On the Rising and Setting of the Stars: A Dissertation

[The current page is the beginning of this translation.]

^A The twenty-third is the winter solstice. The fourth of the month of January, the Dolphin rises. The fifth, the Eagle sets in the evening; and there is strong turbulence after two days. The fifth, the bright star in Leo sets; it stirs the air three days before. The twenty-eighth, the Dolphin sets in the evening. The twenty-ninth, the Lyre sets in the evening. The sixth of the month of February, the West Wind blows. The twenty-second, the mast of the Ship sets in the evening, and there is great turbulence of the air. The twenty-fifth, Arcturus rises in the evening. The twenty-sixth, swallows fly and appear.

DISSERTATION ON THE RISING AND SETTING OF THE STARS

DISSERTATION

PREFACE

^C To the position of the sun in the zodiac, and to investigating the regions of stars rising and setting in the same, they wish, first of all, that it be observed on which days of the months the sun made its entry into each dodecatemory [sign] in those times in which those ancients flourished; and that this be collected from Columella, Pliny, Ovid, and the rest. Then, that the degrees of the zodiac with which the risings and settings of those stars might correspond be diligently noted. For from this it is easy to conjecture on which days these are to be compared, when we have learned to which sign the sun arrived in that century. This is indeed correct so far. However, in defining the place of the sun, they hold a little less of an accurate method. For they establish the entry into the dodecatemories not according to the truth of the matter, but according to the false persuasion of certain ancients. Thus, in the time of Julius Caesar, they say the sun entered Aries on the fifteenth day before the Kalends of April, that is, the eighteenth of March; into Taurus on the seventeenth of April; into Gemini on the nineteenth of May. Which, as it is false in itself, so, with that being posited, it is necessary that the risings and settings of the stars be wrongly and tied to alien days. For as the sun into Taurus, for ex-

example, would have undergone its appearance on the 15th day of April, the Pleiades, which in the 27th degree of Taurus were making their morning rising in the first Julian year, as has been demonstrated above, would have risen on May 15th or 17th, when in fact it occurred on the 20th. Thus, there is an error of about eight days in that description. The other intervals of the rising stars are of the same nature; and in their pronunciation, an error occurs for these reasons, which certainly needs correction. Therefore, it is necessary to speak in this place about this opinion of certain ancients and the redirection of their annual cardinal points, so that these matters may serve to illustrate those authors whom we have included in this edition, especially Geminus, Hipparchus, Ptolemy, and Tatius.

CAPUT I. Concerning the partition of the equinoctial and the zodiac as instituted by the Chaldeans, Egyptians, and Greeks.

There are two circles to which the positions and revolutions of the stars are referred: the equinoctial and the zodiac; from the partition of which the longitude of the stars is taken, and from their distance their latitude. And it seems that stars were compared to the equinoctial in both ways before the zodiac, not only in Greece, but also among the Egyptians and Chaldeans; by whom astronomy is believed to have been either discovered or more diligently cultivated and propagated to others. It is handed down to the memory of the Greeks that Anaximander the Milesian was the first of all to have discovered the obliquity of the zodiac in the fifty-eighth Olympiad. After him, Cleostratus of Tenedos discovered the signs in that circle, and first of all Aries and Sagittarius, as Plinius writes, book II, chapter VIII. Hyginus adds in book II of his *Poetic Astronomy*, in the chapter on the Charioteer (Heniochus), that the Kids were also first noted by him in the heavens. ^B

Moreover, Sextus Empiricus sets forth in book V what the method of partitioning was among the Chaldeans and Egyptians. For he says that they designated some bright star in the zodiac, by whose revolution and ^A *apokatastasis* (restoration) to the same place, they defined the interval of the celestial circuit; "having observed one of the bright stars in the zodiac rising, the ancients, etc."; where he also explains the method by which the zodiac was divided into twelve parts, and how the times of both it and the individual segments, that is, *anaphora* (ascensions), were established. Macrobius described this from that author in book I, *In Somnium Scipionis*. His chapter is: To the Chaldeans, who before the twelve-fold partition noted seven stars scattered in the sky, it later pleased them to divide the whole into twelve parts. Therefore, they observed some bright star, whose revolution from its rising to the same rising they measured by a water clock. How much water had dripped drop by drop into the vessel placed underneath, they took an ounce of this to measure the *anaphora* (rising) of the twelfth part of the circle; and they terminated that part with a bright star, which was either found in that very place of the circle, or had the same time of rising: "From this*anaphora* (says Sextus), I mean that of the dodecatemorion, they marked the final limit from a certain bright star observed according to it* (rising from some those further north or further south). From this ascension of the twelfth part, they designated the final limit with some bright star that was situated in that very limit; or from another of those further north or south, which would cause them to rise together."

