; and the smallest, with regard to our habitation, are the arctic circles. One must conceive of these circles as having no width and being discernible by reason, formed by the position of the stars, the theory of diopters, and our own power of conception. For the only circle in the world that is visible is the Milky Way; the others are discernible by reason.

Only five parallel circles are drawn on the sphere, not because these are the only parallels in the world. For the sun, every day, according to our perception, describes a circle parallel to the equator following the revolution of the world; thus, between the tropical circles, parallel circles are traced by the sun twice; for that is the number of days between the solstices.

All the stars are also carried in parallel circles every day. And yet, not all of these are inscribed on the sphere, because, while they contribute much to other astronomical treatises—for it would not be possible to map the stars correctly on a material globe without all the parallel circles, nor could the lengths of the nights and days be accurately determined without the ^B aforementioned circles—they are not inscribed on the sphere as they offer no utility for the primary introduction to astronomy. But the five parallel circles, because they offer certain specific benefits for the primary introduction to astronomy, have been inscribed on the sphere. For the arctic circle defines the stars that are always visible; the summer tropical circle contains the solstice and is the limit of the sun's passage toward the north; the equator circle contains the equinoxes; the winter tropical circle is the end-point of the sun's progress toward the south and contains the winter solstice; and the antarctic circle defines the stars that are not visible. Since, therefore, they contain clear principles and benefits for the introduction to astronomy, they have been reasonably inscribed on the sphere.

Of the aforementioned five parallel circles, the arctic circle is entirely contained above the earth, ^{C D} and is the greatest of all for those who dwell under it; for of the others, the farther each one recedes from the equator, the smaller it is. The ratio which the smaller circles hold to the greatest is investigated by the method we touched upon in the seventh book. For as the radius is to the sine of the complement of the distance of any parallel, so is the equator to the parallel. Let the summer tropic be distant 24 degrees from the equator; the complement of its distance is 66 degrees, the sine of which is 91355. Therefore, the proportion of the equator to the tropic is as 100000 to 91355, which is about 10 to 9. Thus the arctic circle of Aratus is distant from the equator by 49 degrees, and from the pole by 41. The sine of the degrees is 75471. Accordingly, the ratio of the equator to this arctic circle is as 100000 to 75471; which proportion is nearly sesquitertian, that is, 4 to 3.

^A The summer tropic circle is cut by the horizon into two unequal parts, and the larger segment is taken above the earth, the lesser below the earth. But the summer tropic circle is not cut by the horizon in the same manner through all regions and cities; rather, according to the diversities of the climates, a different excess of the segments happens to occur; and for those who live further north than we do, it happens that the summer tropic is cut by the horizon into more unequal parts. And finally, there is a certain region in which the entire summer tropic circle occurs above the earth. But for those who live further south than we do, the summer tropic circle is cut by the horizon into less unequal parts. And there is a certain region situated to the south of us, in which the summer tropic circle is divided equally by the horizon: in this climate, however, it is cut in such a way that, when the whole circle is divided into eight equal parts, five parts are taken above the horizon, and three below the horizon. It seems that Aratus also composed his treatise on phenomena for this climate. For, discoursing on the summer tropic circle, he says thus: Hoc maxime in octo æquales partes diviso, Earum quinque meridianæ volvuntur per supremas partes terræ, Tres vero in hemisphærio sub terra: æstatis huic [sunt conversiones.

From this division it follows that the longest day becomes 15 equatorial hours, and the night 9 equatorial hours. In the horizon of Rhodes the summer tropic circle is cut by the horizon in such a way that, when the whole circle is divided into 48 parts, 29 parts are taken above the horizon, and the remaining 19 below the earth. From this division it follows that the longest day in Rhodes becomes 14 1/2 equatorial hours, and the night 9 1/2 equatorial hours.

The equinoctial circle is cut equally by the horizon throughout the whole habitable earth, so that a semicircle is taken above the earth, and a semicircle below the earth: for which reason the equinoxes occur from this circle. ^{B C} The winter tropic circle is cut by the horizon in such a way that the lesser segment is above the earth, and the larger below the earth. The inequality of the segments has the same diversity in all climates that occurred also in the summer tropic circle. For the alternate segments of the tropic circles are always equal to each other. For which reason the longest day is equal to the longest night. The antarctic circle is hidden entirely below the horizon.

Of the five aforementioned parallel circles, some

^A retain their magnitudes throughout the whole earth, while others change these same magnitudes according to the climates, and in some places the circles become larger, and in others smaller. For the tropics and the equinoctial circle remain equal in magnitude throughout the entire world. But the arctic circles change in their magnitudes, and become larger in some places and smaller in others. For to those who dwell toward the north, the arctic circles become larger; for the pole appearing more elevated, it is necessary that the arctic circle, which touches the horizon, should always become larger. In some places, for those who dwell toward the north, the circle that is the summer tropic becomes also the arctic circle, so that the two circles coincide with each other—namely, the summer tropic circle and the arctic—and receive one position. ^B And toward regions further north, the arctic circles become even larger than the summer tropic circle.

There is finally a certain region situated toward the north, in which the pole is vertical; and the arctic circle occupies the place of the horizon, and conforms to it according to the revolution of the universe, and takes on the same magnitude as the equinoctial, so that the three circles—the arctic, the equinoctial, and the horizon—take on the same arrangement and position.

Again, for those who dwell to the south of us, the poles become lower, and the arctic circles smaller. And there is finally a region situated to the south of us; this is what is said to be under the equinoctial, in which the poles are on the horizon, and the arctic circles are entirely removed; so that instead of five parallel circles, there are only three parallels, namely the two tropics and the equinoctial. For one should not think, on account of the matters mentioned above, that there are universally five parallel circles, but that their number is set forth with respect to our own habitation. For there are some horizons in which there are only three parallel circles.

There are also habitations on the earth, of which the first is the habitation in which the summer tropic circle touches the horizon and takes the position of the arctic circle; the second is the habitation called "under the pole"; the third is the habitation for which we spoke a little earlier, and which is called "under the equinoctial."

Whence not even the order of the five parallel ^C circles is the same among all, but in the habitation that is ours, the first is called the arctic, the second the summer tropic, the third the equinoctial, the fourth the winter tropic, and the fifth the antarctic.

To those who dwell further toward the north than we do, there becomes at times first the summer tropic circle, second the arctic, third the equinoctial, ^D fourth in the day has the likeness of the horizon. The second habitation is where the vertex is the pole of the world. For there is no arctic circle there, just as there is none in the third, which lies beneath the equator.

fourth, the Antarctic; and fifth, the winter tropic. For among those for whom the Arctic circle becomes greater than the summer tropic, it is necessary that the aforementioned order of the circles should exist. Similarly, the powers of the five parallel circles are not the same among all those who dwell on the earth. For the summer tropic circle that is with us becomes the winter tropic circle for the antipodes; and that which is the summer tropic for them becomes the winter tropic with us.

For those who dwell under the equinoctial, in terms of their power, there are three summer tropic circles; for they lie under the very transit of the sun: but with regard to the diversity of the circles among themselves, that circle which is the equinoctial with us becomes the summer tropic for them; and the two tropics become their winter ones. For by nature, one might say, and universally regarding the whole inhabited world, the summer tropic circle is the one closest to the place of dwelling; for which reason, for those dwelling under the equinoctial, the equinoctial circle becomes the summer tropic. For then ^B the sun is at the zenith for them. And all the parallel circles become equinoctial circles for them. For there is always equinox among them. For all parallel circles are bisected by the horizon.

Nor do the distances of these circles [(19)] from one another remain the same throughout the entire inhabited world; but for the depiction of the spheres, the meridian is divided as follows: The entire meridian being divided according to latitude into 60 parts, the Arctic is inscribed distant from the pole by 6 of these parts; the summer tropic is inscribed distant from the Arctic by 5; the equinoctial is distant from either tropic by 4; the winter tropic circle is inscribed distant from the Antarctic by 5; and the Antarctic is distant from the pole by 6 such parts.

At not all regions and cities are these circles ^C the same. [(19)] The inconsistency of this author, and of many others, in the position of the heavens and [entry omitted: regarding the correction of certain points]. For frequently they mix up the Macedonian or Aratean climate with the Rhodian, and with both others, the Greek or Attic. Our author had signified a little before (p. 10) that, where he was then dwelling, the pole is elevated by 41 degrees, which is to say that the longest day is 15 hours. The same author, however, on that page, attributes to that region an Arctic circle which corresponds to Attica and Greece, as we have demonstrated above. But in this place, he has inadvertently transferred the matter to the Rhodian parallel. The ancients were accustomed to divide the circle into sixty parts, by which ratio thirty parts corresponded to the semicircle. In this manner Eratosthenes and others measured the intervals of the parallels, whether they conceived of them by sexagesimal parts or by stadia. This is evident from Strabo, Book II, Achilles Tatius, *Isagoge*, chapter 39, and others. From the interval which Geminus assigns here, one gathers the elevation of the pole such as the tenth part of 360. Wherefore, since the Arctic circle, whose semidiameter is the altitude of the pole, is distant from the pole by 6 parts, of which the whole circle contains 60, the same altitude will be of parts such as the circle has 360. Thus, the twelfth part is 5; as the twelfth part of the number 360 is 30; wherefore from the Arctic of the Rhodian parallels to the solstitial tropic is 30 degrees, or 5 sexagesimal parts, and so on in the others. The same distribution exists in Achilles Tatius in the cited place, where the numbers are faulty, and should be corrected by this reasoning. Hyginus also, in his *Astronomica Poetica*, uses the same. It appears the astronomers willingly assumed the Rhodian [parallel] as an example and specimen, on account of the convenience of the partitions and those things which are established in the duodenary number. For the duodenary number is 12. Indeed, Ptolemy in his book uses that parallel most of all. This fact has caused others, through inadvertence, to adapt what is proper to it to all the rest. And Geminus a little below warns that all circles in common spheres are calibrated to the horizon of Greece, which not even he himself held accurately. For the latitude of Greece, that is, of Attica, is about 37 degrees, as Hipparchus teaches in Book I. But because Rhodes is a Greek city, and a part of Greece, as indeed is most of the Peloponnese, it is situated under the same parallel: therefore, he attributed this same one to the whole of Greece. In vain do learned mathematicians strive to reconcile this inconsistency of Proclus, or rather of Geminus, by means of refractions. Its true origin is what I have touched upon. ^D

^A And the circles have distances from one another; but the tropical circles have the same distance from the equinoctial at every climate; while the tropical circles do not have the same distance from the arctic circles in all horizons, but some are more distant, others less. Similarly, neither do the arctic circles have an equal distance from the poles at every climate; but some have a smaller [distance], others a larger. However, all the circumferences are marked out in relation to the horizon of Greece.

Those circles passing through the poles are what some call colures, which happen to have the poles of the world on their own circumferences. They are called colures because certain parts of them are invisible. For the remaining circles are seen in their entirety according to the rotation ^B of the world; but some parts of the colure circles are invisible, namely those which are taken up by the antarctic [circle] beneath the horizon. These circles that are drawn through the poles are written through the solstitial and equinoctial points, and they divide the circle passing through the middle of the zodiac into four equal parts.

The oblique circle is that of the twelve zodiacal signs; it consists of three parallel circles, of which some are said to define the breadth of the zodiacal circle, while the one [in the middle] is called the circle passing through the middle of the signs. This touches two circles that are equal and parallel: namely, the summer tropic at the first degree of Cancer, and the winter tropic at the first degree of Capricorn; and it cuts the equinoctial ^C in two at the first degree of Aries, and at the first degree of Libra. The breadth of the zodiacal circle is twelve degrees. The zodiacal circle is called oblique because it obliquely cuts the parallel circles.

A horizon is a circle that distinguishes for us the visible and the invisible part of the cosmos, and bisects the whole sphere of the cosmos, so that one hemisphere is taken to be above the earth, and one hemisphere beneath the earth. There are two horizons: one that is sensible, and another that is understood by reason. The sensible horizon is that which is marked out by our sight according to the limit of vision, which does not have a diameter greater than 2000 stadia; but the horizon reckoned by reason ^D extends to the sphere of the fixed stars, and bisects the whole cosmos. It is not the same horizon for every city and country; but as regards the senses, the same horizon remains for nearly 400 stadia, so that the lengths of the days, and the climate, and all appearances remain the same. But when more stadia are involved according to the difference of the habitation, a different horizon arises, differing in climate, and all the appearances are changed. Nevertheless, it is necessary that even if it reverts to the same, the meaning of the common reading remains constant and should not be rashly altered.

^A Divergence of habitation, which exceeds 100 stadia, is to be accepted according to the approach toward the north and the south. For to those who dwell under the same parallel and are distant from one another by ten thousand stadia, the horizon is indeed different, but the climate is the same, and all appearances are similar. But the beginnings and ends of the days will not be the same for all who dwell under the same parallel. According to the exact judgment of reason, however, as soon as a minimal movement occurs toward any part of the world, both the horizon and the climate change, and all appearances are various.

The horizon is not depicted on ^B spheres for the following reason: because all the remaining circles, as the world is carried from the east to the west, revolve together along with the motion of the world. But the horizon is by nature immobile, and always preserves the same position. If, therefore, horizons were to be depicted on spheres, as the spheres were moved, it would happen that the horizon also moved and became vertical: this is not to be thought of, and is alien to the doctrine of the sphere. The position of the horizon is, however, understood from the receptacle of the sphere.

The meridian is the circle that is described through the poles of the world and through the vertical point, at which, when the sun arrives, it creates the midpoints of the days and the midpoints of the nights. This circle also is immobile in the world, and retains the same place throughout the whole revolution of the world. ^C Nor is this circle depicted on the starry spheres, for the reason that it is both immobile and admits of no change.

Moreover, the same meridian is not everywhere for all regions and cities; but according to sense, it remains the same meridian for nearly 300 stadia; according to the judgment of reason, however, as soon as even the slightest movement occurs either toward the east or toward the west, another meridian comes to be. For according to movement toward the north and toward the south, even if ten thousand stadia intervene, the meridian remains the same; but according to movement from the east toward the west, differences of meridians exist. ^D

The circle of the Milky Way is also oblique. For this circle is inclined with a greater breadth than to be contained between the tropics, and it is composed of a nebular thinness; it alone also is visible in the world. Its breadth is not distinct; but according to some parts this circle is wider, and according to others it is narrower. For which reason, in most spheres, the circle of the Milky Way is not even depicted. This also is one of the greatest circles. For those circles are called greatest on spheres which have the same center as the sphere. There are seven greatest circles: the equator, the zodiac, and that which is through the middle of the

signs, the circles through the poles, the circle that in every habitation separates the visible part of the world from the invisible, the meridian, and the circle of the Milky Way.

CHAPTER V. Concerning day and night.

^A Day is spoken of in two ways: in one way, as that time which is from the rising of the sun to its setting; in another way, day is called the time from one rising of the sun to its next rising. And day, according to the second mode, is the revolution of the world, and that arc of the circumference which the sun traverses while it moves in the revolution of the world contrary to the world. For which reason, neither is that time composed of night and day taken together equal to any and every night and day; but as regards sensation, the magnitudes are equal, yet according to the judgment of reason there is a small and imperceptible difference. For the revolutions of the world are equal to one another in time; but the ascensions of the arcs which the sun traverses during the revolution of the world are not equal in time. For which reason, that composed time—namely, every night and day—is not equal to that other composed time, to wit, any and every night and day.

According to the second mode of the division of days, we say the month is of 30 days, ^B and the year is of 365 1/4 days; and the time composed of night and day is 24 equinoctial hours, and an equinoctial hour is the 1/24th part of the time composed of night and day.

Not in every country and city are the magnitudes of the days the same; but for those who dwell toward the north, the days become longer, and for those toward the south, they become shorter.

For in Rhodes, the longest day is 14 1/2 equinoctial hours; around Rome, the longest day is 15 equinoctial hours; for those living a little beyond the Propontis toward the north, the longest day becomes 16 equinoctial hours; and for those even further north, the longest day becomes 17 and 18 hours.

^C To these places, Pytheas the Massaliote also seems to have come. He says, therefore, in the books on the Ocean composed by him, that "The barbarians were pointing out to us where the sun sleeps." For it happened that about these places the night became very small, in some places of 2 hours, in others of 3, so that after the sunset, a small interval having elapsed, the sun would immediately rise again. ^D Crates the grammarian says that Homer also mentions these places, in those lines where Ulysses speaks of: "The routes of day and night,"

^A *High-gated Laestrygonia, where shepherd calls to shepherd,* *And one hears the other as he drives in, while he who drives out answers.* *There a sleepless man could earn double wages,* *One by herding cattle, another by pasturing shining sheep.* *For the routes of night and day are near.*

For when the longest day in these places is twenty-one equinoctial hours, the night is left as being altogether small, of three hours; so that the sunset approaches the sunrise, with a very small arc of the summer tropic being intercepted below the horizon. If anyone, therefore, he says, could keep watch for such long days, he would carry off double wages; one by herding cattle, another by pasturing shining sheep. He then adds the reason, which is mathematical and consistent with spherical theory: *For the routes of night and day are near.* This means that the sunset is placed next to the sunrise.

As we proceed still further toward the north, ^B the entire summer tropical circle comes to be above the earth, so that at the summer solstices the day among them becomes twenty-four equinoctial hours. For those who dwell still further toward the north, some part of the zodiacal circle is always above the earth; and among those for whom a magnitude of one sign of the zodiac is intercepted above the horizon, a monthly day occurs for them; among those for whom two signs are intercepted above the earth, the longest day happens to be two months long. Finally, there is a certain place located furthest to the north, in which the pole of the world becomes vertical; six signs of the zodiac are intercepted above the horizon, and six are cut off below the horizon; and the longest day for them becomes six months long, and likewise the night.

It seems that Homer also makes mention of these places, as Crates the grammarian says, when he speaks concerning the habitation of the Cimmerians: ^C *There the towns and cities of the Cimmerian men,* *Are covered by mist and cloud. Nor ever does* *The shining sun look down upon them with his rays,* *Neither when he ascends to the starry heaven,* *Nor when he turns back from heaven to earth;* *But sad night is extended over wretched mortals.*

For when the pole of the world is vertical, it happens that the day and the night become six months long. For there is a period of three months, in which time the sun ^D moves from the equinoctial circle, which holds the place of the horizon, to the summer tropical circle; and another trimestrial period...

[Regarding the later text:] ...concerning which hereafter. (24) And where the magnitude of the zodiac. Manilius, Book III: ... *If you proceed further thence,* *Single parts are hidden among the whole,* *And they will draw thirty nights in the connected time,* *And take away as many nights.*

For the poet speaks of these men for whom a whole dodecatemory does not rise or set, not of those for whom the days are interrupted by at least a small night in Cancer, as Scaliger wished, which happens at a pole altitude of 66 degrees, 30 minutes.

A three-month day, in which it descends from the summer tropic to the horizon. And for all this time it is carried along the parallel circles that are above the earth. But since it happens that this habitation is in the middle of the frigid and uninhabitable zone, the place must of necessity always be covered by clouds, and clouds must be gathered in a great depth of air, and the rays of the sun are not able to break through the clouds; so that it is reasonable that there is night and darkness among them at all times. For when the sun is above the earth, there is darkness among them because of the thickness of the clouds; and when the sun is below the horizon, because of natural necessity, there is night among them: so that their habitation is always deprived of light. This, therefore, he says, is what is meant by the poet: ^A ...... nor ever does The shining sun look down on them with its rays.

Whether Homer intends these things, that is another discussion; but that there are certain places, since the earth is spherical, which have the aforementioned durations of days relative to each other, is manifest from the very figure of the sphere. Yet it happens that these places are uninhabitable because of the excess of cold. For they are situated in the middle of the frigid zone. Conversely, for those living towards the south, the days always become smaller and smaller; among some the longest day is 14 equinoctial hours, among others 13.