Now, regarding the daily rotation, he relates that they measured the circuit of the heavens, and that they distributed this space into twelve equal parts. Therefore, from the ascensions, and what the craftsmen call "times," they computed the lengths of the dodecatemoria in the equinoctial circle, not in the oblique one of the zodiac, from the beginning; although they distinguished the limits of the segments by certain stars, as if by hinges. In this way, the twelve segments in the zodiac were unequal; but in the equinoctial they were equal, contrary to what happened later. For today the dodecatemoria in the zodiac circle are equal, both in the straight and in the oblique position of the heavens; in the equinoctial, due to the diversity of the ascensions, they are in both cases larger or smaller. Although Picus Mirandulanus, in book VI *Against Astrology*, chapter VI, says that the Chaldeans did not use signs but images. But nevertheless, that inequality existed. Since the images, or segments of the eighth sphere, marked by certain stars, are unequal, so that some do not fill their dodecatemoria, as Cancer; while others exceed and overflow into the neighborhood, as Leo, as Hipparchus and Geminus testify. But those images of the Chaldeans and Egyptians were different from the common ones of the Greeks, and ones that are still current today, as Achilles Tatius testifies at the end of his *Prolegomena*.

This division of the zodiac among the Chaldeans and Egyptians, as has been said, arrived in Greece quite late. Indeed, another partition did not immediately follow this twelve-fold one, which distributes individual segments into thirty parts. And very different divisions have been instituted among the ancients, especially the Greeks. From which the most famous was that which distributed the circles into sixty parts: which Strabo mentions in book II, where he divides the equinoctial into as many, and Achilles Tatius in his *Prolegomena*, chapter XXVI; Hyginus in book [II] of his *Poetic Astronomy*, in the chapter on the configuration of the spheres of the circles: "In thirty parts," he says, "each hemisphere is divided, so that the dimension might appear to be signified in the whole sphere by being made into sixty parts." In this way, five parts belong to any sign, and six degrees to individual parts. Otherwise, Posidonius, in Cleomedes book I, chapter IX, divided the entire zodiac into forty-eight parts, cutting each dodecatemoria into four. Others, furthermore, with any dodecatemorion divided into twelve other parts, divided the whole zodiac into one hundred and forty-four parts, as Sextus Empiricus teaches at the beginning of book V.

Finally, matters progressed to the point that both the equinoctial and the zodiac circle were cut into twelve parts, and those into thirty minutes, so that in the whole circle, three hundred and sixty were numbered; names from the starry images were also given to the twelfth parts of each circle: which at that time were evidently contained in them.

They continued to do this, ^A even if later they made a longer progression toward the following signs. In the beginning, indeed, because the rotation of the starry sphere was not yet known, the system of astronomy was simpler. For only one zodiac was held to exist in the eighth sphere along with the equinoctial, which is also distinguished by the stars. For that was the first thing the ancients called "movable." Later, Hipparchus noted that this sphere moved in consequentia (in the order of the signs); and Ptolemy subsequently confirmed this more reliably. Hence, a double zodiac began to be distinguished by experts: one of which is attributed to the sphere endowed with a single and simple motion, in which there are no asterisms, and its sections are made perpetually at the same points of the dodecatemoria as the equinoctial; the other, placed below it in the starry orbit, has different intersection points ^B *eis ta proēgoumena* (toward the preceding signs), and the *zōdia*, or asterisms, little by little shift *eis ta epomena* (toward the following signs), and they draw farther away from the dodecatemoria named after them.

After these, a new motion was found in the system of the celestial orbs, according to which the zodiac or ecliptic has a greater or lesser distance and obliquity from the equator: from which it was believed that the starry sphere is twisted from south to north, and reflected from north to south. Hence, therefore, a third zodiac was added to the intermediate sphere, whose property is that libration which deviates slightly from the zodiac of the prime mover toward the north or south, and twists whatever is immediately subject to itself with the same agitation. But passing over that, since the system of ancient astronomy alone is being brought forward by us here, we shall be content with a double zodiac: of which one, peculiar to the first heaven, retains the same perpetual declination from the equator and its intersection at the same point; the other continually carries the starry images in its progression in consequentia, and makes its sections with the equator at different points, and changes the dodecatemoria themselves. Moreover, when we speak absolutely of the zodiac and its segments, which are called signs, we understand the first and constant zodiac of the prime mover, or the one corresponding to it in the eighth sphere. For it is agreed that in all this doctrine it should be known that whatever is fashioned for the sake of method regarding the circles and segments in the higher spheres, the same thing and in the same way is accommodated to the lower and subject ones; and indeed, some are applied to the very globe of the earth, upon which its own equinoctial, as well as the other parallels, are accustomed to be delineated.

These things being noted, since the position of the stars can be considered either directly or transversely, that is, according to longitude and latitude—the former of which begins from the vernal intersection of the zodiac and the equinoctial; the latter is taken from intermediate points of the sphere toward the poles—each can be estimated in two ways. For longitude is either viewed on the equinoctial, which is divided into twelve parts with the beginning made from the vernal intersection, and with the parts in it designated by great circles, or the six colures that go through the poles of the world ^C or on the zodiac, with the beginning likewise taken from the vernal intersection, and with great circles drawn through the poles of the zodiac and every thirtieth degree concluded. Latitude, likewise, is either the distance of a star from the equinoctial, which is measured by the arc of the colure, or the great circle produced from the pole of the world through the center of the star to the equinoctial, intercepted between the star and the equinoctial; or it is the distance of the same star from the zodiac, or the arc of the great circle passing through the poles of the zodiac, intercepted between the star and the zodiac. The following chapter will show that the ancients defined latitude in both ways, especially. For it is less certain concerning longitude, whether it was taken by them according to the zodiac, since it is gathered from Hipparchus in the following chapter that it was calculated on the equinoctial circle.

After Ptolemy, the longitudes of the stars were judged according to the zodiac: the right ascensions of which are held as the longitudes of the former type. Thus the zodiac is divided into twelve equal parts, the equinoctial into as many unequal ones. Truly, latitude is the distance of a star from the zodiac or ecliptic. But distance from the equinoctial is commonly called not latitude, but declination.

CHAPTER II.

That the view of the ancient astronomers concerning the longitude and latitude of the stars was that both were considered with respect to the equinoctial circle.

That which we said in the previous chapter about the longitude of the stars, that among the ancients it was accepted according to the equinoctial, we shall demonstrate from Hipparchus by citing some examples: from which let the first four come to the middle, which are read in Book I, number 8, where he says that the head of Ursa Major is situated primarily in a little less than the third part of Leo, according to the circle equidistant to the equinoctial. However, the head of Ursa is the more northerly of the two preceding in the list, according to the opinion of the ancients, who placed no stars except the seven of the *Hamaxa* (Wain) in the asterism of the Helix. Likewise, the last in the tail of Draco is in the third part of Leo according to the parallel circle. "For the one in the tip of the tail of Draco occupies, as if according to a parallel circle, 3 degrees of Leo; but the mentioned star in the *plinthion* [square] occupies of Leo a little less than 3 degrees." Both are false if the position of those stars is viewed in the zodiac. For the former, which was the head of Ursa to the ancients, was moving in the 15th part of Cancer in the time of Hipparchus; the last of the tail of Draco in 10 degrees, 36 minutes of Cancer. The right ascension of the former was 122 degrees, 32 minutes in the year of the Julian Period 4550; of the latter, a few years later, it was 123 degrees, 57 minutes. Divided both by 30, they result in: in the former, 4 signs, 2 degrees, 32 minutes; in the latter, 4 signs, 3 degrees, 57 minutes. Thus it is true what Hipparchus says concerning the places of both, if they are considered in the equinoctial circle according to right ascensions, or, what is the same thing, in that parallel which the stars delineate by their diurnal motion.

Again, in the same place Hipparchus writes, ^D of the southern...

part of the two succeeding stars in the list, that it holds almost the twenty-fifth part of Leo. But its place in the zodiac was, in Hipparchus’ time, at 0° 44' of Leo. Therefore, this position must be calculated from right ascension, which I find to be 145° 32'. With these divided by thirty, they become 4 signs, 25°, 32', that is, a little more than the twenty-fifth degree of Leo, on the equinoctial or the parallel circle equidistant to it. Likewise, the end of the tail of the Lesser Bear is placed at the fourth part of the Claws, or Libra. The place was at 27° 10' of Leo. The right ascension is 6 signs, 4° 4', exactly as Hipparchus intended, at 4° of Libra. Therefore, the places of the stars are designated not to the zodiac, but to the equinoctial or parallel. In number XII Hipparchus says that the furthest part of the tail of the Lesser Bear is situated at 18° of Pisces. If the ratio of the zodiac were maintained, it would have been at 29° of Taurus in Hipparchus’ time. The right ascension is 346° 16', which, when divided by 30, results in 11 signs, 16° 16', that is, 16° 16' of Pisces, according to the parallel circle. Now, that the same author asserts in number XIV that the head of the Lesser Bear, or the more northerly of those preceding in the list of the Wain, is situated at the end of Scorpio, this does not agree with the zodiacal position, which was 13° 15' of Cancer in Hipparchus’ time, but it does agree with the right ascension, which was 8 signs, 1° 26', so that by this reasoning it was to be considered at 1° of Sagittarius.

Item, at the end of book I, number XXVII, he writes that the preceding stars in the head of Hydra occupy more than 10° of Cancer, which agrees remarkably with the right ascension: which I find in Hipparchus’ time to be 3 signs, 10°, the same at more than 10° of the degree. And we find the right ascension of the southern ^B [star] of the shoulder or arm to be 10 signs, 10°. Hipparchus reports it to be placed at 25° of Aquarius. The right ascension agrees, which is 10 signs, 26° 26'. But the place in the zodiac was at 3° 48' of Aries. Furthermore, in the left hand of Boötes, he locates the preceding star there at more than 13° of the Claws. The right ascension is 6 signs, 11° 47'; the place in the zodiac, at 28° 38' of Leo. Furthermore, in book II, Hipparchus teaches that the most southern star in the left foot of Boötes occupies 1° of Libra. The right ascension of this miraculously ^C agrees with the observation; for it is 6 signs, 1° 27'. But the place in the zodiac in Hipparchus’ time was at 19° 35' of Virgo. We could add more examples to these: but these which we have selected sufficiently show that which we wish to demonstrate, namely, that the longitude of the stars is set by Hipparchus according to right ascensions on the equinoctial or parallel circle, not, as is done today, in the zodiac.