Finally, there is a certain region situated more to the south than we are, which is said to be under the equator, in which the poles of the world fall upon the horizon; the sphere of the world is established as right. And all the parallel circles which are described by the sun according to the daily rotation of the world are bisected. ^B For which reason there is always an equinox among them. For inequality of days does not exist for any other cause than the elevation of the pole, which is called the inclination of the world. For it happens, because of the elevation of the pole, that the segments of the circles described from the equator to the summer tropic are greater above the earth, and smaller—[text missing in source, but implied by context: *beneath* the earth]; while of the circles described from the equator to the winter tropic, smaller segments are above the earth, and greater ones below the earth. But where the poles of the world lie upon the horizon, the cause of the inequality of the days being removed (which was the inclination), it reasonably happens that there is an equinox among them at all times. ^C For the sun travels through all the parallel circles—both the greater and the smaller—in equal times, because the rotation of the world takes place around certain fixed points, namely the poles. And so it is not because of the magnitudes of the circles, but because of the inequality of the segments, in which the sun is carried below the earth and above the earth, that the inequality of the days occurs. The increases, however, of the days and nights are not equal in all the signs, but are very small around the tropic points. ^D

being altogether small and imperceptible, ^A so that the same magnitude of days and nights remains for nearly forty days. For the sun, both approaching and again withdrawing from the tropic points, makes its lateral transits imperceptible; so that, reasonably, there occurs for the aforementioned number of days an abiding of the sun in that place, as far as the senses are concerned. For which reason the greatest heats and the greatest colds also occur after the turnings. ^B For since the sun continuously traverses the same place twice, and makes its approaches and withdrawals imperceptibly, it reasonably produces an intensification of heat at one time, and of cold at another, on account of its lingering in one place; and this is manifest also from the sundials. For the tip of the shadow on the gnomon remains for nearly forty days on the tropic lines. Around both equinoxes, however, great increases in the days occur, so that the following day varies sensibly from the preceding one. On which account, in the clocks, the tip of the shadow on the gnomon makes sensible daily distances from the equinoctial circle. The cause, moreover, of the inequality and the increase of the days is the obliquity of the zodiacal circle. For it touches the tropic circles, and the point of contact extends for a great length, ^C so that in a large space the distance from the summer tropic is small. It follows from this that the change in the segments in which the sun is carried above the earth is also small and imperceptible. But on the equinoctial circle occurs a section of the zodiacal circle toward the equinoctial; and from the section, the inclination toward either side takes on a great distance from the equinoctial. It follows from this that a great change in the days also occurs, on account of the excess of the segments in which the sun is carried above the horizon. For this cause, therefore, around the tropic circles, small and imperceptible increases of the days and nights are accomplished, and the increases have nearly the same amount of change: so that the daily increase around the equinox is nearly ninety times greater than the daily increase around the turnings. The same reasoning applies both to the diurnal and to the monthly [changes]. ^D For always, by as much as the day increases, by so much also the night diminishes. For the days become greater than the nights in the six signs, Aries, Taurus, Gemini, Cancer, Leo, and Virgo, which semicircular [part] of the zodiac, from the first part of Aries to the thirtieth part of Virgo, is northern. Again, the nights are greater than the days in the remaining signs, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces, which is again the semicircular [part].

of the zodiacal circle, from the first degree of Libra to the thirtieth degree of Pisces, which is southern ^A. The increase of days occurs from the first degree of Capricorn to the thirtieth degree of Gemini; this is the semicircular [part] of the zodiacal circle. From the winter solstice to the summer solstice, the increase of days occurs. But the increase of nights occurs from the first degree of Cancer to the thirtieth degree of Sagittarius, which is again the semicircular [part] of the zodiacal circle from the summer solstice to the winter solstice.

Some, therefore, assumed that the longest days occur in Cancer, since the summer solstices occur in the aforementioned sign; and that the longest nights are in Capricorn, since the winter solstices occur in Capricorn. ^B In this matter they commit an error similar to that which they commit regarding the syzygies (or combinations). For if the solstices occurred throughout the entire signs, what was said before would be true; but now the tropical points are things considered by reason. Actually, the whole sign of Cancer has the same distance from the summer tropical point as Gemini, and is comprised by the same parallel circles, and from the same place it makes its rising, and into the same place it makes its setting. For these signs are to one another according to a syzygy or combination. Hence, the magnitudes of the days and nights are equal in Gemini and Cancer. For indeed, on sundials, the extremity of the shadow of the gnomon traces the same lines in the aforementioned signs. ^C The same reasoning applies also to the winter solstices. For it must not be thought that in those, the longest nights occur in the whole of Capricorn; rather, there is some one point, to be understood by reason, which is common to Capricorn and Sagittarius, which has the same distance from the winter tropical point, is comprised by the same parallel circles, and is according to a syzygy or combination to its fellow; whence also the magnitudes of the days and nights are equal in Sagittarius and Capricorn. Universally, as many signs as are to one another according to a syzygy exist, these signs contain equal days and nights. There will be, therefore, equal days in Gemini and Cancer, in Taurus and Leo, in Aries and Virgo, in Pisces and Libra, in Aquarius and Scorpio, [and] in Capricorn and Sagittarius. ^D

Since the universe is spherical and moves in a circular motion from east to west, it happens that all points on the sphere are carried on parallel circles. From this it is manifest that even all the stars make their motion on parallel circles. For this reason, all the fixed stars rise from the same place and set into the same place; and similarly, the parallel circles rise from the same place and set into the same place. But the zodiacal circle, being oblique in its position toward the

^A rising, does not have all its parts rising from the same place, and setting into the same place; for which reason the 12 signs do not rise from the same place and set into the same place. For the zodiacal circle makes its risings and settings in latitude. Its latitude of rising is the semicircle from the first degree of Cancer as it rises, up to the first degree of Capricorn as it ascends. For as great as the revolution of the zodiac on the horizon is, which is between these days, so great is the progress according to latitude of the zodiac on the horizon. Aratus confirms this in agreement, saying thus:

But this one so much of the waters of Ocean traverses, As from Capricorn rising, most greatly Toward Cancer rising it rolls; as much as on every side The rising contains, just so much does it set elsewhere.

^B For in these verses he defines the progress of the zodiacal circle which it makes according to latitude at the rising and the setting, and this is in agreement with the mathematicians and with the phenomenon. Such being the inclination of the zodiacal circle, it comes to pass that the dodecatemoria, although equal in size, perform their risings and settings in unequal times. For those signs which, when the zodiac becomes straight, perform their rising, perform their rising and setting in the greatest time. For they fall straight toward the horizon, so that the rising of the sign occurs according to each individual point, and for this reason a great amount of time is consumed in the rising and setting. But those which make their rising when the zodiac is oblique to the horizon rise in a shorter time. For the oblique signs fall into the horizon in such a way that they make their rising according to many other parts simultaneously, and therefore a quick rising comes to pass. Whence also that which is said in Aratus is questioned: how it is that even in the longest nights and in the shortest, six signs rise and six set, although the diversity of the nights is great. Aratus speaks as follows:

For in every night Six twelve-parts of the circle always set, And as many rise; to such length does each...

^C ...in every night Six always set, twelve-parts of the circle As many rise:— [the rest of the verse is lost]

^D ...writes, which is intercepted between the rising point of Capricorn and [that of] Cancer. Thus it is the same which [the text]... but it seems it should be expunged, for which in an old codex *touto* is read, which is no more authentic. But the verses of Aratus, which are explained by Geminus, are most obscure; so that we are less surprised that they were not sufficiently understood by Theon, or the miscellany of scholiasts, and by Avienus. For they explain it thus, as if Aratus meant this: that as much of that circle extends above the earth from the rising of Capricorn to the rising of Cancer, so much is under the earth from Cancer to Capricorn. Thus Theon. But Festus Avienus [says]:

That one, however, descends as much into the plain of the Ocean, As the distance from blue-colored Cancer to Capricorn [is].

Which interpretation is trifling and does not pertain to the matter. For this applies to all great circles which are divided equally by the horizon. Indeed, in a straight sphere, this is common, that is, to all parallels. But Aratus, in these verses, has embraced something peculiar to the zodiacal circle. To be brief, both according to latitude, as they call it, or rising, or [not] according to length, it must be understood, as Geminus teaches. As much as he says the interval is between the point of the horizon from which Capricorn rises and that from which Cancer makes its rising, so much latitude of rising or setting the zodiac has, and encompasses so much space, raising itself from the Ocean, that is, the horizon, and similarly setting.

(29) *For in every night*—if you listen to Solinianus [i.e., Salmasius], Aratus will get a beating, for he said *duodecada* [for the twelfth part], when he [the zodiac] is the whole duodenary itself. For he refutes Casaubon, who...

^A *Night is always extended, as much as half the circle / Beginning from night, it is lifted up above the earth.* It is asked, then, how even in the longest and shortest nights a semicircle of the zodiacal circle both rises and sets. This happens because of the inclination of the zodiacal circle. For because of its obliquity, the semicircles of the zodiac rise and set in unequal times. For when the zodiacal circle is at its lowest position relative to the horizon, which happens when the first degree of Capricorn holds mid-heaven, it makes the semicircle from the first degree of Aries to the thirtieth degree of Virgo rise rapidly; for it falls obliquely to the horizon and makes many parts rise at once. But when the zodiacal circle is at its most upright, which happens when the first degree of Cancer holds mid-heaven, it causes the semicircle from the first degree of Libra to the thirtieth degree of Pisces to rise rapidly; whence it takes a long time to complete its rising. Reasonably, therefore, both in winter nights and in summer nights, six signs rise and six signs set. For the rising times, though the signs are equal in magnitude, become unequal in their durations. And in winter nights those signs that produce a slow rising are carried up; in summer nights, those that produce a rapid rising emerge.

The ancients, therefore, just as they went astray regarding the signs in conjunction, so too did they err concerning the rising times of the signs. For having posited that the zodiacal circle is at its most upright ^B when the first degree of Cancer holds mid-heaven—since at this time Libra rises and Aries sets—they asserted that Libra rises in the longest time, and Aries sets in the longest time. Again, since the zodiacal circle is at its lowest when the first degree of Capricorn holds mid-heaven, and at this time Aries rises and Libra sets, they asserted that Aries rises most rapidly and Libra sets in the shortest time. Again, since the zodiacal circle assumes a middle inclination toward the horizon when the first degree of Aries holds mid-heaven, and when the first degree of Libra holds mid-heaven—for Cancer rises and Capricorn sets—they asserted that Cancer has a mean time of rising, and Capricorn a mean time of setting; and again, when the Claws [Libra] are in mid-heaven, Capricorn will have a mean time of rising, and Cancer a mean time of setting. ^C This exposition of the rising times by the ancients is erroneous. For since Gemini and Cancer have the same inclination in the zodiacal circle toward the horizon, and the same distance from the summer tropic sign, and [yet] the magnitudes of the days...

^D Strabo, book II, ordering that *sexagesimas partes* [sixtieth parts] be restored for another corrupted word, interpreted it as *sexagesimas*. Salmasius (p. 664) criticizes this, arguing that by that notion it ought to be written *sexagenarius*, not *pars sexagesima*; just as it is not *decima pars*, but *decuria*. According to this grammatical prohibition, Aratus will be summoned to court, nor will he be able to refuse citation to the tribunal of Salmasius, because he wrote *duodecada* instead of... For it is the mark of one who legislates over names, not one who speaks truth, to want to form *sexagesimas* from what is *sexagesima*, or *decadas* or *duodecadas*. Away with these inanities; to speak with the Nazianzen, it is the mark of one who legislates over names, not one who speaks the truth, concerning the *sexagesimae*. Finally, Strabo himself restrains this license of the corrector, for a few lines later in him, the word is found.

^A equal days; and when Gemini is at midheaven, Virgo rises; when Cancer is at midheaven, Libra rises; Virgo and Libra rise in an equal amount of time. And since the zodiacal circle becomes most upright when Gemini and Cancer are at midheaven, Virgo and Libra rise in the greatest amount of time, and not only the Claws (*Chelæ*), as the ancients supposed.

Again, since Sagittarius and Capricorn have the same inclination toward the horizon, when Sagittarius is at midheaven, Pisces rises and Virgo sets; when Capricorn is at midheaven, Aries rises and Libra sets; and the zodiacal circle becomes most low when Sagittarius and Capricorn are at midheaven: Virgo and Libra set in the shortest amount of time.

Again, since, when Pisces is at midheaven, Gemini rises; when Aries is at midheaven, Cancer rises; and while Pisces and Aries are at midheaven, the zodiacal circle has a mean inclination: therefore, Gemini and Cancer contain a mean duration of time for rising, while Sagittarius and Capricorn contain the same for setting.

Similarly, since the zodiacal circle is said to have a mean inclination when Virgo and the Claws are at midheaven, and when Virgo is at midheaven, Sagittarius rises and Gemini sets; when the Claws are at midheaven, Capricorn rises and Cancer sets: Sagittarius and Capricorn will have a mean duration of time for rising, and Gemini and Cancer for setting.

^C From these things it is manifest that those signs which are equally distant from the tropical points and the equinoctial points rise and set in equal times; and since every night six signs rise in 12 hours, and every day six signs rise in 12 hours, it is manifest that both in the day and in the night the signs rise in 24 hours, and one sign in [two] hours, according to the mean time of the risings. And again, since every night six signs set in 12 hours, it is manifest from the same that one sign sets in two hours, and all the signs rise and set in 24 equinoctial hours, and the time of the rising and setting of all the signs, taken together, is equal to the time of 24 equinoctial hours; and that whatever signs rise in the longest time, these set in the shortest time; and those which rise in the shortest time, these set in the longest time.

CHAPTER VI. On the months.

A month is the time from conjunction to conjunction, or from full moon to full moon. Now the conjunction is when the sun and the moon are in the same part—which occurs about the thirtieth day of the moon. It is called a full moon when the moon [is] at the diameter...

^A of the sun. This occurs about the middle of the month. The monthly period is 29 1/2 1/33 days; and in the monthly period the moon travels through both the circle of the zodiac and also the arc which the sun traverses in the monthly period toward the succeeding signs of the zodiac. This arc is approximately one sign; so that in a monthly period the moon traverses approximately 13 signs. The exact monthly period is, as has been said, 29 1/2 1/33 days; but the monthly periods taken more generally for civil use are of 29 1/2 days, so that the biennial period becomes 59 days. Whence, for this reason, the months according to the city are observed alternately full and hollow, because the lunar biennial period is of 59 days.

From these things, it is gathered that the lunar year is of 354 days. For if we multiply the days of the month, which are 29 1/2, a dozen times, the days of the lunar year will result as 354. For one is the solar year, and another is the lunar. For the solar year has the circuit of the sun through the signs, which is 365 1/4 days; but that of the moon contains the time of 12 lunar months, which is 354 days, since neither the month consists of complete days, nor [does] the solar year. ^B Therefore, a time was sought by the astronomers which would contain whole days, and whole months, and whole years.

For it was the intention of the ancients to regulate the months according to the moon, but the years according to the sun. For as to what was enjoined by the laws and oracles, to sacrifice according to three things, namely, ancestral [custom], months, days, years; all the Greeks handled this in such a way that they regulated the years in agreement with the sun, but the days and months with the moon. Now to regulate the years according to the sun is that the same sacrifices to the gods should be performed about the same seasons of the year, and the vernal sacrifice always be accomplished in the spring, and the summer [sacrifice] in the summer; and similarly that the same sacrifices fall in the remaining seasons of the year. ^C For they supposed this to be acceptable and pleasing to the gods. But this could not happen otherwise unless the solstices and the equinoxes occurred in the same places. But to regulate the days according to the moon is such that the appellations of the days might correspond to the illuminations of the moon. For the appellations of the days were named from the illuminations of the moon.

For in the day in which the moon appears new, it was called by contraction *neomenia* [new moon]; and in that in which...

it makes its second appearance, they called it the second moon; the appearance of the moon which happens about the middle of the month, from the event itself, that is, the half of the month, they named, and in short, all the days were named from the illuminations of the moon. Whence also the thirtieth day of the month, being the last, they called from the event itself *triacada*. Consistent with these things, Aratus also declares himself regarding the nomenclature of the days, saying thus:

Do you not see, when the moon with small horns Appears at evening, it teaches of the waxing Month, when the first light is scattered thence, As much as it casts on its way to the fourth day. Eight days in the middle of the orb it gives the half of the month 35 With full face. But always inclining other faces at another time, He will have said how many dawns of the month revolve.

For in these lines he explicitly says that the names of the days were denominated from the illuminations of the moon. And a proof that the Greeks keep the days accurately according to the moon is this, that the eclipses of the sun happen on the *triacada*, that is, the thirtieth day. For then the moon is in conjunction with the sun, and comes to be in the same degree. But the eclipses of the moon happen on the night leading to the middle of the month. For then the moon is placed opposite the sun along the diameter, and falls into the shadow of the earth. When, therefore, both the years are accurately kept according to the sun, and the months and days according to the moon, then the Greeks think they are sacrificing according to their ancestral rites; and this is to perform the same sacrifices to the gods at the same times of the year. ^B Indeed, the Egyptians 34 held an opinion and purpose contrary to the Greeks. For they neither keep the years according to the sun, nor the months and days according to the moon; but they have used a certain peculiar principle. For they wish the sacrifices to the gods not to be made according to the same time of the year; but to pass through all the quadrants of the year, and for the summer festival to happen, and the winter, and the autumnal, and the vernal. For they keep the year of 365 days; for they keep twelve months of thirty days each and add five epact days. But they do not intercalate that quarter of a day for the reason aforesaid; so that, namely, their festivals may anticipate. For in four years the Egyptians fall short of the sun by one day; in forty years they will fall short by ten days because of the solar year. ^C And so they also anticipate the festivals by as many days, so that they may not happen according to the same quadrants of the year. But in 120 years there will be a monthly variance, considering both the solar year and the quadrants of the year. For which reason also that error which is circulated among the Greeks, since because of the length of time it has been held worthy of approval, has been believed to be true even down to our own times. For very many of the Greeks think... ^D

^A that the winter solstices occur simultaneously with the Isia among the Egyptians and according to Eudoxus: which is entirely false. For the Isia shifts by a whole month in relation to the winter solstices. This error flowed from the aforementioned cause, for one hundred and twenty years ago it happened that the Isia were held at the very winter solstices, and in four years there occurred a shift of one day. This, therefore, did not have a perceptible shift relative to the seasons of the year. In forty years, a shift of ten days occurred. Not even thus does it happen that the shift is perceptible. Now, however, since a monthly shift occurs in one hundred and twenty years, those who assume that the winter solstices occur in the Isia according to the Egyptians and according to Eudoxus do not leave behind any excess of ignorance. For it is possible for them to differ by one day or two, but it is impossible for a monthly shift to go unnoticed. For the magnitudes of the days are able to prove it, having a great shift relative to the winter solstices. And the records of the sun-dials make the solstices that occur in truth manifest, and especially among the Egyptians, who have been diligent in observation. ^B Whence the Isia previously were held at the winter solstices, and before that even at the summer solstices, as Eratosthenes (36) also mentions in his commentary *On the Octaeteris*; and it will be held again at the autumn, and at the summer solstices, and at the spring, and at the winter solstices. For in one thousand four hundred and sixty years every festival must pass through all the seasons of the year, and again be restored to the same time of the year. The Egyptians, therefore, hold their own according to the inherent nature of the proposed end; the Greeks, however, holding the opposite opinion, regulate their years according to the sun, but their months and days according to the moon.