The same author very often makes mention of declinations from the equinoctial circle: but nowhere of latitude from the zodiac. Although I do not doubt that Hipparchus also had a method for this, after the artificers measured that circle in the heavens and noted its obliquity. Indeed, Hipparchus observes that Eudoxus, and Aratus following his example, dealt in their asterisms with the distance from the zodiac, ^D that is, the latitude, and also with the southern stars: which Hipparchus himself also held. Furthermore, Geminus, who flourished about eighty years after Hipparchus, does not obscurely signify that in his age both the longitudes and latitudes of the stars were accommodated to the zodiac. For at the beginning of his book he asserts that the zodiac is distributed into twelve equal parts, which are signs: by which method it is necessary that the equinoctial be divided into unequal parts. And yet the same author nonetheless makes mention of parallel circles, which a star designates by its diurnal circuit equidistant from the equinoctial. Wherefore it is probable that the ancients thought of the longitudes and latitudes of the stars in both ways; according to what was expedient for the treatise they were planning. For unless they had occasionally employed their latitude from the zodiac, they would not have distinguished their northern positions from the southern ones with reference to the zodiac, but only to the equinoctial: from which alone they might have repeated their latitudes. Hence it is clear that what Josephus Scaliger affirms in the first chapter of his book *De anticipatione aequinoctiorum* is false, namely, that before Ptolemy no other longitude or latitude of stars was in use than that which is taken relative to the equinoctial; and that Ptolemy was the first to transfer both to the zodiac. But Geminus, who preceded Ptolemy by more than two hundred years, most clearly declares that both the longitudes and latitudes of the stars were described in the zodiac in his own century, as we demonstrated a little before. That Hipparchus and Eudoxus also used the same thing sometimes, especially as regards latitudes, may be gathered from the same kind of conjecture. For there is nothing else meant by calling stars northern or southern, which recede from the zodiac toward the north or south, than that they have a northern or southern latitude from that same zodiac. But it is clear that this was already used by Eudoxus and the others, as we have already said. Therefore, they also acknowledged this kind of latitude, which is taken from the zodiac. No example, that I recall, is mentioned by Hipparchus from Eudoxus in which the site of a star is specifically expressed; for as to his appearing to place the head of the Great Bear according to the opinion of Eudoxus in the twelfth part of Leo in book I, number XII, the matter stands otherwise. For in order for the place to be integral, he does not say that the head of the Bear itself is referred by Eudoxus to the twelfth part of Leo, but that the star which according to Eudoxus was the head of the Bear, Hipparchus himself seems to place in that degree according to his own opinion: ^D "the head, however, according to Eudoxus," [assigning it to that place], which star Eudoxus indeed constituted as the head of the Bear. For Hipparchus thinks that Eudoxus, and all the ancients, placed the head of the Bear elsewhere than where it is placed today, namely, by calling the more northerly of the two preceding in the list the head in both cases; concerning which a little more will be said later. Add that it does not appear that the division of the signs into thirty parts, or of the whole circle into 360, had yet been instituted in the age of Eudoxus. And not even this passage is uncorrupted; but on account of...

those matters, and things of far greater importance in his book ^A *On the Anticipation of the Equinoxes*, we shall examine them shortly.

For it is one thing for Hipparchus to have written: *“And according to Eudoxus, the head of the Great Bear is at the dodecatemory of Leo.”* Since it was at the 16th degree, he thought it should be read as “16th degree,” and thus “the 16th degree,” as if it were placed in the twelfth part, especially since immediately before, “18th degree of Pisces” had been written. But Hipparchus has shown more than once that the head of the Great Bear is situated in the third part of Leo, not the twelfth. And he is not to be believed to have dissented so much from himself, and from the truth of the matter, in this place as to have set it in the twelfth part.

That Hipparchus contemplated longitudinal positions of the stars not only on the equinoctial, but also in the zodiac by another method and usage, can be proven from his second and third books; where, discussing the *synanatolai* (co-risings) and *synkatadyseis* (co-settings) of the stars, he openly declares that the zodiac is divided into twelve equal parts, each of them into thirty, and that this partitioning proceeds from the beginnings of the signs, as much according to his own opinion as that of the ancients. Yet if the longitudes had been observed only on the equinoctial, the zodiac would not have been divided into equal parts; nor would the individual dodecatemories have consisted of thirty parts.

Others have expressed this hallucination of Hipparchus—that he indiscriminately takes asterisms, or the stellated *zodia* (signs), together with the dodecatemories of the same name—in a similar way. For the scholiast of Aratus writes on the words: *“And at the head are the Twins; in the middle is Cancer, and at the feet of both, Leo shines beautifully;”* in which he says that the Twins lie beneath the Great Bear and correspond to its head, Cancer to its belly, and Leo to its feet. Regarding this scholion, he observes that some reprove Aratus because he signifies that ninety degrees—that is, three dodecatemories—lie under ^B the Great Bear, which extends no more than thirty degrees. To this objection of trifling nonsense, I know not what he brings forward. For he says nothing that would not be better left unsaid. But surely this is what I have warned, that those who objected thus to Aratus thought that he understood the dodecatemories by the names of the Twins, Cancer, and Leo, when he is speaking of the stellated figures. For in this latter sense, what Aratus taught is true, as we demonstrate against Hipparchus. Who would not wonder that those ancient and distinguished astronomers, and their chief Hipparchus, were so blinded that they did not see these things? But they took the handle for the error from the fact that, in their own time, the stellated figures of the signs occupied the dodecatemories of the same name. Therefore, the mutual communion of terms was then slippery and opportune for deception: which happens less today, on account of the *prohyesis* (precession) of the eighth sphere and the asterisms within it. From which it has come about that most *zodia* consist outside their own dodecatemories.

CHAPTER III.

The opinion of Eudoxus, contrary to what Hipparchus thought, is set forth. The error of the same Hipparchus, who confuses dodecatemories with asterisms. Aratus and Servius are illustrated.

Hipparchus, at the beginning of Book II, is the author of the claim that the ancients—either all or most of the mathematicians—attributed the hinges of the solar circuit to the beginnings of the signs of the zodiac; and that Aratus followed this in his work. *“And by nearly all of the ancient mathematicians, or by most of them, this is the way the zodiac ^D circle is divided.”* And in this manner, almost all of those who were mathematicians have divided the zodiac circle. Yet it is established that sometimes, elsewhere than at the beginnings of the signs, the equinoxes and solstices were customarily placed, and not consistently. For some (says Achilles Tatius, chap. XXIV) placed them at the beginnings, others at the eighth parts, others at the twelfth, others at the fifteenth—that is, in the middle of the signs.

That the distinguished mathematician Eudoxus, who lived in the age of Meton, placed the hinges themselves in the middle of the signs is accurately proven by Hipparchus in Book II (page 120), with the words of Eudoxus himself brought forward: which, if anyone wishes to weigh with us, will not easily agree with Hipparchus concerning Eudoxus's opinion. For it is far otherwise.

^A Sunt autem in ipso media Capricorni, et pedes Aquarii, et cauda Ceti, et Fluvii flexus. » He adds the Hare, and the feet of the Dog, and the rest, until it arrives at the same middle of Capricorn through Sagittarius. For this reason, in the same book, no. XXII and following, Hipparchus describes the two tropics and the equinoctial circle from Eudoxus’s opinion and enumerates the celestial images through which they pass. Just as he asserts that the summer tropic passes through the middle of Cancer and Leo, and the equinoctial through the middle of Aries and a part of the Claws. From which it is clear that Eudoxus understood asterisms and celestial figures. For just as when he says the summer tropic passes through the middle of Leo according to longitude, and through the other constellations; and likewise the summer tropic [passes] through Sagittarius, Cetus, the River, etc.: he designates not the dodecatemories of any circle, but starred images: so when he says the same circles pass through Cancer, Capricorn, Aries, and the Claws, he understands not the signs themselves, or dodecatemories, but asterisms. But Eudoxus himself removes all evasion when he names those very things through which he says the circles pass "stars," which signifies nothing else than asterisms and images. Achilles Tatius in *Phenomena*, ch. XIV, wishes an "asterism" to be a system of several stars. And he confirms this by the testimony of Aratus. But Eudoxus, as Hipparchus bears witness, when speaking of the colures, says, "There are, however, these stars in them: first, the pole of the world which is always visible. Then the middle of the Bear in longitude; and the middle of Cancer," and next he adds the tail of the southern Fish, and the middle of Capricorn. These are concerning the solstice colure. Speaking of the other, he writes that there are contained in it, among other asterisms, the "middle of the Claws in width, and the backs of Aries likewise in width." What could be said more clearly, so that it appears that Eudoxus, when he calls them the middle of the Claws, of Aries, and of the rest, refers to the images themselves? For "backs," "widths," and the like can only be used of figures. For the middles of the signs or dodecatemories are not in themselves reckoned by width, but only by longitude. ^{B C D} For those very words of Eudoxus, from which Hipparchus argued, are written down in other places, but more completely; when he institutes a discourse concerning the circles described by Eudoxus as parallels. As in book I, no. III, concerning the tropic circle: "There are in it the middle of Cancer, and those which pass through the body of Leo according to longitude," etc. He adds the neck of the serpent of Ophiuchus; the right hand of the Kneeler; and other stars which that circle traverses. Finally, it revolves into the same middle of Cancer. Concerning the winter tropic also, "It is in this, the middle of Capricorn," etc. What of the fact that Hipparchus himself, in book I, no. III, when about to cite the testimonies of Eudoxus, calls them stars, and says that Aratus, following the imitation of Eudoxus, distributes them so as to begin from those more to the north? Presently: "But concerning the stars which are borne on the summer tropic, as well as on the equinoctial circle, Eudoxus indeed speaks concerning the summer thus: 'There are, however, in this the middle of Cancer.'" He uses the same manner of speech regarding the winter tropic and the equinoctial. Therefore, asterisms and starred forms, not

To say nothing of the tropics, certainly the equinoctial will not divide Aries according to its length (κατὰ μῆκος ἐληλαμένον), but transversely and according to its breadth (κατὰ πλάτος). Indeed, the intersections of the equinoctial and the zodiac are placed by Eudoxus, as Hipparchus thinks, in the middle of the signs.