^C It is worth noting that Achilles Tatius is involved in the same error, as is clear at the end of his *Isagoge*. For the ignorant assumed that because the Isia had once fallen on the solstices, this was perpetual. Geminus refutes them from the fact that one hundred and twenty years before he was writing, this had happened, and consequently in his own time the festival’s fixed month had already anticipated. Scaliger, in his book *De emendatione temporum*, in the chapter on the octaeteris of Eudoxus, inferred from this passage of Geminus that Eudoxus had begun his octaeteris from the Isia, as if Geminus meant that from that time, from which Eudoxus started his octaeteris, to his own age, one hundred and twenty years had elapsed. Furthermore, since he judges that Eudoxus began his octaeteris in the third year of the eighty-first Olympiad, ^D the three hundred and eighty-second year of Nabonassar; if you add to this the one hundred and twenty years, you reach the five hundred and fourth year of Nabonassar, in which Geminus was writing. Thus he would be more ancient than Hipparchus. He confesses that he has nothing to answer to this objection. But there was no place for hesitation here. For Geminus does not mean that the Isia happened in the very first year of Eudoxus’s cycle, one hundred and twenty years before he was writing, but on that very day to which Eudoxus had assigned them; and all posterity thereafter thought them to be fixed to those days, being ignorant of the solar anticipation. We have shown that Eudoxus established his octaeteris around the ninety-seventh Olympiad, at which time the true winter solstice fell on December 25th, the mean on the 26th. Now the Isia, of which Geminus speaks, seem to be those which occurred from the 17th day of Athyr to the 20th, as Plutarch is a witness in his tract *De Iside et Osiride*. For he writes that they were also funeral rites; and among their causes he mentions this, that with the days being contracted, the nights become longer. But Achilles Tatius, in chapter 23, teaches that for this same reason the Isia, which fall in the stated time, were accustomed to be celebrated by the Egyptians. Wherefore there is now no doubt as to which Isia Geminus is to be understood as meaning. For it is certain that he is dealing with those which began on the 17th of Athyr. Athyr, I say, vague, not Julian and fixed. With this posited, it will be easy to investigate what time is designated by Geminus in this place. For in order for the 17th day of Athyr to fall on December 26th, it is necessary that the Neomenia of Thoth falls on October 11th. That happened first in the year of Nabonassar 552, the fourth year of the 145th Olympiad, of the Julian period 4517. Add therefore 120 years, and the year of the Julian period 4637 will emerge, the fourth year of the 175th Olympiad, from the founding of the City 677. Therefore our Geminus flourished in the time of Sulla. In his book *De doctrina temporum*, chapter 6, we have not departed much from this calculation. But we established the octaeteris of Eudoxus, according to the common and Scaligerian opinion, on the fourth day after the solstice, on December 30th, so that our argumentation might proceed from the hypothesis and the matters conceded by him. (36) Eratosthenes is mentioned, and Tatius.

The ancients, moreover, observed months of thirty days, and intercalary ones every other year. But since the truth was quickly exposed by observation, because the days and months did not agree with the moon, and the years did not align with the sun, they sought a period that would agree with the sun in years, and with the moon in months and days. The duration of this period contains whole months, whole days, and whole years. They first established the octaeteris (eight-year) period, which contains 99 months—in which there are 3 intercalary months—and 2,922 days, and eight years. They established the octaeteris in this manner: Since the solar year is 365 1/4 days, and the lunar year is 354 days, they took the excess by which the solar year exceeds the lunar. This excess is 11 1/4 days. ^A If, therefore, we conduct the months according to the moon, we will fall short of the solar year by 11 1/4 days. They sought, therefore, how many times these days, when multiplied, would make whole days and whole months. Multiplied eight times, therefore, they make whole days and whole months: 90 days, and three months. Since, then, in one year we fall short of the sun by 11 1/4 days, it is manifest that in eight years we will fall short of the sun by 90 days, which are three months. For which reason, three intercalary months are kept in every octaeteris, so that the deficit occurring each year from the sun may be compensated, and that again, from the beginning, when eight years have passed, the festivals may coincide with the same seasons of the year. When this happens, sacrifices to the gods will always be performed at the same seasons of the year.

^B Now, having arranged the intercalary months as evenly as was possible—for one ought neither to wait until a monthly variation regarding the phenomenon takes place, nor anticipate the solar course by a whole month—for this reason they ordained that the intercalary months be kept in the third, fifth, and eighth years; two months, that is, with two years intervening, and one with only a single year intervening. Yet it makes no difference if someone were to make the same arrangement of intercalary months in other years. The lunar year is of 354 days; for which reason (37) they supposed the lunar month to be...

^C ...in the same year, but distributed gradually, as Geminus excellently demonstrates; he, indeed, as a writer, on account of not only the antiquity but also the practice and knowledge of this doctrine, excels Solinus and Macrobius by far. The Solinian commentator (Salmas., Plin. exercit. p. 19 B et C) believes that in that description of the Greek intercalation, Macrobius and Solinus do not disagree: because Solinus wrote that three months, or ninety days, are intercalated in the ninth year—which, restored in the ninth year, would make four hundred and forty-four days—while Macrobius says that it is completed every eighth year. There is no disagreement between them; nor does Solinus teach that it is intercalated at the beginning of the ninth year, since he [describes that result as] in the eighth...

and the last of the octaeteris is the same as the eighth of the period, and the ninth from the last of the preceding one. Wherefore, every intercalation used to take place in the ninth year from the previous intercalation, and nevertheless in the eighth of its own period. Thus, every Olympiad games used to be held both in the fifth year from the preceding, and in the fourth of its tetraeteris, if we begin the tetraeteris from the one who is next to the commissioning of the games. Hence, some writers said that those games were celebrated every fourth year, others every fifth; nor do they disagree with one another because of this. The same also happens with the Roman leap-day. It was the concern of a critical person to notice this, not to joke and hallucinate about a nothing.

As for the fact that Macrobius (Saturn. I, 6, 13) cites Glaucippus as his authority, beware of thinking that this ancient writer committed to memory such a story as those men fabricate regarding the Greek year; namely, that at the end of an octaeteris ninety days or three solid months were added to the year. For he wrote nothing other than that the Greeks had inserted superfluous days into the last month of their year, which he used in reference to a few days, not to whole months. For about three days used to accrue to the heccaidecaeteris, as Geminus is the author.

Finally, it should be noted concerning that ratio of Geminus (p. 21) which he brings forward, as to why it was intercalated in the third, fifth, and eighth year, namely that it should not have been delayed, lest the year precede by a solid month; which the skilled workers of our own computation ^B also once applied to the intercalary month. See Book VI of *De Doctrina Temporum*, chapter 6, in what sense Geminus, in describing the logic of the Greek year, asserts that the Greeks strove to make their year equal with the sun, and their months with the moon; which we have had enough reason to warn about more than once, because of the Spanish jurist who obstinately asserts that, according to the mind of Geminus, the Greeks organized their years in such a way that both individual months were lunar and individual years solar. Geminus does not teach this, but rather that each month was equalized with the course of the moon; but with the sun, the system of many years, such as the octaeteris and the enneadecaeteris.

(38) *But not only must we*. Observe, you who are studious, in what sense the year [should be described].

(39) *Since, therefore, that which is according to the moon*. The first octaeteris consisted of 2922 days, having 99 months, of which 96 were ordinary, and the remaining three were intercalary. Those were full and hollow. These were all full and thirty days long. The subsequent octaeteris is composed of days 2922 1/2. Thus, the individual months consist of days 29 1/2 and 1/33, that is, they have 12 hours above the days, and 21/33 of one hour, or 8/11. For in the former mode of the octaeteris, the individual conjunctions collect 29 days, and 12 12/5 hours, or 4/11 of one hour. For if you multiply 99 by 29 1/2 and 1/33 of a day, the number 2923 1/2 days will result. Therefore, Scaliger is wrong in his book *De Emendatione*, chapter 11, which is entitled *Elenchus Octaeteridis*, thinking that there is an error in Geminus [where he states] something about the month requiring 2/33 above the 29 1/2 days. If that were true, the syzygy of days would be 29, and 15 5/55 of hours, or 15, 27', 16" 4/11. The octaeteris, however, is 2923 1/2 days ^{C D}.

to the hours of the sun; which is a month. For this reason, one intercalary month is removed from the octaeterides over the course of 160 years. For instead of the three months that ought to be kept during those years, only two are intercalated; so that again, from the beginning, by the month being removed, it may agree with the moon as regards months and days, but with the sun as regards the years.

^B Such a correction having been made, it does not even then happen to agree with the phenomenon; for the whole octaeteris has happened to be in error, both regarding the months, and the days, and the intercalary months. For the monthly time has not been taken precisely. For the monthly time, when taken precisely, is 29 days, and 31 first sexagesimals, and 50 seconds, and 8 thirds, and 24 fourths. Consequently, it will sometimes be necessary to intercalate 4 days in the 16 years in place of the intercalary days. Therefore, it is not proper in any period to have an equal number of hollow and full months, but for the full months to be more numerous than the hollow ones. For if the monthly time were only 29 1/2 days, it would be proper to have an equal number of full and hollow months; but now there is a noticeable fraction in the monthly time, which completes the daily magnitude. For which reason it will be necessary—

(40) *For the monthly time is.* This place is in error. It should be written, as it is in the ancient version, which is the Hipparchian month according to Ptolemy, lib. IV, cap. 2, namely 29 days, 12 hours, 44', 3", 20"". Since, however, ancient astronomers in their calculations use sexagesimals of days more often than hours and hours' scruples; contrary to what is usually done today, it is helpful, for the sake of beginners, to write down here two tables by which both hours and hourly scruples may be reduced into daily scruples; and conversely, daily scruples may be converted into hourly ones.

Table I: Conversion of daily scruples into hourly.

Table II: Conversion of hours and hourly scruples into daily scruples.

The method of both tables is as follows: The daily sexagesimals proposed, to be reduced into hours and their scruples, are to be sought in the first line of the former table, and the corresponding hours and sexagesimals of hours are to be noted. Just as if one wishes to inquire how many daily scruples 31', 50", 8'", 20"" are when resolved into hours, let them be sought one by one in the first

column, counting how many correspond directly to them in the ratio of the hours; so that if the daily scruples are firsts, those which correspond to them should be taken as hours and first scruples of hours. If the daily scruples proposed are seconds, the hours should be taken as being equivalent to first scruples, and the first scruples as seconds; and thus in order they descend by one degree. By this method, therefore, we shall calculate these things.

Hours 12 24' 0" 0"" Daily scruples 31' 50" Seconds 8'" Thirds 20"" Sum of hours 12 44' 3" 20""

Again, from the second table, let us investigate how many 12 hours, 44', 3", 20"" are converted into daily sexagesimals, the same caution being maintained, that if the hours proposed are, those which correspond to them should be taken as first, second, etc., sexagesimals, as they are marked in the table. If, however, scruples are proposed instead of hours, then the hours are to be converted into the first hourly sexagesimal, and the first sexagesimal into the second. In this manner, therefore, the calculation will consist.

Hours 12 30' 0" 0"" Scruples 44' 1" 50" 0"" Scruples 3" 0" 0" 7" 30"" Scruples 20"" 0" 0" 0" 50"" Sum 12 51' 50" 8'" 20""

^A For which reason it is necessary that there be more full months than hollow ones. Nor, in fact, are there three intercalary months in eight years. For if the lunar year were 354 days, the solar year would have an excess of 11 1/4 days. These, multiplied eight times, would fill up three intercalary months. But now, the lunar year is precisely 354 1/3 days approximately. If, therefore, we subtract 354 1/3 from 365 1/4, there will remain 10 11/12 days; these, multiplied eight times, produce 87 1/3 days approximately. These days do not fill up three months. For which cause it should not be ignored that there cannot be three intercalary months in eight years. And this is made manifest even through the enneakaidekaēteris, that is, the period of 19 years. For in 19 years ^B 7 intercalary months are counted, and in longer cycles the enneakaidekaēteris will agree with the usage of the months. Therefore, in eight periods of 19 years, there will be 56 intercalary months. In the octaeteris, three intercalary months are counted; therefore in 19 octaeterides, which make 152 years, 57 intercalary months are counted. In the same time, in the decennovenal period, which agrees with the appearances, 56 intercalary months are counted. Thus, the octaeteris exceeds the decennovenal period by one intercalary month. The octaeteris therefore does not have three intercalary months; but in this also, the period has failed.

Therefore, since it happened that the octaeteris was erroneous in everything, the astrologers around Euctemon, Philippus, and Calippus ^C established another period, namely the decennovenal one. For they observed in 19 years... [the text continues through the 19-year period derivation] ...

The astronomer Gemini

^A They observed, therefore, that within the 19 years there are contained 6940 days, and 235 months including the intercalary ones. Furthermore, in the 19 years there are 7 intercalary months. Thus, according to them, the year consists of 365 and 5/19 days. In the 235 months, they set 110 as hollow and 125 as full; so that it is not the case that a hollow and a full month alternate one after the other, but sometimes even two full months follow consecutively. For nature, in the phenomena, allows this in relation to the moon, which was not the case in the octaeteris. In the 235 months, they established 110 as hollow for this reason: since there are 235 months in the 19 years, they posited all of these as 30-day months; and 7050 days are collected. But 110 hollows had to be spoken of, for which reason in the decemnovennial period the days according to the moon become 6940. Since, therefore, all months are reckoned at 30 days, these 7050 days exceed the 6940 days by 110 days. Therefore the 110 months are grouped as hollow, so that in the 235 months the 6940 days of the decemnovennial period might be completed; so that, in as much as it was permitted, the administration of the exemptible days might happen as equitably as possible, they divided the 6940 days by 110. The result is 63 days. Therefore, every 63 days, it is necessary to make an exemptible day in that same period. Nor does the 30th day always become exemptible, but [rather] the one that falls after the 63 days is said to be exemptible. In this period, the months seem to be well chosen, and the intercalary ones arranged in harmony with the phenomena. But the annual time chosen is in accord with the phenomena. For the annual time, observed over many years, agrees that it is 365 1/4 days. But the year derived from the enneadecaeteris consists of 365 5/19 days, which number exceeds the number 365 1/4 by 1/76. For which cause, those around Calippus ^B corrected the excess of the day, and established a period of 76 years, consisting of four decemnovennial periods, which contain 940 months, of which 28 are intercalary, and 22,759 days. They used a similar order for the intercalary months. And this same period seems to agree most of all with the phenomena.

CHAPTER VII.

On the illuminations of the moon.

Luna is illuminated by the sun, for it always has its shining part turned toward the sun: ^D and when it rises before the sun, its shining part has [it turned] towards the sun and when it appears before the sun.

on some days, the moon has been observed, in rare instances, to set after the sun, and to have its shining part looking toward the west. But when it shifts at night toward the sun, and rises before the sun, it is seen to have its shining part toward the east. From which it is clear that the moon is illuminated by the sun. Such things as these have also been observed. For when the sun is at the winter solstice and rises, then the midpoint of the illuminated part of the moon faces the sun, so that the straight line which joins the horns of the moon is cut in two and at right angles by the straight line drawn from the center of the sun to the bisecting point of the moon; and when the sun is at the summer solstice and rises, again the middle of the illuminated part is turned toward the middle of the sun, so that in like manner the aforementioned straight line is bisected and cut at right angles. The same thing happens also at the settings, so that through this sign as well it may be gathered that the moon is illuminated ^B by the sun. Yet the middle part of the moon is always illuminated like a hemisphere; however, the same illuminated portion does not always appear to our sight, on account of its distances from the sun. For when, on the thirtieth day, the sun and the moon are in the same degree, then the hemisphere turned toward the sun, but turned away from our sight, is illuminated, for the moon is borne beneath the sun; ^C but when the moon shifts with respect to the sun around the new moon, then the moon is seen as a crescent; for a small part of the illuminated hemisphere inclines toward our sight; but when in succeeding days the moon is further from the sun, more and more of the illuminated part is seen by us. When the moon is distant by a quarter of the zodiacal circle, it is seen as halved; for then half of the hemisphere illuminated by the sun is turned toward us. As the distance of the moon from the sun becomes greater, the illuminated part also becomes greater; and when it is diametrically opposite to the sun, the illuminated hemisphere is presented to our view. And to speak generally, the magnitudes of the illuminations are observed according to the ratio of the distances. Lastly, when the moon passes under the sun, it is seen devoid of light. Its illuminated hemisphere is turned upward toward the sun; whence it reasonably follows that the illuminated part of the moon is not visible to us. From which it is clear that the moon is illuminated by the sun. The moon receives all four configurations in a monthly period, completing them twice. These configurations are: crescent, halved, gibbous, and full. ^D The crescent occurs around the beginning of the months; the halved, around the eighth day of the month; the gibbous, around the twelfth; and the full, around the middle of the month. And again, the gibbous occurs after the middle of the month; the halved, around the twenty-third; and the crescent, around the end of the months.

^A However, the moon does not complete the same configurations on the same-named days, but on different days according to the irregularity of its motion. For when the moon is slowest, it appears as a crescent on the day of the new moon; when slowest, on the third day. And it remains a crescent, sometimes until the fifth day, and sometimes, at its slowest, until the seventh day. It becomes halved, at its fastest, around the sixth day, and at its slowest, around the eighth. It becomes gibbous at its fastest around the tenth day, and at its slowest around the thirteenth. It becomes full, at its fastest, around the thirteenth day, and at its slowest, around the seventeenth. It becomes gibbous for the second time, at its fastest, around the eighteenth day, and at its slowest, around the twenty-second. It becomes halved for the second time, at its fastest, around the twenty-first day, and at its slowest, around the twenty-third. It becomes a crescent for the second time, at its fastest, around the twenty-fifth day, and at its slowest, around the twenty-sixth. The entire monthly period is ^B 29 1/3 days. For a month is the time from conjunction to conjunction, or from full moon to full moon. Conjunction is the time in which the sun and the moon are found in the same degree, which happens on the thirtieth day of the month.

CHAPTER VIII. Concerning the Eclipse of the Sun.

☀️ Eclipses of the sun occur due to the interposition of the moon. For since the sun is borne in a higher position and the moon in a lower, when the sun and the moon are in the same degree, the moon passes beneath the sun and obstructs the rays of the sun that are being carried toward us. ^C For this reason, they should not even be called eclipses in the proper sense, but interpositions. For no part of the sun ever really fails; rather, it is rendered invisible to us on account of the encroachment of the moon. For this cause, eclipses do not occur equally; but according to the differences of the climates, great fluctuations occur regarding the magnitudes of the eclipses. For at the same time, for some, the whole sun fails; for others, half of the sun; for others, a part smaller than half; for others, no part of the sun at all appears to fail. For those who dwell in the perpendicular line of the moon's interposition, the whole sun is hidden from them; but those who are outside the perpendicular line and have some part of the interposition, to them some part of the sun appears to fail; but to those who dwell entirely outside the interposition, ^D no part of the sun fails. That the sun fails according to the interposition of the moon is the greatest argument, for eclipses do not occur on any other day than the thirtieth only, when the moon is conjoined with the sun; and hence the same thing is known, that the magnitudes of the eclipses occur in proportion to the locations.

(43) As to whether the whole sun sometimes fails, or a part of it always emerges so that it cannot be entirely obscured, this is not agreed upon among the masters of that art. For in our own age Tycho Brahe denied that the whole orb of the sun could be obscured by the moon, however much it might be cast in its path, and he posited that the visible diameters of the moon are smaller in the syzygies than the solar ones. But the authority of the ancients struggles against this, as well as the experiments themselves of the great masters. See Kepler, in the chapter of *Astronomical Optics*, where he proves with many examples that the sun can sometimes fail entirely, which our Gemini affirms here.

CHAPTER IX. On the eclipses of the moon.

^A Lunar eclipses occur according to the incidence of the moon into the shadow of the earth. For just as other bodies, when they are illuminated by the sun, cast shadows, so also the earth, when it is illuminated by the sun, projects a shadow. And indeed, due to the magnitude of the earth, its shadow happens to be manifest and profound. When, therefore, the moon is diametrically opposed to the sun, then also the shadow of the earth is diametrically opposed to the sun. Whence the moon, being carried lower than the shadow, necessarily falls into the earth's shadow. Moreover, that part of it which falls into the shadow of the earth is always deprived of light from the sun because of the interposition of the earth. For then the sun, the earth, the shadow of the earth, and the moon are established on the same straight line. ^B For which reason lunar eclipses do not occur on any other day except at the full moon. For then the moon is diametrically opposed to the sun. However, all lunar eclipses are equal; for the incursions which occur in solar eclipses are rendered diverse on account of the places of habitation, for which reason the magnitudes of the solar eclipses are also rendered diverse: but the incidences of the moon into the shadow are all equal in the same eclipse. Yet it is not always an equal part of the moon that fails. For when the moon makes its passage through the middle of the ecliptic circle, it falls entirely into the shadow of the earth; and therefore it is necessary that it should suffer a total eclipse. But when it touches the shadow, ^C some part of the moon suffers an eclipse: and the part of the circle which causes the moon to fail is of two degrees. For in this place it happens that all eclipses of the moon occur. From these things it is manifest that lunar eclipses occur according to the incidence into the shadow of the earth; for by reason of the daily motion of the moon according to latitude, the magnitudes of the eclipses become congruent, and lunar eclipses do not occur on other days except at the full moon.