Not dissimilarly, as I myself believe, misled by homonymy, Hipparchus accused Eudoxus, Aratus, and Attalus in the tenth number of his first book, because they place Gemini under the head of the Greater Bear, Cancer under the Middle Bear, and Leo under its hind feet. Here they are undoubtedly speaking of the asterisms, for the verses of Aratus, which Hipparchus cites, cannot be understood in any other way. But Hipparchus refutes this on the grounds that the head of the Ursa ^B is in the third part of Leo, namely in the dodecatemorion of Leo, which he places in the equinoctial or parallel. Yet this type of argumentation is external and struggles with homonymy. But this passage of Hipparchus will be discussed at greater length in the third chapter of the third book.

Finally, a similar ambiguity deceived Servius in his Commentaries to the first Georgic, where, in explaining these lines, "Where the place between Erigone and the following Claws," he annotates certain things that it would be better to relate here. "The Egyptians," he says, "assert that there are twelve signs, but the Chaldeans eleven. For they take Scorpio and Libra as one sign. For the Claws [Chelae] make the Libra of the Scorpion. The same Chaldeans want the parts to be equal in all the signs, but that, according to their quality, one sign has twenty parts, another forty, while the Egyptians want there to be thirty parts in all. Thus, he was speaking according to the Chaldeans, saying he could have a place between Scorpio and the Virgin." Signs are used in two ways. They are either the dodecatemoria of the equinoctial or the zodiac, or they are the asterisms, which Hipparchus calls ὡρισμένα ζώδια [defined signs]. Some of these are smaller than their dodecatemorion, others larger, and they overflow into neighboring regions, as we said above. When a grammarian had read this somewhere, he mixed up those two kinds of signs and taught a matter altogether absurd and inextricable, that all signs were described by equal parts, and yet that one consisted of thirty, another of forty, according to its quality. In the former way, the signs are dodecatemoria; in the latter, they are asterisms, of which some occupy fewer parts, some more. Thus, the asterism of the Claws [Chelae] is a part of the asterism of Scorpio, so that in this way there are only eleven ὡρισμένα ζώδια, or stellated figures, among the Chaldeans. For the Egyptians, who substituted Libra for the Claws, obtained the legitimate number: both, indeed, employed twelve signs. Furthermore, the asterism of the Virgin formerly occupied parts of Leo and Libra, beyond its just portion. But between this and the Claws of Scorpio, which were situated in the dodecatemorion of Libra, there is a hollow interval that pertained to the same dodecatemorion of Libra: in which space Virgil destines a seat for the deified Augustus. That was the poet's meaning, which Servius does not grasp. But Martianus Capella, in book VIII, chapter on the fixed signs, correctly states this,

^A the words we have taught, he explains in these terms: "This the zodiac discerns: which indeed makes up twelve equal portions of signs. But it has eleven signs. For Scorpio occupies as much of its own space with its body as the Claw occupies of Libra."

CHAPTER IV.

Since it is concluded from the words of Eudoxus that the cardinal points were by no means established in the middle of the signs, as Hipparchus thought, let us now inquire in what part he fixed them; furthermore, what reason was adopted by those who knew those cardinal points to be elsewhere than at the beginnings of the signs.

Geminus, in chapter XVI, writes that according to Eudoxus the winter solstice takes place on the fourth day after the sun has entered Capricorn, but the vernal equinox on the sixth day of the Ram. The same author reports, according to the opinion of Euctemon, that the winter solstice is engaged upon on the first day: as also the autumnal equinox. According to Calippus, however, the four cardinal points themselves were strictly contained at the beginnings of the signs. But Columella, in book IX, chapter XIV, writes that Meton and Eudoxus, and the ancient astronomers, placed the solstices and equinoxes in the eighth parts of the signs; and that Hipparchus, having changed the method, transferred them to the beginnings of the signs. "Nor does Hipparchus's method escape me," he says, "which teaches that the solstices and equinoxes are not completed in the eighth, but in the first parts of the signs. But in this science of the fields I now follow the calendars of Eudoxus and Meton, and the ancient astrologers, which are adapted for public sacrifices, because that old opinion formed by farmers is also better known. Yet the subtlety of Hipparchus is not necessary for the 'coarser,' as they say, letters of the rustics." See how he makes Hipparchus the author of that system which accommodates the cardinal points to the beginnings of the signs, whereas the ancients ascribed them to the eighth parts. In which he disagrees partly with Geminus, and partly with Hipparchus himself; for Geminus nowhere says that the cardinal points were established in the eighth part of any sign; but Hipparchus, as we saw in the previous chapter, taught that they were transferred by Aratus, and almost all the ancient mathematicians, to the beginnings of the signs. I do not doubt that the authority of Hipparchus is stronger in this matter than that of Columella; as one who was both much older and more intelligent in these matters, and more well-versed in the reading of the ancient astronomers than Columella was. And yet, by the authority of this man, almost everyone today is led to believe that the equinoxes and solstices were customarily assigned by astronomers in the most ancient centuries to the eighth parts of the signs. Which Scaliger defends more zealously than others: indeed, he establishes it as the sole foundation for that doctrine which he explained concerning the years of the Greeks and other peoples. But I would not fundamentally deny that there were those who, before Hipparchus, transferred the cardinal points elsewhere than to the beginnings of the signs: which Geminus, Columella, Achilles Tatius, and others confirm; and by Julius Caesar, according to a common and received opinion, the same was ^B considered translated in just the same way by all.