CHAPTER X. That the planets make a motion contrary to the world.

The world is moved by a circular motion from the east to the west. For whatever stars are seen toward the east after the setting of the sun, as the night proceeds, ^D are seen to be elevated more and more; then they are seen in the middle of the sky. But as the night progresses further, these same stars are seen to decline toward the west, and finally they are seen to set. And this happens daily in all the stars. Therefore it is manifest that the whole world with all its parts is moved, and indeed from the east toward the west. That it makes a circular motion is manifest from the fact that all stars rise from the same place and set in the same place; furthermore, all the stars observed through dioptra are seen to make a circular motion in the total rotation of the dioptra.

^A But the sun is carried from the west toward the east, contrary to the motion of the world. This is evident from the stars that rise before the sun. For as many stars as are observed rising before the sun, in the following nights they are seen to rise earlier; and this happens continuously on all nights. From which it is evident that the sun moves towards the following signs, moving from west to east contrary to the world's motion. But if the sun were carried from east to west, it would always happen that the stars rising before it would remain unobserved. For in passing over to the preceding parts, it would necessarily obscure them with its own rays; for stars that are near the sun always remain unobserved, being lit up by the sun. But now this does not happen; rather, the stars rising before it are seen in the following nights to have ever greater distance from the rise; so that in a month's time the whole sign of the constellation rises before the sun, which before was hidden by the rays of the sun. For that sign which follows the sun always becomes invisible due to the sun’s rays, while that which precedes the sun is observed. In the monthly time, meanwhile, the following sign always becomes invisible as the sun moves into it, while the preceding sign is seen at a distance of two signs; and this happens with all twelve signs. From which it is clear that the sun, moving contrary to the motion of the world, makes its transit into the following signs, and not into the preceding ones.

^C But the motion is seen more clearly in the moon; for it too is seen to move contrary to the motion of the world, from west to east; and this can be grasped in a single night by observation, as the appearances provide testimony. For when the moon has been observed near one of the fixed stars, as the night advances it is distant from that observed star toward the east, and that star is distant from the moon toward the west; and often in a whole night the moon is distant from that observed star by a degree toward the east, so that in one night the motion contrary to the world is observed. For it does not advance toward the preceding stars, but toward the following ones.

^D Some, however, say that the sun and moon make their transition into the following signs; nevertheless, they do not move contrary to the world, but because of their magnitudes they are overcome by the sphere of the wandering stars; and it seems to us that that transition into the following signs occurs according to the contrary motion; but this is not true; rather, the sun and moon are carried from east to west; but being caught up by the world before they complete the circle, they are seen in the following signs. Some also make use of this analogy. For if someone, they say, were to station twelve runners using the same speed,

^A moving in a circle, and were then to introduce another one among them moving more slowly, while still making a movement in the circle similar to theirs, he would indeed appear, as he is overtaken, to be moving in the following direction; but in reality this will not be the case. Instead, moving similarly to them, he will appear, due to his slowness, to be moved in the contrary direction. They say that this same thing happens in the case of the sun and the moon. For since they move toward the same parts as the universe, they are carried to the following signs because of their slowness; just as ships carried along on rivers, when they are outstripped by the current, appear to be moved backward; and they say this happens also in the case of the sun and the moon.

This opinion, although stated by many philosophers, is inconsistent with the visible phenomena. For if they were moving by way of falling-behind, with those bodies being carried below because of their sizes, the falling-behind ought to take place on parallel circles, just as all the fixed stars are carried on parallel circles, because the motion of the universe also is circular from east to west. But in fact they are not falling behind on parallel circles. The sun, while moving on the circle passing through the middle of the signs, at the same time also makes a passage according to latitude from solstice to solstice—assuming, as I think, that it possesses its own motion: one from east to west, and the other from west to east—while the moon makes its passage in the whole latitude of the zodiacal circle. Yet none of those carried by way of falling-behind can at the same time move according to latitude; rather, it ought to make that falling-behind in accordance with the motion of the universe. ^C But what refutes this opinion as false, more than anything else, is the motion concerning the five wandering stars. For they are sometimes left behind by the fixed stars, and sometimes they precede them; and sometimes they remain at the same stars—which are even called stations. Since such is the motion concerning them, it is clear that the transition into the following signs does not happen by way of falling-behind; for they would have been falling behind throughout. But as it is, there is a certain individual sphere for each, according to which they at one time shift into the following signs, at another time into the preceding ones, and at another time they are stationary. Thus, then, there is also for the sun, and for the moon, a certain individual, and elective, and natural motion according to latitude, according to which, while moving from west to east, they at the same time make that motion of latitude.

That they cannot make their progress into the following signs of the zodiac by way of falling-behind is manifest also from the fact that these transitions do not happen in proportion to their sizes nor to their distances. For if they were being carried below because of the sizes of the bodies, having a slower motion than the fixed stars, the fallings-behind ought to have occurred in proportion to their sizes and distances. Since this does not happen, it is necessary to say that the contrary motion is natural for the wandering stars. Indeed, however, because of the individual sphere of each...

^A one, it happens that different progressions occur.

CHAPTER XI.

Concerning risings and settings.

When the world moves from the east towards the west, it is restored by day and night from the east back toward the east; and in the rotation of the world, all the stars rise and set daily. Now a rising is an apparition above the horizon, but a setting is an occultation, which occurs daily below the horizon. However, "rising" and "occultation" are spoken of in another way, which some people, through ignorance, suppose to be the same meaning. There is, however, a great difference between a rising and an apparition. For the rising is that which was mentioned previously; but an apparition is the rising that occurs towards the horizon, being perceived ^B along with the distance from the sun. The same distinction exists between a setting and an occultation. For a setting is spoken of in one way as that which is the daily one below the horizon, but in another way as an occultation that occurs simultaneously at the horizon and with the sun.

There are, moreover, two risings for every star; for some are called matutine, and others vespertine. A matutine rising is when some star rises at the same time the sun is rising, and is at the same moment on the horizon. A vespertine rising is when, as the sun is setting, some star rises, being placed simultaneously on the horizon.

There are two differences between matutine and vespertine risings. For some of them are called true, and others apparent. They are true when a star genuinely rises ^C at the same time it is placed on the horizon while the sun is rising; and this rising is not seen on account of the rays of the sun. But in the days immediately following, the sun, since it moves contrary to the motion of the world, passes into the following signs; and the star rises before the sun by exactly the amount that the sun has moved into the following signs during the daily interval. Nevertheless, the rising of the star cannot yet be discerned; for it is still obscured by the sun. Again, in the next day, the sun has passed into the following signs; and the star rises before the sun by the amount that the sun has progressed in two days. Then, in the following days, ^D as the star rises ever more and more timely before the sun, when it has risen so far beforehand that the rising of the star can be seen, because it has escaped the rays of the sun, then this star is said to make an apparent matutine rising. For this reason, apparent risings of the stars are also predicted in tables; for true risings are invisible and unobservable. But apparent risings are both predicted and observed. The same reasoning applies again to vespertine risings. For there are two differences in these as well; for some of them are called true, and others apparent. They are true, indeed, when simultaneously and in truth, as the sun is setting, the star rises...

^A. But these risings are invisible because of the sun’s rays. In the following days, because of the sun’s progression, the distance between it and the star being reduced, the star rises before the sun sets, but, still obscured by the sun, it is invisible. Yet when, after the sun has set, it is finally seen to have escaped the sun’s rays, then it is said to have made an apparent evening rising. And in the succeeding nights it appears ever more and more elevated.

Likewise, there are said to be two differences of settings; for some of them are matutinal, and others vespertinal. "Matutinal" settings are spoken of when, as the sun is rising, a star sets. A "vespertinal" setting is spoken of when, as the sun is setting, a star is carried down with it, arriving at the same time beneath the horizon ^B. There are two differences of matutinal settings. For some are true, and others are apparent; true, indeed, when both the sun and the star are situated at the horizon, the sun rising and the star setting. But these settings are invisible because of the sun’s rays. An "apparent" matutinal setting is when, before the sunrise, the star is seen to set for the last time. Similarly, there are also two differences of vespertinal settings. For some of them are true, and others are apparent; true, indeed, when both the sun and the star are situated precisely at the horizon, both setting. And these settings are also invisible because of the sun’s rays. But the vespertinal settings are "apparent" when, after the sun’s setting, a star is seen by us to set subsequently.

Therefore, of the matutinal risings and settings, the true ones occur first, and the apparent ones later; but of the vespertinal risings and settings, the apparent ones occur first, and the true ones later. A matutinal rising from a matutinal rising, and a vespertinal rising from a vespertinal rising, and in general every similar type from a similar type, occurs for all stars throughout the year; for the sun, having traversed the zodiacal circle in a year, arrives again at the same stars ^C.

A matutinal rising from a vespertinal rising occurs after an interval of six months for those stars situated on the zodiacal circle; and a matutinal setting from a vespertinal setting likewise. But for those stars situated further north of the zodiacal circle, the matutinal rising from the vespertinal rising occurs after a period of time longer than six months; and for those situated towards the south of the zodiacal circle, the matutinal rising from the vespertinal rising occurs after a period of time shorter than six months. This time in excess of six months is not the same for all stars, but for some it is longer, and for others shorter. Indeed, for those stars situated ever more towards the north, the time becomes ever longer and longer, because greater segments are carried above the earth for those situated ever more towards the north. For those situated more towards the south, the time becomes ever more and more shorter; for those stars which are situated towards the south ^D

^A are carried in smaller segments above the earth.

Conversely, for those stars situated towards the north of the zodiacal circle, the time from morning setting until evening rising is less than a half-year; but for those towards the south, the time from morning setting until evening rising is more than a half-year. The variation of the times occurs in accordance with the positions from the zodiacal circle, corresponding to the variation of the segments which are intercepted above the earth by the horizon.

For those stars situated ^B in the zodiacal circle, morning rising and evening setting happen at the same time, and again morning setting and evening rising happen at the same time. For the remaining stars, the aforementioned phenomena do not occur at the same time; rather, they vary according to the times, since the stars have a circular motion from the east towards the west. For those stars among them which are situated on the equinoctial circle have an equal course above the earth and below the earth; for the equinoctial circle is bisected by the horizon. But those stars which are situated towards the north of the equinoctial circle are carried for a longer time above the earth, and for a shorter time below the earth. For of all the circles ^C upon which the fixed stars are carried, larger segments are intercepted above the earth by the horizon, and smaller segments below the earth, on account of the elevation of the pole. But those stars which are situated towards the south of the equinoctial circle have a smaller motion above the earth and a larger motion below the earth. For again, of the circles upon which the fixed stars are carried, the southern ones have smaller segments above the earth and larger segments below the earth. Since such is the motion of the fixed stars, it happens that not all things which rise together also set together; but of those which rise together, those situated more towards the south always set earlier, because they are carried in smaller segments above the earth. Similarly, neither do those that set together rise together; but of them, those situated more towards the north rise earlier, because they are carried in smaller segments below the earth. Again, neither do those which rise earlier also set earlier; but some of those which rise earlier also set at the same time, and some later. Similarly, of those which set earlier, some do not rise earlier, but rise and set at the same time, some earlier, some later. Aratus also makes mention of these things to an extent, saying as follows: ^D But Taurus is always swifter than Auriga To descend to the other side, although it rises at the same time.

For in these lines he says that Taurus, having risen at the same time as Auriga, nevertheless sets earlier. This happens because of the excess of the segments in which the fixed stars are carried above the earth and below the earth. And because of this sphericity, not all stars rise at the

^A same time every night; but some rise and set, others rise but do not set, while others neither rise nor set. Those positioned further to the north appear even higher after sunset and before sunrise, whereas those positioned further to the south are seen neither rising nor setting, but are carried below the earth for the entire duration of the night. Hence, some stars are called "twice-appearing," as is Arcturus; for after the sun has set, it is often seen to set in that same night, and to rise again before the sun. For this reason it is called "twice-appearing," because it is observed to set in the evening and to rise in that same night. Others have the contrary order: those that set before the sun sets and rise after the sun has risen, so that throughout the whole night they are seen neither rising nor setting; these some call "night-walkers." Yet these properties do not always apply to the same stars at every season, but oscillate according to the passages of the sun, both with regard to their rising and their setting.

CHAPTER XII. On the zones on the earth.

CHAPTER XIII. On the habitations.

tendency of their motion, if a straight line is joined from any habitation of those which are in our inhabited earth to the center of the earth, and it is extended, those who are situated at the end of the diameter in the southern zone become the antipodes of ^A those who dwell in the northern zone.

Our inhabited earth is divided into three parts: Asia, Europe, and Libya. The length of the inhabited earth is almost twice its breadth; for which reason those who construct geographical descriptions according to reason use oblong tablets, because the length is twice the breadth. But those who draw geographical descriptions as round are very much led astray from the truth; for the length becomes equal to the breadth, which is not the case in nature. It is therefore necessary that the symmetries of the distances in round ^B geographical descriptions not be maintained. For the inhabited part of the earth is a certain segment of a sphere, having its length double its breadth, which segment cannot be bounded by a circle.

Now, the greatest circle of those on the earth along the meridian of the world having been measured, and found to be 25 myriads and 2,000 stadia, and the diameter 8 myriads and 415 stadia; and the meridian circle being divided into 60 parts, one sixtieth segment is called, which becomes 4,200 stadia. For if the 25 myriads and the 2,000 stadia are divided into 60 parts, the sixtieth becomes 4,206 stadia. The distances between the zones are therefore defined in this way. The breadth of each of the two frigid zones is 6 sixtieths, which is 25,200 stadia; the breadth of each of the two temperate zones is 5 sixtieths, which makes 21,000 stadia; and the breadth of the torrid zone is 8 sixtieths. ^C Thus, from the equinoctial to either side toward the tropics there are 4 sixtieths, which makes 16,800 stadia.

(44) This measurement of the greatest circle is Eratosthenian, as Strabo lib. ii and Plinius lib. ii, cap. 108 attest; which he says fulfills the Roman computation of 31,500,000 paces, which is also true. For the stadium consists of 125 paces. Consequently, if 252,000 is multiplied by 125, it makes 31,500,000 paces, which are 31,500 miles. But Cleomedes lib. 1, cap. 10, reports that the circumference of the earth was defined by Eratosthenes as 250,000 stadia: and he describes the method by which that measure was detected, namely from the fact that the angle, which is enclosed by the gnomon and the sun's ray at Alexandria, when the sun is situated at the tropic of Cancer at noon, is a fiftieth part of four right angles, ^D just as the periphery of the circle drawn on the sundial, upon which that angle rests, is a fiftieth part of the whole circle. Wherefore, since the interval between Syene and Alexandria, which are under the same meridian, is 5,000 stadia: which is a fiftieth part of the circumference of the earth: the total circumference will collect 250,000 stadia. But when it is certain from so many ancient witnesses that Eratosthenian measurement which we mentioned was what was written down for the earth's circumference; it seems that it was a little more than the fiftieth part, both of the angle which the gnomon contains with the ray, and of the circumference of the greatest circle, that had been attributed by that author to the *sciothericon*. Strabo in the cited place says that Hipparchus took the same circuit of the earth as Eratosthenes, of 252,000 stadia. Pliny, however, asserts that he added a little less than 25,000 stadia to Eratosthenes' measurement. By which calculation the greatest circle will be 277,000 stadia. To return to our Geminus, since he circumscribes the circumference of the earth according to the opinion of Eratosthenes at 252,000 stadia, it is false that he makes the diameter, as a consequence, consist of 80,415 stadia. For since that ratio of the diameter to the circumference is as 7 to 22: it behooves the diameter of the earth to collect about 80,182 stadia.

(45) The ancient astronomers divided the meridian circle into sixty parts, as we said above. Thus 4,200 stadia correspond to each sixtieth part. But if the circle is divided into parts, any part requires [number omitted] stadia. We warned that this dimension is referred to the Rhodian, in which the semidiameter of the arctic circle is 36 degrees. Hence he also defines the frigid zone by the arctic circle proper to that place: so that those for whom the pole is raised by 54 degrees, and subsequently by more, are considered to be in the frigid zone, which is absurd.

^A From the pole of the world to the arctic circle that is on earth, there are 25,200 stadia; again, from the arctic circle on earth, which lies under the celestial arctic, to the terrestrial tropic, which is placed under the celestial summer tropic, there are 21,000 stadia; again, from the summer tropic to the terrestrial equator, which is situated under the celestial equator, there are 16,800 stadia; again, from the equator to the other tropic there are 16,800 stadia. Then from that tropic to the arctic circle there are 21,000 stadia; finally, from the arctic circle to the other pole there are 25,200 stadia, so that the distance between the poles is brought to 12 myriad and 6,000 stadia, which is half the circumference of the earth; for the distance from pole to pole is a semicircle. The division of these sixtieths is also the same in armillary spheres. ^B For armillary spheres are prepared thus: from the pole, the arctic is distant 36 parts, which are 6 sixtieths; for six times six is 36. The arctic is distant from the summer tropic by 50 degrees, which make 5 sixtieths; the summer tropic is distant from the equator by 24 degrees, which are 4 sixtieths; the equator is distant from the winter tropic by the same 24 degrees; the winter tropic is distant from the antarctic by 30 degrees; the antarctic is distant from the south pole by 36 degrees; so that again, from pole to pole, 180 degrees are collected, and 30 sixtieths; for upon this one climate both the armillary and solid spheres are prepared, since only the arctic circles are changed in certain habitations according to distances. However, the zones on earth take their division of those dwelling on earth according to the aforementioned one climate. ^C Therefore, those who dwell on the same parallel have the same phenomena occurring according to their habitations, and the magnitudes of the days are equal, and the magnitudes of the eclipses are similar, and the markings of the horological instruments are the same, and, in sum, all things that happen concerning dwellings situated on the same parallel are the same. For the inclination of the world remains the same. Because of the inclination of the world, different appearances arise. Yet the beginnings of the days and the ends do not occur for all simultaneously, but for some earlier and for others later. And the first hour is the same for all, while for others it is midday, and for others sunset. Now, indeed, as regards the senses, for nearly 400 stadia from the east towards the west, the horizon remains the same. ^D Therefore, as regards the senses, sunrise and sunset happen to them simultaneously. But where the distance is greater than 400 stadia, there antecessions of sunrises and sunsets occur. For those who dwell on the same meridian, the variety of climates becomes insensible up to [400] stadia. Nevertheless, because of that distance which exceeds more towards the north or the south, a different inclination occurs. Thus all appearances [are changed].

For the magnitudes of the days, the magnitudes of the eclipses, and the descriptions of the sundials become different for those who live on the same meridian. For the inclination shifts, either towards the north or towards the middle of the days and the middle of the nights at the same time, the transition taking place as one moves along the meridian. These changes, however, occur for all who reside on the same meridian.

^B When we speak of the southern zone, and of those who reside in it, and furthermore of those who are called its antipodes, it is proper to understand it as follows: that we have received no historical account concerning the southern zone, nor whether any people dwell in it; but rather that, by reason of the whole spherical [construction] and the shape of the earth and the passage of the sun which takes place between the tropics, there exists also another zone situated towards the south which possesses the same temperament as the northern zone in which we live. Similarly, also, when we speak of the antipodes, we do not mean that anyone dwells in the exact same diameter as we do, but that there is some habitable place on the earth along the same diameter as us.

Some of the ancients, among whom is the Stoic philosopher Cleanthes, have declared that the Ocean has been poured between the tropics under the torrid zone; consistent with whom, Crates the grammarian, arranging the wanderings of Ulysses and describing the whole sphere of the earth with defined circles, as we have mentioned before, imagines the ^C Ocean to be situated between the tropics, saying that he makes the arrangement of the whole earth in accordance with the mathematicians.

But such an arrangement is foreign to both mathematical and physical doctrine, and is not recorded among any of the ancient mathematicians as being situated between the tropics, as Crates asserts. For in our own times, many habitable places have already been inspected and discovered, and they are not everywhere encompassed by sea. And since the space of that intermediate interval, which is from the summer tropic to the equator, is 16,800 stadia, [or] nearly to 20,800 stadia, according to the extent of our opportunity for investigation, the history of these matters has been written down, having been explored through the kings in Alexandria. Hence, those who opine that the Ocean is poured between the tropics are wrong. From these things, it is also manifest that the further opinion, namely that the region situated between the ^D tropics is uninhabitable due to the excess of heat—and especially that region which is in the middle of the torrid zone—is false. For the Ethiopians, who inhabit the extremities of the torrid zone, have the sun at their zenith during the conversions, or solstices. For it must be assumed that there are, by nature, two Ethiopias, since Ethiopians dwell both around the summer tropic circle, which is the one near us, and around that tropic which is for us the wintry one, but for the antipodes the summer one. Crates states this...

and says that Homer ^A also speaks of this in these lines: Ethiopians, who are divided in two, the furthest of men, Some at the setting of Hyperion, others at his rising.

Crates, therefore, while indulging in paradox, transfers the themes spoken of by Homer in an archaic and particular way to the true formation of the sphere. For Homer and almost all the ancient poets, so to speak, posit the earth as flat and associate the Ocean as surrounding it in a circle, holding the place of the horizon, and they assume that risings occur from the Ocean and settings into the Ocean. Consequently, they assumed that the Ethiopians who were near the sunrise and sunset were scorched by the sun. But this preconception is consistent with the aforementioned arrangement, yet is foreign to the natural spherical formation. For the earth lies in the middle of the entire universe, holding the position of a point; and the risings and settings of the sun take place from and into the ether, with the sun always being equidistant from the earth. Whence the aforementioned Ethiopia ^B is not to be contemplated; but those parts lying under the tropics of the world, which exist at the extremities of the torrid zones, exist according to nature. However, it must not be assumed that the torrid zone is uninhabitable. For by now, some have reached many places in the torrid zone, and very many places have been found to be habitable.

Whence it is also asked by many whether the places around the middle of the torrid zone are more habitable than the habitations that exist around the extremities of the torrid zone. Polybius the historian, therefore, treats of this in a book which bears the inscription, *On Habitation around the Equator*; and this is in the middle of the torrid zone. He says that these places are inhabited, and that they have a ^C more temperate habitation than those who dwell around the extremities of the torrid zone. He brings forward partly histories of those who had seen these habitations and who, furthermore, provided testimony to the phenomena; and partly he reasons from the natural movement of the sun. For the sun dwells for a long time around the tropical circles, according to its approach to them and its withdrawal, so that it remains, so to speak, for forty days in the tropical circles in terms of perception. For which reason the lengths of the days remain the same for almost forty days. Whence, upon the lingering that occurs towards the habitations ^D situated under the tropics, it is necessary that this habitation be scorched by heat, and become uninhabitable on account of the excess of heat. But from the equinoctial circle, the withdrawals happen to be swift; whence also the lengths of the days around the equinoxes take on great increases. It is reasonable, therefore, that those habitations also which are situated under the equator be more temperate; since the ascent takes place over the point of the true...

to be more temperate, yet the sun retreats rapidly. For all who dwell between the tropical circles are situated similarly with respect to the approach of the sun; however, it remains for longer times with those who dwell around the tropics. For this reason, it happens that the habitations which are around the equator, and which are situated in the middle of the torrid zone, are more temperate than those who dwell around the extremities of the torrid zone, and who are positioned beneath the tropical circles. ^A

CHAPTER XIV. On the significations of the stars.

The discourse concerning significations creates a different opinion among the unlearned, as if the mutations of the air occur on account of the risings and settings of the stars. ^B But the mathematician and the physicist have a different opinion. And first of all, it must be established that these significations of rains and winds, which occur, happen around the earth, and do not reach to a greater altitude; for they are exhalations from the earth, varied and without order, so that it is impossible for them to extend as far as the sphere of the fixed stars; nor, indeed, do the individual clouds reach there because of their altitude. Those, therefore, who ascend Cyllene, the highest mountain in the Peloponnese, and sacrifice to Mercury, to whom the summit of the mountain is dedicated, when they ascend again after a year and perform the sacrifices, find the thighs and the ash left by the fire remaining in the same place in which they had left them; and they are changed neither by winds nor by rains, because all clouds and the constitutions of the winds form below the summit of the mountain. ^C Often, also, those who ascend Satabyrium make their ascent through the clouds, and behold the formations of the clouds below the summit of the mountain. And the altitude of Cyllene is indeed less than 15 stadia, as Dicaearchus demonstrates geometrically; but the perpendicular height of Satabyrium is less than 14 stadia. For all clouds, as we have said, since they have their exhalation from the earth, form around the earth. Moreover, the predictions of the significations which are made in the parapegmata do not consist of certain fixed precepts, ^D nor are they handed down by any art such that they have a necessary effect. But those who, from that which usually happens, take the agreement through daily observation, these record them in tables. And this collection and observation came about in the following way. For, taking the beginning of the year, and observing in which sign the sun was at the principle of the year, and ascribing the degree, they recorded for each day and for each month the total mutations of the air, of winds, of rains, and of hail, at the positions of the sun through each sign and degree. Observing this through many years,

^A they recorded in tables the mutations that occur most frequently in the same regions of the zodiac, not taking the description from any art or fixed method, but taking what fairly agrees from experience. Since indeed they could not record an exact day, or month, or year in which any of these things was accomplished, because the beginnings of the years are not the same for everyone, and the months do not have the same names among everyone, nor are the days ordered in the same way, they wished to determine the mutations of the air by certain fixed signs. Hence, the mutations of the air occur at the risings of the stars at determined times, not because the stars have power over the change of winds and rains, but because they have been taken as signs for the purpose of our foreknowing the ^B circumstances concerning the air. And just as a torch or beacon is not itself the cause of a warlike situation, but is a sign of a time of war, in the same way the risings of the stars are not themselves the causes of the mutations in the air, but are set forth as signs of such circumstances. For those who from the beginning observed and composed those tables, having examined the regions of the zodiacal circle in which the mutations of the air occur for the most part, looked to see which of the stars rises or sets at those times, and used the risings and settings of these as signs for the foreknowledge of the aforementioned things. For the true risings and settings happen to be invisible; but they were able to see the visible risings and settings, and to distinguish them around the stated times, in that the Pleiades, when setting, have such power as to generate a certain humidity around the air, or when rising, to ^C signify the beginning of summer. Whence also Hesiod says: When the Pleiades, daughters of Atlas, arise, Begin the harvest: and the plowing, when they set. Not because of the power of the star—for that is entirely foolish; for whether the stars are fiery, or whether they are ethereal, as it pleases some, all have shared in the same essence and power, and have no sympathy with the things happening on earth. For the whole earth has the position of a center in relation to the sphere of the fixed stars, and no influence or effluence reaches from the fixed stars to the earth. How then are we to suppose that these are the causes of rains and winds and hail, from which no power falls to us? For from the sun and moon indeed, power reaches to the earth according to their ^D transits, both greater and lesser; whence it is reasonable that there should be a sympathy with them according to the power of each. But the risings and settings of the fixed stars occupy the rank of a sign, as we said before. Whence one must not even assume that the same signal signs are accomplished by the same stars; but according to

the varieties of the same climates, different risings and settings of the stars occur, and indeed each horizon has its own signs for the change of air. ^A For the same parêgma [table of signs] cannot agree in the city of Rome, and in Pontus, and in Rhodes, and in the city of Alexandria; but it is necessary that the observations be different in different horizons, and that in each city other stars should be taken as producing indications.

From which it is manifest that the risings and settings of the stars do not naturally generate the affections of the air; but that in each horizon different observations and changes of the airs have occurred. Wherefore not even all the indications recorded in the tables always agree; but sometimes they do not occur at all, and risings and settings which contain the greatest storms bring about serenity: sometimes there is serenity in the city, but rain in the fields. Often someone has indicated a change of air by the rising or setting of a star after three or four days: sometimes he anticipates the indication by four days. Whence those who err in the predictions of the indications have an excuse, in that they anticipated the indication, or in that it happened later. ^B From all which it is manifest that those things which pertain to the indications are recorded in the tables in a rough manner, not being handed down by any art or necessity, but recorded from continuous observation. For this reason they often fail. Whence astrologers are not to be accused, if they have erred in the indications. But if someone, predicting an eclipse or the rising of a star, errs, reasonably both the study and the one who practices it will be held worthy of accusation. For all things which are handed down by art ought to have an infallible prediction or enunciation. But those things which pertain to the indications, neither do we find them to possess perfect praise when we attain them, nor do they deserve accusation when we err from them. For this is a certain part of astrology that is devoid of art, and unworthy to be brought into the middle. ^C The same is to be thought to happen also regarding the rising of the Dog Star. For all think that this star has a peculiar power, and is the cause of the intensity of the heat, as it rises simultaneously with the sun. But this is not so: but since this star rose according to the hottest time of the year, they noted from its appearance the change of the air into heat. But the sun is the cause of the intensity of the heats. For first, when we are chilled from winter, according to the approach which is made toward us, the sun begins to warm us; yet it does not yet make the warming manifest, as the chilling which is from winter still remains; when, however, a lingering occurs, and the sun approaches always more and more, it happens that a sense of warming is made; then it happens that the sun approaches the same habitation twice in succession. For in the progress toward the summer tropic circle, and in the recession, the sun passes through the same habitations. Whence it happens, on account of this cause, that intensities of heats occur. ^D Furthermore, the approach to the summer tropic and

the departures are altogether small and insensible; for it happens that it lingers for almost forty days upon the summer tropical circle. Whence the magnitudes of the days around the solstices have an insensible increase. But since at this time the Dog Star was rising, they marked by its appearance the time of the intensification of the heats, not because the star itself was ^A becoming the cause, but because the sun has the cause. ^B If, therefore, one takes the rising of the Dog Star as a sign of the time, he takes it correctly, just as Homer says of the Dog thus: "And it is made an evil sign." For it is not to be thought that it has a power of its own with regard to the intensification of the heats, but that the Dog was taken for the sake of a sign. However, those of the poets and philosophers who attribute the power of the intensification of the heats to the Dog are very far strayed from the truth and from natural doctrine. For this star has shared in the same essence as all the stars. For whether the stars are fiery or ethereal, they all have the same power, and the influence from the Dog ought to be overcome by the multitude of the stars. For there are others that exceed the star of the Dog in magnitude, and they are infinite in multitude. If, therefore, ^C the power from them all does not reach as far as the earth, nor contribute anything to the power of the sun, how is it credible that the influence from one star should cause such an intensification of the heats? And if all the fixed stars, having shared in the same power, do not help at all, it is not possible for the heating proceeding from one star to produce a sensible variation in its co-risings with the sun. The sun itself is the cause of the heats, continuously going through the same place of habitation. But since they could not determine a common day for all men, in which the intensifications of the heats occur, and since at this time this star was rising, they marked the time by its appearance. That this star is not the cause of the intensification of the heats will be manifest from the things that are to be said. For, first, many and larger stars often rise together with the sun, and they produce no ^D sensible variation, but sometimes, on the contrary, at their risings and settings, storms occur and cold winds blow, as if they contributed nothing to the intensification of the heats; and often the greatest of the five planets—Phaethon (Jupiter), Phosphoros (Venus), and Pyroeis (Mars)—are in the same zodiac sign with the sun, from which powers also fall upon the earth, and yet, on account of their cause, nothing becomes more different regarding the air. From which it is manifest that neither the fixed stars nor the wandering stars contribute anything to the intensification of the heats; for if the Dog had brought some power, it would have been necessary for the intensification of the heats to occur at its true rising. For then

it rises together with the sun. But this does not occur; rather, the greatest heats occur at its apparent rising. For about this season, the sun, on account of the aforementioned causes, is the partial cause of the intensification of the heats. In Rhodes, indeed, the star rises thirty days after the solstice, but in other places forty days after the summer solstice, and in others fifty; so that it is not the case that its rising causes the intensification of the heats for everyone. It is manifest that the season encompassing the intensification of the heats is one—namely, the thirty days after the summer solstice—and in this time, among some, the Dog rises and signals the season, while among others, some other of the ^B constellation stars; for the risings and settings do not happen for all stars at the same time.

But that which is said by the majority, that it rises together with the sun about this season, is utterly ignorant. For at this time the star is at the greatest distance from the sun. For the sun traces its path entirely on the summer tropic circle, while it [the Star] lies on the winter tropic circle; so that they are at the greatest distance from one another. How then could the Dog be the cause of the intensification of the heats? It would indeed cause intensification, if the star had any power, when it was conjoined with the sun at the winter turnings, when the star was being carried on the same circle as the sun. For then one would have to expect a perceptible change in the air, contrary to what appears. But this does not occur, but rather the opposite—winter. ^A Hence, a sign is placed in the tables. So it is manifest from all of this, that neither this star, nor any other, has such power as to effect changes in the air; but the primary cause is the sun, and the risings and settings of these [stars] are set down for the recognition of changes in the air. For which reason, they do not always correspond. Hence, one might better use those signs which are given to us by nature, as Aratus also used. For he considered the changes of the air that happen from the risings and settings of the stars to be false, but he separated those that occur naturally and with some cause in his *Phenomena* treatise, at the very end of the whole volume. For he takes his prognostications from the rising and setting of the sun, and from the risings and settings of the moon, and from the halo that forms around the moon, and from the falling stars, and from brute animals; for the prognostications from these, occurring with some natural cause, have necessary effects. ^D Hence also Boethus the philosopher, in the fourth book of his exposition of Aratus, [discusses] physical causes, both of winds and [of other things].

(49) But how puerile was the mathematician’s hallucination! For what sort of reasoning is his, I ask you? He demonstrates that the Dog Star, when conjoined with the sun at the time it is commonly said to rise, contributes nothing to increasing the summer heats, from the fact that at that time the sun is furthest from it. He concludes this from the fact that at that time the sun occupies the summer tropic, while the Dog Star is situated in the winter tropic; wherefore, if its conjunction with the sun had any power to kindle the heats, that power would appear most strongly when the sun is situated in the winter tropic—that is, in the same circle as the Dog Star. Nothing is falser than this argument. Which would hold true if winter were summer, or if the Dog Star were situated in Capricorn itself. For at that time, it was located at approximately the 15th degree of Gemini. It was distant from the equinoctial by nearly 16 degrees, and from the tropic and the sun by nearly 40. But when the sun stood in the tropic of Capricorn, the interval between it and the Dog Star was more than a semicircle. What then was Geminus thinking when he wrote that the Dog Star is closer to the sun when the latter occupies the winter tropic than when it dwells in the summer one?

^A Migne’s Latin text: “imbrium exposuit, ex prædictis generibus præcognitiones ostendens. His signis et Aristoteles philosophus usus est, et Eudoxus, et plures alii astrologi.” The philosopher Boethus, in his fourth book of commentary on Aratus, has offered the natural causes for winds and rains, making his forecasts from the aforementioned types. The philosopher Aristotle also used these signs, as did Eudoxus and many other astrologers.

CHAPTER XV. On Evolution.

^A rest.

Such being the arrangement of the numbers, the mean motion of the moon of 13 degrees, 10 minutes, and 35 seconds has been discovered by the Chaldeans; and since the moon completes 717 revolutions in 19,756 days, if we wish to know in how many days the moon completes one revolution, we shall divide the multitude of days by the multitude of the revolutions. There are 27 days, and 33 first sexagesimals of one day, and 20 seconds. In so many days, therefore, the moon proceeds from its minimum motion to its minimum motion.

And since in every revolution ^B the times are equal, they took the fourth part of 27 days, 33 minutes, and 20 seconds, and there result 6 days, 53 minutes, and 20 seconds. In so many days, therefore, the moon proceeds from its minimum motion to its mean, and from its mean to its maximum; and again similarly from its maximum to its mean, and from its mean back to its minimum. For these four times are equal to one another.

And since, if there are three numbers exceeding one another by an equal amount, the extremes taken together are twice as large as the middle one; and in the motion of the moon there are three numbers exceeding one another by an equal amount—namely the minimum motion, the mean, and the maximum—if, therefore, ^C we add together the maximum motion and the minimum, they will be twice the mean motion. Now the mean motion was 13 degrees, 10 minutes, 35 seconds. They multiplied these twice, and there result 26 degrees, 21 minutes, 10 seconds. The maximum motion of the moon, therefore, and the minimum, added together precisely, are 26 degrees, 21 minutes, and 10 seconds. But the degrees taken from observation are not exactly the maximum and minimum motions of 26 degrees. What remains, therefore, are those sexagesimals which escaped the observation made by appearances and instruments, namely 21 first sexagesimals of one degree, and 10 seconds. These, therefore, must be added to both the minimum and maximum motion, so that these two motions compounded may make 26 degrees, 21 minutes, 10 seconds. ^D One must add this necessary appendix in such a way that the minimum motion is not brought to more than 12 degrees, nor the maximum to more than 16 degrees. We shall distribute them thus: Since the moon in 6 days, 53 minutes, and 20 seconds proceeds from the minimum motion to the mean, and from the mean to the maximum, and always uses an equal increment and decrement, one must find a number which, multiplying the fourth part of the time of revolution, will produce a certain number which, when added to the mean motion, gathers a certain number greater than 15 degrees but less than 16, and when subtracted from the mean motion, leaves a certain number greater than 11 degrees but less than 12. And the things added to the 15 degrees and to the 11 will be, in all, 21 first sexagesimals and 10 seconds. This is found to be done by the number of the first sexagesimals

for if these be multiplied by the fourth part of the restoration, namely by 6 days, 13', and 20", there are produced 2 degrees and 4' first sexagesimals. These ^A I added to the mean motion of 13°, 10', 55", and they become 15°, 14', 35". I subtracted from the mean motion these 2 degrees and 4', and there remained 11°, 6', 35". Found, therefore, is the minimum motion of the moon of 11°, 6', 11", 55"'; the mean motion of 13°, 10', 35"; the maximum motion of 15°, 11', 35"; and the daily increment of 18' first sexagesimals.

CHAPTER XVI.

The sun passes through Virgo in 30 days. On the 5th day, according to Eudoxus, a great wind blows, and it thunders. According to Calippus, the shoulders of Virgo rise, and the Etesian winds blow. ^A On the 10th day, according to Euctemon, Vindemiator appears; Arcturus also rises, and Sagitta sets in the morning. There is a storm at sea. According to Eudoxus, rain, thunder, and a great wind blow. On the 17th day, according to Calippus, the middle of Virgo rises and signifies, and the rising Arcturus is visible. On the 19th day, according to Eudoxus, Arcturus rises in the morning, and for the 7 following days, winds blow, generally with clear weather. As this period ends, a wind from the east arises. ^B On the 20th day, Arcturus is visible to Euctemon. It is the beginning of autumn, and Capra rises—a great star in Auriga—and then it signifies. There is a storm at sea. On the 24th day, according to Calippus, the ear of corn of Virgo rises.

The sun passes through Libra in 30 days. On the 1st day, according to Euctemon, it is the autumn equinox, and it signifies. According to Calippus, Aries begins to set. It is the autumn equinox. On the 3rd day, according to Euctemon, the vespertine Kids rise. A storm arises. On the 4th day, according to Eudoxus, Capra rises in the evening. On the 5th day, according to Euctemon, the Pleiades appear in the evening from the east. According to Calippus, the rising of Virgo ceases. ^C On the 6th day, according to Euctemon, Corona rises. There is a storm. On the 8th day, according to Eudoxus, the Pleiades rise. On the 10th day, according to Eudoxus... rises in the morning. On the 12th day, according to Eudoxus, Scorpius begins to set in the evening, and a storm arises, and a great wind blows. On the 17th day, according to Eudoxus, the whole of Scorpius sets in the evening; Capra sets entirely. According to Calippus, the Claws begin to rise; they signify. On the 19th day, according to Eudoxus, north and south winds blow. On the 22nd day, ^D according to Eudoxus, the Hyades rise in the evening. On the 28th day, according to Calippus, the tail of Taurus sets; it signifies. On the 29th day, according to Eudoxus, north and south winds blow. On the 30th day, according to Euctemon, there is a great storm at sea.