Just as this was instituted by them, and for what reason those disagreements of the writers can be reconciled among themselves, we shall explain next.

I believe it could have happened in two ways entirely, that among the ancient mathematicians the equinoxes and solstices were established elsewhere than at the very beginnings of the signs. For either they declared it in reality, and following art and judgment, or, when they thought otherwise about the more exact location of the cardinal points, they indulged the uses and perceptions of the people by this other, less accurate class of cardinal points. To begin with the former, those things must be repeated in particular, which we handed down concerning the Chaldeans and Egyptians in the first chapter; namely, by what reasoning they instituted the partition of the celestial signs. For they marked a certain notable star in the sky, from the rising of which they first designated the dodecatemorion in the equinoctial circle. This beginning having been established, they then divided the anaphoric time of twenty-four hours of the whole circle into twelve equal parts: of which they described each one by other stars likewise, whether positioned in the zodiac or outside it, and rising at the same moments, just as signs and boundaries. For so Sextus Empiricus teaches, that with the beginning of the first dodecatemorion designated, the rest were numbered by an even division of the equinoctial. Wherefore, it is likely that those who in good faith and seriously fixed the cardinal points in the middle of the signs, or in the eighth, and other parts, did not begin the start of the first dodecatemorion from the very intersection of the equinoctial and the zodiac; ^C but some space before: which was subsequently preserved in the rest. But since they began the start of the vernal season from some notable star, as we have said, let that star be chosen which is in the preceding horn of Aries. That, according to the most accurate observation of Tycho, in the year of Christ 1600 was situated at 27 degrees, 56 minutes of Aries, whose latitude is 7 degrees, 8 minutes. But since the starry sphere moves in consequence, and traverses one degree in about seventy-two years, it follows that some centuries ago the very point of the vernal section fell upon that star, and again in more ancient centuries it preceded it. But the ratio must be taken not so much of the place itself, which belongs to the star in the zodiac, and which is designated by the circle of latitude, as of its oblique ascension, so that we may be able to estimate into what part of the dodecatemorion the equinox fell.

^D Godefridus Vendelinus, a man especially learned in astronomy, wrote to me that about the year 1263 before the Christian era, which is 3450 of the Julian period, that was the time at which the ascension of the first star of Aries preceded the vernal equinox by fifteen degrees. At which time also the New Moon of Thoth, and the rising of the dog-star, and the solstice, and the new moon fell on the same day, which was the fifth of July, and that in the Heliopolitan tract: which gave to the memory of posterity a notable beginning for the Sothic period, which Clemens Alexandrinus mentions in *Strom. I*, three hundred and forty-five years after the migration—

^A And so, the text records that the period of the Israelites' exodus from Egypt began at that time. Thus it is in the Greek. But the interpreter wrote four hundred. During this same time, the first star of Aries was in the seventeenth degree, twelfth minute of Pisces, and it preceded the equinoctial point by twelve degrees and forty-eight minutes, which is fifteen ascensional times. Truly, in that very year we detected the first star of Aries, by our method, at the seventeenth degree, fiftieth minute of Pisces: the right ascension being three hundred forty-six degrees; the oblique ascension for Memphis, or Heliopolis, being three hundred forty-five degrees, six minutes, such that it precedes the equinox by fifteen degrees. The true new moon in the same region occurred on July 5th, at the twelfth hour and forty-sixth minute, when the true place of the sun was at the twenty-ninth degree, nineteenth minute of Gemini. Wherefore, on the following day, at the fifth hour of the morning, it was at the very Cancer solstice. In this same first degree of Cancer, Sirius also resided, which then made its morning rising with the sun on the first day of Thoth, which fell on that same day.

^B There is no doubt that this admirable concurrence of four things at the same time—the new moon of Thoth, the lunar month itself, the rising of Sirius, and the solstice—deserved singular observation among the Egyptians, such that this became a notable epoch, even if no memory of it survives in the monuments of the ancients. And yet that very year is considered in our Chronology to be the one-hundredth before the fall of Troy; and two hundred twenty-seven years after the migration from Egypt, from which date, indeed, the Sothic period could rightly have begun.

^C Hence that passage from Porphyry’s book *On the Cave of the Nymphs*, which Wendelinus interprets, where he says that the Egyptians begin the year from Cancer, as the Romans do from Capricorn, and from the rising of Sothis. "To the Egyptians, the beginning of the year is not Aquarius, as it is to the Romans, but Cancer. For Sothis is next to Cancer, which the Greeks call the star of the Dog. The new moon for them is the rising of Sothis, which provided the beginning of generation for the world." He seems to speak here of the beginning of Cancer. Wherefore he understands that time above all when the cosmic rising of Sirius falls into the beginning of Cancer. Wherefore, if, as Sextus Empiricus and Macrobius teach, the dodecatemories were first established by the observation of some star, and by the succession of degrees of ascension in equal division, as we mentioned in the first chapter, it was possible for that first star of Aries to be noted by the Egyptians at that time, and for the division of the segments to proceed from it; and for the vernal equinox to fall in the middle of the first dodecatemory: which, once decreed by them, would have been propagated for some centuries, until the *metaptoisis* (shift) of that star could be discerned by the senses in the consequent degrees: and for the equinox to shift by twelve, eight, six, or four ascensional times. Whence that variety of opinions concerning the moments of the cardinals had its origin: for once the beginning of the first dodecatemory was established, the rest were distinguished in sequence by equal partitioning; from which it came to pass that the remaining cardinals fell into that same part of their dodecatemories, just as the vernal equinox had occupied the first.