The sun passes through Scorpius in 30 days. On the 3rd day, according to Dositheus, there is a storm. On the 4th day, according to Democritus, the Pleiades set at early dawn; winter winds generally blow, as well as cold and frost. It is customary for a wind to blow. The trees especially begin to shed their leaves. According to Calippus, the forehead of Scorpius rises, with wind.

^A On the 5th, according to Euctemon, Arcturus sets in the evening, and great winds blow. On the 8th, according to Eudoxus, Arcturus sets at the end of the night in the morning, and it gives a sign; a wind blows. On the 9th, according to Calippus, the head of Taurus sets in the morning: rains. On the 10th, according to Euctemon, Lyra rises in the morning, and there is winter weather with rain. On the 12th, according to Eudoxus, Orion begins to rise in the evening. On the 13th, according to Democritus, Lyra rises together with the rising sun; and the air for the most part becomes wintry/tempestuous. On the 14th, according to Eudoxus: rain. On the 15th, according to Euctemon, the Pleiades set, and it gives a sign, and Orion begins to cause a tempest both in the middle of the month and at the end of it. ^B On the 16th, according to Calippus, the bright star in Scorpius rises, it gives a sign; and the Pleiades set visibly. On the 18th, according to Eudoxus, Scorpius begins to rise in the morning. On the 19th, according to Eudoxus, the Pleiades set in the morning; and Orion begins to set, and it is wintry/tempestuous. On the 21st, according to Eudoxus, Lyra rises in the morning. On the 27th, according to Euctemon, the Hyades set; and furthermore it rains. On the 28th, according to Calippus, the horns of Taurus set; rain. On the 29th, according to Eudoxus, the Hyades set, and there is a great tempest. The sun travels through Sagittarius in 29 days. On the 7th, according to Euctemon, the Dog-star sets, and it is winter-weather. According to Calippus, Sagittarius begins to rise, and Orion sets visibly. There is winter-weather. ^C On the 8th, according to Eudoxus, Orion sets in the morning. On the 10th, according to Euctemon, the sting of Scorpius rises. On the 12th, according to Eudoxus, the Dog-star sets in the morning, it is winter-weather. On the 14th, according to Eudoxus: rain. On the 15th, according to Euctemon, Aquila rises, the south wind blows. On the 16th, according to Democritus, Aquila rises together with the sun, and it is accustomed to give a sign of thunder and lightning, with water or wind, or both for the most part. According to Eudoxus, ^D the Dog-star rises in the evening, and according to Calippus the Gemini pass by, setting, with southerly weather. On the 19th, according to Euctemon and Eudoxus, it sets. On the 21st, according to Eudoxus, Scorpius rises in the morning, and it is winter-weather. On the 23rd, according to Eudoxus, the Goat sets in the morning. On the 26th, according to Eudoxus, Aquila rises in the morning. The sun travels through Capricorn in 29 days. On the 1st day, according to Euctemon, it signifies the winter solstice.

According to Calippus, Sagittarius ceases to rise; the winter solstices occur, and a storm happens. ^A On the 2nd day, according to Euctemon, the Dolphin rises, and a storm arises. On the 4th day, according to Eudoxus, the winter solstices occur, and a storm arises. On the 7th day, according to Euctemon, the Eagle sets in the evening, and a storm happens. On the 9th day, according to Eudoxus, the Corona sets at nightfall. On the 12th day, according to Democritus, the south wind blows, as it rises. On the 14th day, according to Euctemon, it is mid-winter. A strong winter south wind blows across the sea. On the 15th day, according to Calippus, Capricorn begins to rise, the south wind [blows]. On the 16th day, according to Euctemon, a winter south wind [blows] across the sea. On the 18th day, ^B Perseus sets in the evening after the sun, and the south wind blows. On the 27th day, according to Euctemon, the Dolphin sets in the evening. According to Calippus, Cancer ceases to set; there is a storm. The sun travels through Aquarius in 30 days. On the 2nd day, according to Calippus, Leo begins to set; there is rain. According to Democritus, there is winter. On the 4th day, according to Eudoxus, the Dolphin sets at nightfall. On the 11th day, according to Eudoxus, Lyra sets at nightfall. Rain occurs. On the 14th day, according to Eudoxus, it is clear; sometimes the zephyr also blows. On the 16th day, according to Democritus, the zephyr begins to blow, and it continues for 43 days from the solstices. ^C On the 17th day, according to Euctemon, it is time for the zephyr to blow. According to Calippus, the middle of Aquarius is rising; the zephyr blows. On the 25th day, according to Euctemon, it sets in the evening, and there is a very violent storm. The sun travels through Pisces in 30 days. On the 2nd day, it is time for the swallow to appear, and the *ornithiae*, or bird-winds, blow. According to Calippus, Leo ceases to set, and the swallow appears, [and] it signifies [this]. On the 4th day, according to Democritus, there are variable days which are called the halcyon days. According to Eudoxus, Arcturus rises at nightfall, and rain occurs, the swallow appears, and for the following 30 days the north winds blow, and especially those which are called *proornithiae*, or pre-bird-winds. ^D On the 12th day, according to Euctemon, Arcturus rises in the evening, and the Vindemiator becomes visible. Furthermore, a cold north wind blows. On the 14th day, according to Democritus, cold winds blow which are called *ornithiae*, for about nine days. According to Euctemon, the Horse sets in the morning: furthermore, a cold north wind blows. On the 17th day, according to Eudoxus, there is a storm, and a kite appears. According to Calippus, the southern part of Pisces rises, [and] the north wind ceases. On the 21st day, according to Eudoxus, the Corona rises at nightfall, [and] the *ornithiae* begin to blow. On the 22nd day, according to Euctemon, a kite appears, [and] the *ornithiae* blow until the equinox.

On the 29th day, according to Euctemon, the first stars of Scorpio set; a cold north wind blows. ^A On the 30th day, according to Callippus, the northern star of the Fish finishes setting; a kite appears, the north wind blows.

The sun passes through Aries in 31 days. On the 1st day, according to Callippus, the bond of the Fish rises. It is the spring equinox, and a fine drizzle occurs; there is a great storm, it portends. On the 3rd day, according to Callippus, Aries begins to rise; there is rain or snow. On the 6th day, according to Eudoxus, it is the equinox; rain occurs. On the 10th day, according to Euctemon, the Pleiades are hidden at nightfall. On the 13th day, according to Eudoxus, the Pleiades set at nightfall; and Orion begins to set at nightfall; rain occurs. According to Democritus, the Pleiades are hidden together with the rising sun and are invisible for 40 nights.

On the 21st day, according to Eudoxus, the Hyades set at nightfall. On the 23rd day, according to Euctemon, the Hyades are hidden, and hail occurs, and the west wind blows. According to Callippus, Libra begins to set, and in many places there is also hail. On the 27th day, according to Eudoxus, Lyra rises at nightfall.

The sun passes through Taurus in 32 days. On the 1st day, according to Eudoxus, Orion sets at nightfall; rain. According to Callippus, Aries finishes rising; rain, and in many places also hail. On the 2nd day, according to Euctemon, the Dog is hidden, and hail occurs. On the same day, Lyra rises according to Eudoxus. The Dog sets at nightfall, and rain occurs. According to Callippus, the tail of Taurus rises; it is humid. ^B On the 7th day, according to Eudoxus, rain occurs. On the 8th day, according to Euctemon, the Goat rises in the morning; clear weather; it rains with a southern wind. On the 9th day, according to Eudoxus, the Goat rises in the morning. On the 11th day, according to Eudoxus, Scorpio begins to set in the morning, and rain occurs. On the 13th day, according to Euctemon, the Pleiades rise; it is the beginning of summer, and it portends. According to Callippus, the head of Taurus rises; it portends.

On the 21st day, according to Eudoxus, the whole of Scorpio sets in the morning. On the 22nd day, according to Eudoxus, the Pleiades rise, and they portend. On the 25th day, according to Euctemon, Aquila sets at nightfall. On the 30th day, according to Euctemon, [it] rises at nightfall. On the 31st day, according to Euctemon, Aquila rises at nightfall. On the 32nd day, according to Euctemon, Arcturus sets in the morning; it portends. According to Callippus, Taurus finishes rising. According to Euctemon, the Hyades rise at nightfall, and they portend.

The sun passes through Gemini in 32 days. ^{C D} On the 2nd day, according to Callippus, Gemini begins to rise; it is humid. On the 5th day, according to Eudoxus, the Hyades rise in the morning. On the 7th day, according to Eudoxus, Aquila rises at nightfall. On the 10th day, according to Democritus, there is rain. On the 13th day, according to Eudoxus, Arcturus sets in the morning.

DIONYSIUS PETAVIUS’ JUDGMENT CONCERNING THE FOLLOWING SHORT TREATISE OF PTOLEMY.

The title was conceived in the manuscript as we have published it. However, it seems it should be read *On the Phases and Indications of the Fixed Stars*, or, as it is in Suidas, *On the Phase and Indications of the Fixed Stars*. Certain universal items deserve to be noted touching this book. The first is that one may inquire concerning its author: whether it is Ptolemy, or whether it is falsely attributed to him, just like that other work published in Latin only by Leonicus. For regarding that one, there is no need for hesitation in concluding that it is pseudepigraphical. But regarding our own, there are two points that arouse suspicion of fraud. The first is that the autumnal equinox does not agree with Ptolemy’s observation. For he ascribes the equinox to the 28th of the Actian month Thoth, that is, September 25th. Ptolemy, however, observed the same equinox in the year of Christ 139 on September 26th, at almost the 6th hour of the morning; one day later. Our *parapegma* (calendar) agrees with the true entry of the sun into Libra in the first year of the Julian calendar. But the consensus of both regarding the vernal equinox can be opposed to this. For Ptolemy observed the March equinox in the year of Christ 140 on the 22nd, at the 1st hour after midday, which is the 23rd of the Actian month Phamenoth, to which day our *parapegma* also refers: in which both differ from the Julian hinge. The summer solstice in ours—perhaps the fault of the scribes—falls [incorrectly], whereas Ptolemy observed it in that same year of Christ 140, on June 25th. Furthermore, the winter solstice is fixed in the *parapegma* on the 26th of Choiac, or December 22nd, which differs from the Julian solstice. Therefore, this former reasoning is not sufficiently suitable for us to reject this book from Ptolemy.

We can take the second argument from the fact that it does not compare the Julian months with the Egyptian, Augustan, and Actian (that is, fixed) months with sufficient exactitude, as if both had the same beginning and the same end. For example, he inscribes the month Thoth as September, and Paophi as October, even though a part of August occupies Thoth, and a part of September occupies Paophi. Yet not even from this can a firm enough conjecture be drawn against the inscription of this little book. For it is not necessary that the Roman months were added by Ptolemy himself, but by another who noted them according to the months to which the Egyptian ones corresponded for the most part: a practice we see done by others at various times, and nothing prevents them from having been described this way by Ptolemy himself, who could have compiled this calendar, as a *parapegma*, for the use of his own fellow citizens.

Suidas reports that Claudius Ptolemy wrote two books, *On the Apparent Rises and Indications of the Fixed Stars*. The one we are publishing here for the first time is one of these, while the other either does not exist, or the one circulated in Latin by Leonicus presents it, though not in its genuine form, but interpolated and stitched together like a patchwork quilt from various rags; or, in short, having begun to be concealed under the name of Ptolemy some centuries ago, Suidas took it for his genuine work. However the matter stands, ours is to be preferred far above it. For it is not a miscellaneous, tumultuous, and incoherent collection like that other one, but digested with reason and order; nor are the hinges anticipated in it, or placed on different days, as are the risings and settings of the stars, which Leonicus’s Ptolemy assigns to various days. Furthermore, the names of the authors whose individual *phases* or *indications* are described are commemorated in ours, which are omitted in the other. And without knowledge of the authors, and consequently of the places and times in which they flourished, there is no usefulness in these *parapegmata* and notations, which is exactly why our own is deemed exceptional.

There is added at the end a scholion, not very long, but which teaches us some things that it is particularly expedient to know for this science; things which I do not know if they are read elsewhere. I believe I have perceived, even from the style itself and the manner of speaking, that this scholion is none other than Ptolemy’s, because it is equal to and akin to what is seen in the work of the *Syntaxis*. Yet in the inscription of the scholion, which we have prefixed, the opposite seems to be said. But the negative particle has dropped out. It should be read: "What follows was usefully noted by none other than the author of the Hemerologium." From this scholion we have learned that not all those stars which are celebrated by authors were recorded in the Hemerologium, but only those of the first and second magnitude. Hence there is no mention of the Pleiades in it, nor of the Hyades, nor of the Vindemiator, nor others which:

*few indeed, and dim, yet famous,*

as Aratus sang of the Vergiliae. The scholion notes that thirty in total were described; fifteen of the first magnitude; and the same number of the second, which it also recounts one by one. Truly, by the fault of the scribes, as appears, only 14 stars of the first magnitude and 13 of the second are expressed, which we shall list here in alphabetical order.

STARS OF THE PTOLEMAIC HEMEROLOGIUM.

| First Magnitude | Second Magnitude | | :--- | :--- | | 1 Arcturus. | 1 Antares, or the Heart of Scorpio. | | 2 Canis. | 2 Lucida of Aquila. | | 3 Canobus. | 3 Following shoulder of Auriga. | | 4 Capella. | 4 Lucida of the Northern Claw. | | 5 The one in the fore-foot of Centaurus. | 5 Lucida of the Southern Claw. | | 6 The last of the River. | 6 Lucida of the Northern Crown. | | 7 Lucida of the Hyades. | 7 The common one of Equus and Andromeda. | | 8 Tail of Leo. | 8 Head of the preceding Gemini. | | 9 Lucida of Lyra. | 9 Lucida of Hydra. | | 10 Following shoulder of Orion. | 10 Preceding shoulder of Orion. | | 11 The common one of Orion and the River. | 11 Middle of Orion’s belt. | | 12 The southern Fish. | 12 Lucida of Perseus. | | 13 Procyon. | 13 Knee of Sagittarius. | | 14 Spica of Virgo. | |

41 One of the first magnitude is missing, which is the [λμπρὸς τοῦ Ὑδροχόου] or the tip of the Water, which is in the mouth of the Piscis Notius, of the first magnitude according to Ptolemy. Also two of the second magnitude; namely, the bright star of Cygnus, and the head of the following one of the Gemini, which three stars are commemorated in the Hemerologium. Mention is also made of the Piscis Boreius on Phamenoth 20, and of the one which is in the knee on Payni 18; but perhaps erroneously, for the scholion enumerates only thirty.

In this catalog some are omitted which are celebrated among authors; others are referred to the first class, which more recent writers relegate to the second; and conversely, some are placed in the second which are numbered among the first by Tycho. Procyon is a star of the second magnitude in the Tychonic table, but Ptolemy, both in the Asterisms and here, makes it of the first magnitude. Antares, however, being of the second magnitude in Ptolemy both ways, is constituted as of the first by Tycho. Thus the bright star of Hydra, which they call the Heart of Hydra, is first for Tycho, but second for Ptolemy.

Now since there are four phases (φάσεις) of the stars: the heliacal rising, the acronychal rising, the heliacal setting, and the matutine setting (for the other two, the cosmic rising and the acronychal setting, are not phases, nor are the stars visible), if four times thirty are taken, there will be 120 phases in any one parallel. But Ptolemy warns that he compiled his Hemerologium from those authors and parapegmata who observed the risings and settings of the stars under five parallels; which parallels he designates from the one that exhibits a day of precisely 14 hours to the one that gives a maximum day of 15 hours. Therefore, these parallels are: the first, which passes through lower Egypt, and is counted ninth in order by Ptolemy (book of the *Magna Syntaxis*, chap. 6). The second is the tenth, which passes through the middle of Phoenicia, where the day is 14 1/4 hours. The third is the eleventh, passing through Rhodes, where the longest day is 14 1/2 hours. The fourth is the twelfth, passing through Smyrna, extending the day to 14 3/4 hours. The fifth is the parallel thirteenth through the Hellespont, of 15 hours. He attributes the first parallel to his own countrymen, the Egyptians; the third to Dositheus and Philippus; the fifth to Democritus, Caesar, and Hipparchus. The second he explicitly excepts from no one. The fourth likewise is expressly ascribed to no one; but whatever is from 14 1/2 hours to 15, he attributes to Calippus, Eudoxus, Meton, Euctemon, Metrodorus, and Conon.

Moreover, if in each of the parallels thirty-four stars manifest their phases, there will be, multiplying thirty-four by five, 170. But Ptolemy notes that Canopus is seen rising and setting only in the first three parallels: wherefore sixteen phases are to be removed, which they would make in the two remaining parallels. To these, the last of the River is not seen in the fifth parallel. Therefore, four phases are to be removed, that is, twenty in total. Whence only 480 phases are contained in this book. So the scholion.

There is one thing which we could not grasp by any conjecture in this Hemerologium, namely, what those hours mean, which he notes on almost every day. For they are almost always 14, or 14 1/2, or 14 or 15, both in the rising and in the setting of the stars. About which I would gladly be instructed.

PTOLEMY: PHASES OF THE FIXED STARS AND SIGNIFICANT SIGNS.

7. To Metrodorus, intemperate air and atmospheric disorder. To Eudoxus, rain, thunder, and shifting wind. 8. To the Egyptians, rainy weather, winter at sea, or south wind. ^A 9. Hour 14, the bright star of the Swan sets in the morning. To the Egyptians, Zephyrus or Corus. 10. Hour 14, the bright star of Perseus rises in the evening. To Philippus, intemperate air. To Dositheus, stormy weather. 11. To the Egyptians, stormy weather. 12. Hour 15, the bright star of the southern Chelae is hidden. 13. To Dositheus, intemperate air. 14. Hour 14, the so-called Canopus rises. To Caesar, the north winds cease blowing. 15. To Eudoxus, southern wind… 16. …to Calippus, and Canopus marks a change in weather. 17. Hour 14, the bright star of the Swan sets in the morning, and the bright star of the southern Chelae is hidden; and the last star of the River sets in the morning to Metrodorus. It marks a change in weather to Democritus. ^B 18. Hour 15, the star at the knee of Sagittarius is hidden; to the Egyptians, it marks the beginning of autumn. To Dositheus, southerly wind. 19. Hour 15, the bright star of the southern Fish rises in the evening. To Hipparchus, rainy weather. 20. Rainy weather at sea to Metrodorus. 21. The bright star of the southern Chelae is hidden; and [the star] on the following shoulder of Auriga rises in the evening. To the Egyptians, Zephyrus or Lips. 22. Hour 14, the so-called Antares is hidden. To the Egyptians, Zephyrus or Corus. To Eudoxus, ^C humid sky and drizzling rain. 23. Hour 14, Capella rises in the evening. Hour 15, Arcturus rises in the morning. To the Egyptians, dewy sky; and wind to Calippus, and rainy weather to Metrodorus. 24. Hour 14, the common star of the Horse and Andromeda sets in the morning. 25. Hour 13, the bright star of the southern Chelae is hidden. Hour 15, the bright star of the Swan sets in the morning. To the Egyptians, Zephyrus or south wind, and rain during the day. 26. Hour 15, Arcturus rises in the morning. To Eudoxus, rain; to Hipparchus, Favonius or south wind. 27. Hour 14, the common star of the Horse and Andromeda sets in the morning; the last star of the River sets in the morning. 28. Autumnal equinox; and it marks a change in weather to both the Egyptians and Eudoxus. ^D 29. Hour 14, [the star] called Antares is hidden. Arcturus rises in the morning; to Euctemon, it marks a change in weather. To Democritus, rain. 30. The common star of the Horse and Andromeda sets in the morning. It marks a change in weather to Euctemon, Philippus, and Conon.

Paophi, that is, October. 1. To the Egyptians, Zephyrus or south wind. To Hipparchus, marks a change in weather. 2. Hour 15, the bright star of the northern Chelae is hidden. It marks a change in weather to Eudoxus and Euctemon. To Hipparchus, south wind or Zephyrus. 3. Arcturus rises in the morning. Hour 15 and a half, the bright star of the Swan sets in the morning.

^A 4. Splendid boreal Claw sets; winter weather for Euctemon; and to Philippus, rain. 5. Hour 15, the common [star] of Pegasus and Andromeda sets in the morning. To Eudoxus, rain. To Euctemon, it signifies [change]. To Metrodorus, rain. 6. Hour 13, Arcturus rises in the morning; the star at the end of the River sets in the morning; and the bright star of the boreal Claw sets. Antares is hidden; the bright star of the boreal Crown rises in the morning. To the Egyptians and Caesar, rain. 7. Spica rises; and the bright boreal Claw sets. The one in the following shoulder of the Charioteer rises in the evening. 8. Spica rising causes winter weather for Democritus. Time for sowing. 9. Spica rises. For the Egyptians, the north wind blows. 10. The bright star of the boreal Crown rises in the morning. To Hipparchus, south wind. 11. Hour 15, the star at the knee sets in the morning. 12. The one called Antares is hidden. For the Egyptians, the Zephyrus or the Africus blows. To Eudoxus, it signifies [change]. To Hipparchus, the subsolanus. 17. Hour 15, Antares is hidden. For the Egyptians, the north wind and the Africus. 18. Arcturus sets in the evening. To Eudoxus, a change of winds and thunder. 21. The one called Capra rises in the evening, and the bright star of the boreal Crown rises in the morning. For the Egyptians, the Zephyrus or the south wind [brings] rain during the day. To Dositheus, it signifies [change]. 22. Hour 14, the one called Capra rises in the evening. 23. The bright star of the boreal Crown rises in the morning. For the Egyptians, the Zephyrus or the south wind [brings] rain during the day. To Dositheus, it signifies [change]. 24. Hour 14, the one called Canopus sets in the morning. 25. For the Egyptians, inconstant winds. 26. Hour 14, Arcturus sets in the evening. To Eudoxus, it signifies [change]. 27. Hour 13, the bright star of the boreal Crown rises in the morning. Hour 14, the one at the knee of the Archer is hidden. For the Egyptians and to Calippus, it signifies [change]. 28. … To Metrodorus it signifies [change]. For Euctemon and Calippus, a mixture in the air, and winter weather at sea. 30. Hour 14, the one in the following shoulder of the Charioteer rises in the evening. For the Egyptians, very stormy weather.

Month of November, Athyr

^A 4. Hour 14, the bright star of the boreal Claw rises, and Arcturus sets in the morning. For the Egyptians, a south or south-west wind. For Calippus and Euctemon, very strong winds. For Caesar or Metrodorus, a stormy wind.

5. Hour 14, the bright star of the boreal Claw rises, and the one at the knee of Sagittarius is hidden. For Conon and Eudoxus, atmospheric turbulence.

6. Atmospheric turbulence; north or cold south wind.

7. Hour 14, the bright star of the Hyades rises in the evening. For the Egyptians, a bright south wind. For Meton, a west wind, atmospheric turbulence, and rain.

8. Hour 13, the bright star of the Hyades rises in the evening. For Calippus, it portends rain.

9. Hour 15, the common star of the River and the foot of Orion rises. For the Egyptians, rain.

10. Hour 14, the star called Canopus sets in the morning. For the Egyptians, a south or west wind. For Dositheus, it is stormy.

11. Hour 15, the bright star of the Lyre rises in the morning. For Meton, rain and squalls. For Hipparchus, a north-west wind.

12. Hour 15, Arcturus sets in the evening, and the common star of the River and the foot of Orion sets in the morning.

13. Hour 13, the star at the knee of Sagittarius is hidden. For the Egyptians, a south or east wind drizzles rain throughout the day. For Metrodorus, winter weather and squalls.

14. Hour 11, the common star of the River and the foot of Orion sets in the morning. For Philippus and Euctemon, rain and storm.

15. Hour 13, the bright star of Perseus sets; and the bright star of the northern Crown sets in the evening; and the bright star of the Hyades sets in the morning. For the Egyptians and Hipparchus, it is the beginning of winter. For Conon, it portends [weather].

16. Hour 16, the bright star of the Hyades sets in the morning. It is stormy.

17. The beginning of winter, and it portends [weather] for Eudoxus.

18. The star on the head of the forward Twin rises in the evening. For Eudoxus, the beginning of winter, and it portends [weather]. For Democritus, a storm by land and by sea.

19. Hour 14, the bright star of the Lyre rises in the morning. For the Egyptians, a south or east wind. For Caesar, it is stormy.

20. Hour 13, the common star of the River and the foot of Orion sets in the morning; and the bright star of Perseus sets in the morning; and the one on the forward shoulder of Orion sets; and the middle star of the belt of Orion sets in the morning. For Caesar, it is stormy.

^D 21. Hour 15, the one on the forward shoulder of Orion sets in the morning, and the middle one of his belt sets in the morning. For the Egyptians, a north wind throughout the day and night. For Eudoxus, rain.

22. Hour 14, the one on the forward shoulder of Orion sets in the morning.

23. Hour 13, the star called Canopus sets in the morning. The bright star of the northern Crown sets in the evening; and the one on the forward shoulder of Orion; and the one on the head of the forward Twin rises in the evening. For Eudoxus, wintry conditions.

^A

24. Hour 13: the one on the forward right arm of the Centaur rises. The middle of the belt of Orion sets in the morning. For Conon, it sets in the morning. For the Egyptians, wintry state of the sky. For Eudoxus, a cold north wind.

25. The one on the forward shoulder of Orion sets in the morning, and the so-called Antares rises. The bright one of Perseus sets in the morning for Euctemon. For Dositheus, it is wintry, with rain.

26. Hour 13 1/2: the one on the forward shoulder of Orion rises in the evening. The bright one of the Lyre rises in the morning. Antares rises. For Eudoxus, it signifies something violent.

27. Antares rises. The Dog sets in the morning. The bright one of the Swan rises in the morning; and the one on the following shoulder of Orion sets in the morning. For the Egyptians and Hipparchus, a frequent south wind. For Eudoxus and Conon, it is wintry. ^B

28. The one on the forward shoulder of Orion rises in the evening, and the one on the head of the forward Twin rises in the evening. Hour 15 1/2: the middle of the belt of Orion sets in the morning. The so-called Antares rises. For the Egyptians, it drizzles.

29. Hour 13 1/2: the middle of the belt of Orion sets in the morning. Hour 15: the so-called Antares rises.

30. The middle of the belt of Orion sets in the morning at hour 14, and the one on the forward shoulder of Orion rises in the evening. Hour 15 1/2: the one on the head of the following Twin rises in the evening.

Month of Choiak, December.

1. Hour 14: the Dog sets. Hour 15: the bright one of Perseus sets in the morning. For the Egyptians, south wind and rain. For Eudoxus, inclemency of the air. For Dositheus, it signifies weather. For Democritus, the sky is turbulent, and the sea likewise for the most part. ^C

2. Hour 13: the one on the following shoulder of Orion rises in the evening. Hour 13 1/2: the common point of the River and the foot of Orion rises in the evening. Hour 14: the one on the head of the forward Twin rises in the evening. Hour 13 1/2: the one on the following shoulder of Orion sets in the morning. Hour 14: the bright one of the northern Crown sets in the evening.

3. Hour 14: the one on the forward shoulder of the Twins rises in the morning.

4. Hour 15: the bright one of the Lyre rises in the morning, and the one on the following shoulder of Orion rises in the evening; and the middle of the belt of Orion rises in the evening; and the one on the head of the following Twin rises in the evening. For the Egyptians, a west or south wind through the day. For Conon, it is wintry. ^D

5. The so-called Goat sets in the morning; and the one on the head of the forward Twin rises in the evening. The Dog sets in the morning. The one on the head of the forward Twin rises in the evening. For Caesar, Euctemon, and Calippus, it is wintry.

6. Hour 14 1/2: the one on the forward claw of the Centaur rises; the one on the following shoulder of Orion rises. For Metrodorus, wintry state of the sky. For Euctemon and Calippus, disorder of the winds.

7. Hour 14 1/2: the common point of the River and the foot of Orion

rises in the evening. That which is in the head of the preceding Gemini rises in the evening. The middle of Orion’s belt rises. For the Egyptians, it drizzles and is wintry. ^A

8. Hour 14 1/2: that which is in the following shoulder of Orion rises in the evening. For the Egyptians, it drizzles. For Eudoxus, it is wintry.

9. Hour 13 1/2: the Dog sets in the morning. The star called the Goat sets in the morning. And the last of the River rises in the evening. For the Egyptians, and for Dositheus, and for Democritus, it is a sign.

10. Hour 15 1/2: the bright star of the Northern Crown sets in the evening. And the middle of Orion’s belt rises in the evening. For the Egyptians, the southwest wind or the south wind. For Eudoxus, wintry air.

11. Hour 15: that which is in the head of the following Gemini rises in the evening. For Hipparchus, a strong north wind. For Eudoxus, rain.

12. Hour 14: the common point of the River and the foot of Orion rises in the evening. ^B

13. Hour 14: that which is in the following shoulder of the Charioteer sets in the morning; the middle of Orion’s belt rises in the evening. For Caesar, wintry air, rain.

14. Hour 14: the one called the Goat sets in the morning. For Metrodorus, wintry state of the sky. For Democritus, thunder, lightning, water, wind.

15. For the Egyptians, the star known as the Worker is cold, or south wind, and rain. For Calippus, south wind, and it indicates wintry air.

16. Hour 14 1/2: the bright star of the Bird ^C rises in the morning. The common point of the River and the foot of Orion rises in the evening. For the Egyptians, it is wintry.

17. For Hipparchus, south wind and much rain.

18. Hour 14: that which is in the following shoulder of the Charioteer sets in the morning. For the Egyptians, rain with winds; it is winter.

19. Hour 15: the one called the Goat sets in the morning. The bright star of the Northern Crown sets in the evening. For the Egyptians, cold north wind or south wind; rain.

20. Hour 15: the Dog-Star sets in the morning. For Caesar, it is wintry. ^D

21. Hour 15: the common point of the River and the foot of Orion rises in the evening.

22. Hour 15: the Dog-Star sets in the morning. For Hipparchus, south wind.

23. Hour 14: that which is in the following shoulder of the Charioteer sets in the morning; and that which is in the right forward forearm of the Centaur rises. The bright star of the Eagle rises in the morning for the Egyptians. For Dositheus, southwest wind or south wind.

24. Hour 14: the Dog-Star sets in the morning; and the last of the River rises in the evening. For Eudoxus, it is wintry.

25. Hour 13: the Dog-Star rises in the evening, and the Dog-Star sets in the morning. The bright star of the Eagle rises in the morning. It is a sign for the Egyptians.

26. Winter solstice. Hour 13: the Dog-Star sets in the morning; the Dog rises in the evening. The Goat sets in the morning.

^A 27. Hour 13: the bright star of Aquila sets; Procyon rises in the evening. 28. That which is at the following shoulder of Auriga sets in the morning. The bright star of the Southern Fish sets. There is winter for the Egyptians. It is a sign for Meton. Rain. 29. Procyon rises in the evening. It is a sign for the Egyptians and Meton. Intemperies. 30. Hour 14: the bright star of Aquila sets in the evening. For the Egyptians: Africus, and atmospheric intemperies.

January, or Tybi

1. Hour 14: the Dog rises in the evening. Procyon rises in the evening. For Democritus, a tempest is signaled. 2. That which is on the head of the leading Twin sets in the morning. For Dositheus, there is winter. 3. The bright star of Aquila rises. Procyon rises in the evening. It is a sign for Philemon. 4. Hour 13: the bright star of Cygnus rises in the morning. That which is on the head of the following Twin sets in the morning. The bright star of Aquila sets in the evening. The bright star of the Southern Fish sets. For the Egyptians, there is a tempest at sea. For Euctemon, a tempest arises at the appointed time. 5. Hour 14: that which is on the head of the leading Twin sets in the morning. The Dog sets in the evening. ^B 7. Hour 15: the bright star of Aquila sets in the evening. It has a sign for Dositheus. 8. Hour 14: that which is on the head of the leading Twin sets in the morning, and the bright star of the Southern Fish sets. For the Egyptians: thick air. 9. Hour 14: the bright star of Lyra sets in the evening; the bright star of Aquila sets in the evening. It is a sign for the Egyptians. For Democritus: for the most part, a South wind. 10. The Dog rises in the evening at the 10th hour. 11. Hour 15: that which is on the head of the leading Twin sets in the morning. 12. Hour 14: that which is at the knee of Sagittarius rises. For Hipparchus and Eudoxus, there is winter. 13. Hour 14: the bright star of the Southern Fish sets. Hour 15: the outermost star of the River rises in the evening. For the Egyptians: South or West wind; there is winter both on land and at sea. 14. Hour 15: that which is on the head of the following Twin sets. ^C The bright star of Aquarius sets in the morning. The Dog rises in the evening. For the Egyptians: a strong South wind and rain. 15. A great South wind, and thunder and drizzle are signaled at sea. 16. Hour 15: the bright star of Aquarius sets in the morning; and that which is on the head of the leading Twin sets in the morning. For Eudoxus: a South wind is signaled; instability of the winds. 17. Hour 13 [14]: the bright star of the Southern Fish sets. 18. Hour 14: the bright star of Lyra sets in the evening. That which is at the knee of Sagittarius sets in the evening. ^D

19. The bright star of Aquarius sets in the morning. Hipparchus: south or north (wind) makes a storm. ^A 20. For the Egyptians: wintry air. 21. The bright star of Aquarius sets in the morning. Hour 15: that which is at the heart of Leo rises in the evening. Hipparchus: the subsolanus (east wind) blows. 22. That which is at the heart of Leo rises in the evening. Caesar: a violent wind. 23. Hour 13: the bright star of Aquarius... Metrodorus: unsettled rain. 24. Hour 14: the bright star of Aquarius rises in the evening. For the Egyptians: it marks a change. 25. Hour 14: the bright star of Lyra sets in the evening. For the Egyptians: it marks a change. 26. The bright star of Aquarius rises in the evening. For the Egyptians: mid-winter. ^B 27. For the Egyptians: it signifies eurus (southeast wind) or auster (south wind). 28. The bright star of Aquarius rises in the evening. For the Egyptians: rain. 29. Democritus: a storm. 30. Hipparchus: the subsolanus.

February, Mechir. 1. That which is at the knee of Sagittarius rises. Eudoxus: rain. 2. For the Egyptians: a great storm. 3. Africus (southwest wind) or auster (south wind) is stormy. 4. Hour 14 1/2: the bright star of the Swan (Cygnus) sets in the evening. 5. Hour 15: the bright star of Lyra sets in the evening. Hipparchus: south wind or argestes (northwest wind). ^C 6. Hour 13 1/2: that which is at the heart of Leo sets in the morning. 7. Hour 13 1/2: the star called Canopus rises in the evening. 8. Hour 15 1/2: that which is at the tail of Leo rises in the evening. 9. Hour 15: that which is at the knee of Sagittarius rises in the evening. Eudoxus: rain. That which is at the heart of Leo sets in the morning. Hour 12: that which is at the tail of Leo rises in the evening. For the Egyptians: zephyrus (west wind) or auster, interspersed with hail. 10. Hour 14: that which is at the heart of Leo sets in the morning. Eudoxus: clear sky, sometimes also zephyrus. ^D 11. Hour 14: that which is at the tail of Leo rises in the evening. Hour 15: that which is at the heart of Leo sets in the morning. For the Egyptians: a wintry condition, and an intemperate, rainy state of the winds. Dositheus: clear sky and zephyrus. 12. Hour 14: the bright star of the Swan sets in the evening. 13. Hour 15: the end of the River (Eridanus) is hidden. The bright star of Perseus rises in the morning. The bright star of Lyra sets in the evening. For the Egyptians: a windy state. Caesar: rain. Democritus: zephyrus begins to blow. 14. Hour 13: that which is at the tail of Leo rises in the evening. For the Egyptians and Eudoxus: the beginning of spring. Sometimes it is wintry.

^A 15. For the Egyptians and Eudoxus, rain. For Hipparchus, Calippus, and Democritus, the favonius begins to blow. 16. For Caesar and Metrodorus, the beginning of spring. Favonius begins to blow. 17. For the Egyptians and Eudoxus, favonius. For Calippus and Metrodorus, it is wintry. 18. For the Egyptians, subsolanus. For Hipparchus, boreas. 19. Hour 14: that which is at the front right foot of the Centaur sets in the morning. 20. Hour 15: the common star of Equus and Andromeda rises in the morning. 21. Hour 14: the bright star of Cygnus sets in the evening. For the Egyptians, the winds are shifting. For Hipparchus, the south wind blows. For Euctemon, Philippus, and Dositheus, it is wintry. 22. For the Egyptians, instability of winds and rain. 23. Hour 14 1/2: the star called Canopus rises in the evening. 24. For the Egyptians, either the south wind or the favonius brings winter weather; rain. 25. Hour 14 1/2: the last star of Eridanus is obscured. The common star of Equus and Andromeda rises in the morning. For Hipparchus, a cold north wind blows. 26. For the Egyptians, instability of winds. 28. For Hipparchus and Euctemon, the "bird winds," ^B that is, the cold winds, begin to blow. It is time for the swallow to appear. 29. Hour 13 1/2: the common star of Equus and Andromeda is obscured. And for Calippus, at hour 15, the bright star of Cygnus sets in the evening. For the Egyptians, Philippus, and Calippus, the swallow appears, and the air is troubled by the winds. Cold north winds begin to blow. For Eudoxus, rain, the swallow, and the north winds that are called "bird winds" blow. 30. For the Egyptians, the "bird" north winds between the northwest and north. ^C For Hipparchus, cold north winds. For Metrodorus, the swallow is seen. It signifies for Democritus. These are the variable days called the Alcyonids.

Month of March, Phamenoth.

1. Hour 14: the common star of Equus and Andromeda rises. Hour 15: Arcturus rises in the evening. For Caesar and Dositheus, it is wintry. 2. The common star of Equus and Andromeda is obscured. 3. Hour 15: the bright star of Perseus rises. 4. Hour 14: the common star of Equus and Andromeda sets in the evening. 5. Hour 12: the common star of Equus and Andromeda rises. Hour 15: Arcturus rises in the evening. North or south wind, cold. 6. The last star of Eridanus is obscured. ^D For the Egyptians, an africus, or south wind, or hail. For Hipparchus, a cold north wind. 7. Hour 15: the common star of Equus and Andromeda sets in the evening. The bright star of Cygnus sets in the evening. 8. Hour 14: Arcturus rises in the evening. For Euctemon, a cold north wind blows. 9. Hour 15: the bright star of the Northern Crown sets in the evening.

^A The common star of Horse and Andromeda sets in the evening. For the Egyptians, it is winter. For Caesar, the swallow-winds blow for ten days. 10. Hour 12 1/2: the common star of Horse and Andromeda rises. 11. Hour 12 1/2: the bright star of the Southern Fish rises. And the one in the right front frog [hoof/muscle] of the Centaur rises in the morning. For the Egyptians, turbulent weather [prevails]. For Democritus, cold "bird-winds" [ornithiæ] for five days. 12. Hour 14: Arcturus rises in the evening. For Eudoxus, the swallow and the kite appear, and it signifies [change]. For Metrodorus and Philippus, a cold north wind blows. For Hipparchus, the beginning of spring. 13. Hour 13: the one on the tail of the Lion... For the Egyptians, it drizzles. For Metrodorus and Euctemon, a north wind blows. For Dositheus, the kite begins to be seen. For Hipparchus, much south wind. ^B 14. Hour 15 1/2: the bright star of the Northern Crown rises in the evening. For the Egyptians and Calippus, a north wind blows. 15. Arcturus rises in the evening. For the Egyptians and Calippus, a cold north wind blows. 16. Hour 13 1/2: Arcturus rises in the evening; and the last of the River is hidden. For Calippus, a north wind blows. 17. Hour 13 1/2: Spica rises in the evening. For the Egyptians, windy weather. For Euctemon and Philippus, the bird-winds begin to blow; and it is the time for the kites to appear. 18. Hour 14 1/2: the one on the tail of the Lion sets in the morning. For the Egyptians, a west or south wind blows. For Euctemon, a cold north wind. For Hipparchus, north wind, or Argestes. ^C 19. For the Egyptians and Euctemon, a cold north wind. 20. Hour 14: the bright star of the Northern Fish rises. Hour 14 1/2: the bright star of the Northern Crown rises in the evening. 21. Hour 14: the bright star of Perseus rises. For Philippus, a north wind blows, and a kite appears. 22. For the Egyptians and Democritus, it signifies [change]. Cold winds. 23. For the Egyptians, a cold wind for ten days. 24. For Caesar, a kite appears. A north wind blows. 25. Hour 14: the one on the tail of the Lion sets in the morning. For Eudoxus, a kite appears, and a north wind blows. ^D 26. Vernal equinox, and the bright star of the Northern Crown rises in the evening. 27. For Caesar, a north wind blows. For Hipparchus, rain. 28. For the Egyptians, thunder signifies [change], and rain. 29. Hour 15 1/2: the star called the Goat rises in the morning. For the Egyptians and Conon and Meton, it signifies [change]. For Eudoxus, a north wind. 30. Hour 13 1/2: Spica sets in the morning. For the Egyptians, a south wind blows. For Calippus, rain or snow. Month of April, or Pharmuthi. 1. Hour 14: Spica sets in the morning. For Meton, rain. For Euctemon and Democritus, it signifies [change].

^A 2. Hour 13: The bright star of the Northern Crown rises in the evening. Hour 14: Spica sets in the morning; and the one called Canopus is hidden. Hour 15: The one in the tail of Leo sets in the morning. For Dositheus and Calippus, rain. 3. Hour 14 1/2: The bright star of Perseus rises in the morning. 4. Hour 14 1/2: The bright star of the Southern Fish rises. 5. Hour 15 1/2: Spica sets in the morning. 6. Hour 15 1/2: The bright star of the Southern Claw rises in the evening. For Eudoxus, it signifies rain. 7. Hour 13 1/2: The bright star of the Southern Claw rises in the evening. 8. The bright star of the Northern Claw rises in the evening. For the Egyptians and Conon, it signifies [change]. For Eudoxus, rain. 9. Hour 14 1/2: The bright star of the Northern Claw rises in the evening. For the Egyptians and Conon, west wind or south wind, and hail. 10. Hour 14 1/2: The bright star of the Northern Claw rises in the evening. For Hipparchus, south wind and whirlwinds. ^B 11. Hour 14: The bright star of the Northern Claw rises in the evening. For Hipparchus and Dositheus, it signifies [change]. 12. Hour 13 1/2: The one in the tail of Leo sets in the morning. 13. For the Egyptians, south wind or southwest wind. For Eudoxus, rain. 14. Hour 13 1/2: The bright star of Perseus rises in the morning. For the Egyptians, turbulence of winds. For Hipparchus, rain. 15. For the Egyptians, instability and rain. 16. For Eudoxus, intemperance of the air and rain. 17. Hour 14: The common star of the River and the foot of Orion is hidden. 18. Hour 15: The one called Capella rises in the morning; and the bright star of the Southern Fish rises. For Dositheus and Caesar, rain. 19. Hour 15 1/2: The bright star of the Lyre rises in the evening. For the Egyptians, leuconotus [south-southeast wind], thunder, and drizzling rain. 20. Hour 14 1/2: The one called Canopus is hidden. For the Egyptians, intemperance of winds. For Eudoxus, rains and hail. 21. Hour 15 1/2: The common [star] of the River and the foot of Orion is hidden, and the bright star of the Hyades is hidden. For Metrodorus, hail. For Euctemon and Philippus, west wind. ^{C D} 22. The bright star of Perseus sets in the evening. For the Egyptians and Conon, hail and west wind. For Caesar and Eudoxus, rains. 23. Hour 15: The bright star of the Hyades is hidden. For the Egyptians, windy drizzle. 24. Hour 14 1/2: The bright star of the Hyades is hidden. And the common [star] of the River and the foot of Orion is hidden. Hour 15 1/2: The one with the belt of Orion is hidden. 25. For the Egyptians, southwest wind or south wind. Intemperance of the air. 26. Hour 14 1/2: The bright star of Perseus sets in the evening. Hour 14 1/2: The bright star of the Hyades is hidden. And the bright star of the Swan rises in the evening, and

^A in the leading shoulder of Orion. The South wind or the North wind is cold. 27. Hour 14 1/2: The bright star of the Hyades sets in the morning. Hour 15: The star with the belt of Orion is hidden. For the Egyptians and Caesar, it is stormy. 28. Hour 14 1/2: The common star of the River and the foot of Orion is hidden. The bright star of the Lyre rises in the evening. For the Egyptians, the South-West or the South wind; rain. 29. Hour 14 1/2: The bright star of the southern Claw sets in the morning. Hour 15: The star in the leading shoulder of Orion is hidden. For the Egyptians, the South-West or the South wind; rain. For Metrodorus, hail. 30. For the Egyptians, for Eudoxus, drizzling rain.

May, or Pachon

1. Hour 14 1/2: The bright star of Perseus rises in the evening. Hour 14 1/2: The star in the belt of Orion is hidden; and the bright star of the southern Claw sets in the morning. For the Egyptians, the North-West or the West wind; rain. For Euctemon, hail. 2. Hour 14: The star called the Goat rises in the morning; and the star in the following shoulder of Orion is hidden. For the Egyptians, a windy condition. For Calippus, rainy days. 3. Hour 13: The common star of the River and the foot of Orion is hidden. The star called Antares rises in the evening. Hour 15: The Dog is hidden. For the Egyptians, wind. For Eudoxus, rain. 4. Hour 14: The star in the leading shoulder of Orion, and the one with the belt, are hidden; and Antares rises in the evening. Hour 15: For the Egyptians, a calm; the South wind. For Caesar, it is stormy. 5. Hour 13 1/2: The star called Canopus is hidden. Hour 15 1/2: The bright star of the southern Claw sets in the morning. For the Egyptians, it is a sign. For Philippus, a calm or the South wind. Drizzling rain. 6. Hour 13 1/2: The star in the anterior right muscle of the Centaur rises in the evening. Hour 15: The bright star of Perseus sets in the evening; the star in the following shoulder of the Charioteer rises in the morning; and the star in the following shoulder of Orion is hidden. For the Egyptians, drizzling rain. 7. Hour 13: The star in the following shoulder of Orion is hidden; and the star with the belt is hidden; and the Dog is hidden. 8. Hour 14: The bright star of the Lyre rises in the evening; and the bright star of the Swan rises in the evening; and the star in the following shoulder of Orion is hidden. The bright star of the southern Claw sets in the morning. For the Egyptians, a North-West wind and drizzling rain. 9. Hour 14: The Goat rises in the morning. The bright star of the southern Fish rises. For the Egyptians, drizzling rain. 10. Hour 13 1/2: The bright star of the southern Claw sets in the morning. For Dositheus, rain. 11. Hour 13: The star in the following shoulder of Orion is hidden. For the Egyptians, a windy condition. 12. Hour 13: The Goat rises in the morning. The Dog is hidden. The bright star of Perseus sets. For the Egyptians, a windy day. 13. For the Egyptians, the West wind or the North-West wind; rain.

^A 14. Hour 14 1/2: the star in the succeeding shoulder of Orion is obscured. The bright star of the northern Claw sets in the morning. For the Egyptians, rain. 15. Hour 13 1/2: Arcturus sets in the morning. For the Egyptians, rain. Start of summer. For Euctemon, wind. 16. Hour 13: Arcturus sets in the morning; the star in the succeeding shoulder of Orion is obscured. For Dositheus it signifies a change. 17. Hour 13 1/2: the Goat sets in the evening. The bright star of the Lyre rises in the evening. Hour 14 1/2: the Dog is hidden; and the star on the right front foot of the Centaur rises in the evening. For the Egyptians, the West wind or the North-West wind. For Caesar, rain. For Metrodorus, Hipparchus, and Eudoxus, it signifies a change. 18. Hour 13 1/2: Antares sets in the morning. ^B Hour 14: the bright star of the Swan rises in the evening; the star in the succeeding shoulder of the Charioteer rises in the morning. For the Egyptians, the West wind or the South-West wind signifies a change. For Conon, rain. 19. Hour 14 1/2: Antares sets in the morning. For the Egyptians, it signifies a change. 20. The Goat rises in the evening, and Antares sets in the morning. For Caesar, it signifies a change; rain. 21. Hour 15: Antares sets in the morning. For Caesar, it signifies a change. 22. For the Egyptians, the East wind or the South wind; rain. 23. Hour 15: the star in the succeeding shoulder of the Charioteer is obscured. And for the Egyptians, rain and thunder. For Eudoxus, the start of summer; rain. 24. Hour 14 1/2: the Goat sets in the evening; and the star in the succeeding shoulder of the Charioteer rises. The bright star of the Eagle...  ^C For the Egyptians and Hipparchus, it drizzles, and it signifies a change. 25. Hour 14 1/2: the star in the succeeding shoulder of the Charioteer is obscured; the bright star of the northern Claw sets in the morning. 26. Hour 13: Arcturus sets in the morning. For the Egyptians, the North-West wind or the West wind. For Eudoxus, the South wind. 27. Hour 15: the bright star of the Eagle rises in the evening. Procyon is obscured. 28. Hour 13 1/2: the star in the succeeding shoulder of the Charioteer sets in the evening. Hour 15: the Goat sets in the evening. 29. Hour 15: the star at the knee of Sagittarius sets in the morning. For the Egyptians, stormy conditions. 30. Hour 14 1/2: the bright star of the Swan rises in the evening. ^D For Euctemon and Hipparchus, it signifies a change.

Month of June, Payni.

1. Hour...: the star in the succeeding shoulder of the Charioteer rises. Hour 15: the star in the succeeding... sets in the evening. Procyon is hidden. The bright star of the northern Claw sets in the morning. For the Egyptians, a cold North wind. 2. Hour 14 1/2: the bright star of the Eagle rises in the evening. For the Egyptians, it signifies a change. For Calippus, the South wind. 3. Hour 13 1/2: the bright star of the Hyades rises in the evening. Hour 14: Procyon is obscured. For the Egyptians, for Metrodorus, rain.

4. According to Hipparchus, the West wind or the South wind. ^A 5. Hour 14 1/2: the star in the following foot of the Centaur rises in the evening. Hour 15: the star called the Goat sets in the evening; the star in the following shoulder of the Charioteer sets in the evening. 6. Hour 14: Procyon is obscured; the bright star of the Eagle rises in the evening; and the star at the knee of the Archer sets in the morning. 7. Hour 14 1/2: the bright star of the Hyades rises. Arcturus sets in the morning. For the Egyptians, the West wind. For Eudoxus, southerly winds. 8. Hour 10: For the Egyptians, the West wind or the North-West wind blows. 9. Hour 14 1/2: the star at the knee of the Archer sets in the morning. Hour 15: the bright star of the Water-bearer is obscured. For the Egyptians, the North-West wind and a drizzle. For Democritus, water upon the earth. ^B 10. Hour 13 1/2: the star on the head of the leading Twin is obscured. For Caesar, thunder and rain. 11. Hour 13 1/2: the star on the head of the leading Twin is obscured. 12. Hour 14 1/2: the star at the knee of the Archer sets in the morning, and the star on the head of the leading Twin is obscured in the morning; and the bright star of the Hyades rises. 13. Hour 15 1/2: the star on the head of the leading Twin is obscured. 14. Hour 13 1/2: the star at the knee of the Archer rises in the evening; the bright star of the Water-bearer is obscured. 15. Hour 13 1/2: the bright star of the Northern Crown sets. ^C 16. The bright star of the Hyades rises in the morning. For the Egyptians, it drizzles throughout the day. 17. Hour 14: the star at the knee of the Archer rises in the evening; Arcturus sets in the morning. 18. Hour 14: the bright star of the Twins sets; the star at the knee rises in the evening. 19. Hour 13 1/2: the star on the leading shoulder of Orion rises in the evening; and the last star of the River rises. For the Egyptians, a drizzle. 20. Hour 15 1/2: the bright star of the Hyades rises. 21. The Goat rises in the morning. 23. Hour 15: the star at the knee of the Archer rises in the evening. For the Egyptians, the West wind or the South wind. ^D 24. Hour 14 1/2: the star on the leading shoulder of Orion rises; and the bright star of the Water-bearer is obscured. For the Egyptians, rain. 25. Hour 13 1/2: the star on the leading shoulder of Orion rises. 26. Hour 14: the bright star of the Northern Crown sets; the star in the following foot of the Centaur... 27. Hour 13 1/2: the common star of the River and the foot of Orion rises. For Democritus, it signifies change. 28. Hour 15 1/2: the star at the knee of the Archer rises in the evening. According to Hipparchus, the West wind or the South wind blows. 29. Hour ...: the bright star of the Water-bearer is obscured, and the star on the leading shoulder of Orion rises. Arcturus sets in the morning.

Month of July, Epiphi

and the foot of Orion rises. For Hipparchus, the Etesian winds begin to blow. ^A 24. For the Egyptians: Favonius or Caurus (West wind), and heat. 25. Hour xiv: The star common to Pegasus and Andromeda rises in the evening. Hour xv: Procyon rises. For the Egyptians: Caurus or Favonius. 26. Hour xiii 1/2: The bright star of the Eagle sets in the morning. For Metrodorus and Euctemon, the Etesian winds begin. 27. Hour xiv: The Dog Star rises; and the bright star of the Northern Crown, and Procyon, rise. For the Egyptians: during the day, Favonius and heat. For Euctemon: bad weather. 28. Hour xiv: The star on the front right foot of the Centaur is hidden. For the Egyptians, the Etesian winds begin. For Euctemon: a storm at sea. 29. For Eudoxus, the Etesian winds blow. ^B

Month of August, Mesori. 1. For the Egyptians: Favonius or the South wind. 2. The bright star of the Eagle sets in the morning. Hour xv: The bright star of the Southern Fish sets in the morning. For Metrodorus, Conon, and Hipparchus: the South wind. 3. For Euctemon and Eudoxus: the South wind blows. 4. Hour xiv: The bright star of the Lyre sets in the morning. The star common to Pegasus and Andromeda rises in the evening; the Dog Star rises. 5. For the Egyptians: heat. For Eudoxus: beginning of autumn. 6. Hour xiv: The bright star of the Eagle sets in the morning; and the bright star of the Southern Fish sets in the morning. For the Egyptians: Caurus or Favonius, and heat. 7. For Caesar: the South wind blows. 8. For Hipparchus: heat. 9. Hour xiv 1/2: The bright star of the Southern Fish... The Dog Star rises. 10. Hour xv 1/2: The bright star of the Eagle sets. Alpha (the star in the goat) rises in the evening. For Caesar: it portends weather. For Eudoxus: the South wind. 11. Hour xiv: The bright star of Perseus rises in the evening. The last star of the River rises. For Eudoxus: intense heat. 12. Hour xiii: The bright star of the Southern Fish sets in the morning. For the Egyptians: heat. For Dositheus: suffocating heat, and after this, the Etesian winds. 13. Hour xiii 1/2: The star common to Pegasus and Andromeda rises in the evening. Hour xiv 1/2: The bright star of the Lyre sets in the morning. 14. The Dog Star rises. 15. For the Egyptians: Caurus, intense heat, and suffocating air. ^C 16. For the Egyptians: Caurus or a misty South wind. 17. For the Egyptians: intense heat and suffocating air. 18. Hour xiii: The star on the heart of the Lion rises. For the Egyptians: thunder. For Eudoxus: a very great wind. For Hipparchus: a disturbance of the winds. 19. Start of autumn; and the bright star of the Southern Fish rises in the evening, and the star on the heart of the Lion. For the Egyptians: heat. 20. The star on the heart of the Lion rises. For Caesar: it portends weather. 21. For Caesar: it portends suffocating heat. ^D

22. The 13 1/2 hour star in the tail of Leo sets; the bright star of Aquarius rises. 23. The 13 1/2 hour star on the right fore-paw of Centaurus sets; and the one in the tail of Leo sets. For Caesar, a change in the weather. 24. The 14 hour star, the bright star of Aquarius, rises. For Eudoxus, it is a sign. ^A 25. The 15 1/2 hour star, the one in the tail of Leo, sets. 26. The 16 hour star, the bright star of the Southern Fish, rises in the evening. For the Egyptians, a south wind or a zephyr. For Democritus, it is a sign of rain and winds. 27. The 14 hour star, the bright star of Aquarius, rises. For the Egyptians, heat and fog. 28. … 29. The 14 1/2 hour star, the bright star of Perseus, rises in the evening; the bright star of Aquarius rises. For the Egyptians and Caesar, it is a sign; for Eudoxus, foul weather; thunder in the morning. 30. The 15 1/2 hour star, the one in the following shoulder of the Charioteer, rises in the evening. For the Egyptians, a zephyr and north-west wind.

Epagomenae

1. The 15 1/2 hour star, the one in Lyra, sets in the morning; the bright star of Hydra rises. For Eudoxus and Metrodorus, it is a sign. ^B 2. The 14 1/2 hour star, the so-called Canopus, rises; the bright star of the Southern Fish rises in the evening. For the Egyptians, heat. For Eudoxus and Caesar, it is a sign. For Hipparchus, a south wind, and the Etesian winds cease. 3. The 13 1/2 hour star, Spica, sets. The 15 hour star, the one on the head of Leo, rises. For Hipparchus, a swirling of winds. ^C 4. The ... hour star, the one in the tail of Leo, rises. For Calippus, it is a sign. 5. The 15 1/2 hour star, the bright star of the Swan, sets in the morning. For the Egyptians, a zephyr and north-west wind.

What follows was beneficially noted by an author other than the author of the Hemerologium

This, therefore, is the order of exposition: so that they might be at hand, each should be restored to its own proper place. Nor does it seem absurd to collect the list both of the fixed stars that have been enumerated and of the appearances that have been memorized with them, so that if anything has been omitted by the fault of the scribes, it may be recognized. To this end, [there have been noted] also the names of the authors who observed those notations of time, and in which places they investigated each one, so that we may the better and more suitably apply similar observations to those that correspond to the same parallel. ^D

There are, therefore, fifteen stars of the first magnitude: Capella; the bright star of Lyra; Arcturus; the one in the tail of Leo; the bright star of the Hyades; Procyon; the one in the following shoulder of Orion; Spica; the common [star] of the River and the foot

53 of the River; Canopus; the one under the preceding muscle of the Centaur.

Fifteen of the second magnitude. The bright star of Perseus; the one in the following shoulder of the Charioteer; the bright star of the northern Crown; the one on the head of the preceding Twin; the common [star] of the Horse and Andromeda; the bright star of the Eagle; the one in the preceding shoulder of Orion; the bright star of the Water-snake; the bright star of the northern Claw; the middle of the belt of Orion; the bright star of the southern Claw; Antares; the one at the knee of the Archer.

^B Since each of these, in every one of the parallels in which they rise and set, undergoes four appearances annually; it happens, however, that the star of Canopus, as well as the one under the preceding muscle of the Centaur, perform their risings and settings in only three out of the five proposed parallels; while the bright star which is the last of the River does so in only four of the first three, [and] the remaining twenty-seven stars do so in [all] five parallels. Thus, there are gathered in total 580 appearances. The significations of these he has described and committed to this book, according to the Egyptians, and Dositheus, Philippus, Calippus, Euctemon, Meton, Conon, Metrodorus, Eudoxus, Caesar, Democritus, [and] Hipparchus. Of these, the Egyptians made their observations here among us; Dositheus in Colonia; Philippus in the Peloponnese and Locris; Calippus in the Hellespont; Meton at Athens and throughout the Cyclades, in Macedonia and Thrace; Conon and Metrodorus in Italy; Eudoxus in Asia, ^C Sicily, and Italy; Hipparchus in Bithynia; Metrodorus in Macedonia and Thrace. Therefore, it is most fitting to adapt the significations of the Egyptians to those tracts of land which correspond to this parallel: that is, where the longest day is fourteen equinoctial hours; those of Dositheus and Philippus to those regions whose longest day is fourteen and a half hours; those indeed of Democritus, Caesar, and Hipparchus to those places where the longest day is fifteen equinoctial hours; and those of Calippus, Eudoxus, Meton, Euctemon, Metrodorus, and Conon generally to those regions whose longest day is contained between fourteen and a half and fifteen equinoctial hours.