^D At the beginning of the era of Nabonassar, when the star of Aries was situated in the twenty-fifth degree of Pisces, in the Heliopolitan tract, the oblique ascension was three hundred fifty degrees, and it was anterior to the equinox by ten degrees. Furthermore, in the age of Cyrus and Thales, in the same situation, the star of Aries having now progressed to the twenty-eighth degree of Pisces, the oblique ascension was three hundred fifty-two degrees, and the equinox was occurring in the eighth degree. This method of setting the cardinals in certain parts of the signs could be applied repeatedly, according to those things which we explained from Sextus Empiricus in chapter I.

Yet no less probable is that which is gathered from Hipparchus, in which the position of the stars in the equinoctial or equidistant circle is designated by colures drawn from the pole of the world through the center of the star to the equinoctial. If we follow this, it happens even more conveniently that, in that year which we defined above as memorable for such a concurrence of things, the equinox occurs in the fifteenth degree. For the right ascension of the parts is found to be 346, in the 3450th year of the Julian period, so that the equinox falls precisely into the 15th degree. But in the first year of Nabonassar, of the 3967th year of the Julian period, the right ascension of the parts was 352 degrees, 34 minutes; and the equinox was taking place in the eighth degree from there. This latter method is to be preferred to the former not only for the reason that, while bringing the same convenience with it, it has this besides, that it is more consistent with the reasoning of Hipparchus and the ancients, according to his testimony, but also because it shows that the equinox falls about the eighth part of the dodecatemory around the epoch of Nabonassar. For this opinion—which tied the cardinals to the eighth parts of the signs—seems to have been the most used of all and propagated farthest to posterity: which having been established under the beginning of that most noble era by the Chaldeans in Babylon, one may rightly suspect flowed from there to others.

Ammianus Marcellinus in book XXVI, when he deals with the leap year, seems to indicate that the cardinal consists in the second part of Aries according to the opinion of the ancient astronomers; for he lists Meton, Euctemon, Hipparchus, and Archimedes, and explains the turning year, so that, if translated literally, it returns to the dimension from the second part of Aries, the cardinal which he had just before named. Circles among the ancients were divided into sixty parts, as I mentioned above. Therefore, five were imputed to each dodecatemory, each of which had six of our modern degrees. Thus the eighth degree of the signs belonged to the second. Whether Ammianus intended this is a matter for further thought. Furthermore, in the time of Meton and Eudoxus, when the first star of Aries had by then reached the 29th degree of Pisces, and even more, that is to say almost the thirtieth, the right ascension was almost 357 degrees: so that the equinox would fall into the fourth degree from there. However, the oblique ascension...

^A near Athens in about the year 552, and at Heliopolis in about the year 353: and in this he persisted most stubbornly against the astronomical doctrines of Hipparchus; so much so that even in the times of Bede, and subsequently, this same error persisted, which is shown by his Calendar, in which the entry of the sun into the signs is ascribed to about eight days before the equinoxes and solstices. And this is the second of the two reasons according to which we said it could have happened that the cardinal points were fixed by those skilled in astronomy at a different degree than the first of the dodecatemories. For after the matter was established both by the opinion of many ancient authors, as Hipparchus asserts, and by the authority of Hipparchus himself, that the beginnings of the cardinal signs should be taken from the equinoxes and solstices, since this nevertheless could not be extorted from the minds of the common people and the country folk—who believed that the equinoxes and solstices occurred on the eighth parts, or others than the first—something could be indulged to that opinion by the practitioners. Wherefore those who wrote ephemerides and Calendars for rustic men, in order to comply with their grasp and usage, seem to have noted the entry of the sun into the signs before those days which they had attributed to the spring or middle cardinal points. And this is especially fitting to suspect about Sosigenes, from whose fasti it appears that Varro, Hyginus, Ovid, Columella, and Pliny drew these things, which are produced as being consistent with that common persuasion I have mentioned. But neither Sosigenes, nor any of the ancients, separated the moments of the equinoxes and solstices from the ingressions into the signs in the way which Scaliger invented and which some have approved, namely, by placing the former perversely before the latter. And this, just as we have not stated it once, so we do not repeat it in these books more often than is necessary; and so that no hesitation or controversy may remain hereafter, in the following chapter we shall attempt to provide a fuller idea of this matter.

CHAPTER V.

From those things which we have gathered together in a sufficiently long, but necessary, discourse concerning the annual cardinal points of the ancients, this sum is concluded: that the ancient astronomers for the most part assigned the solstices and equinoxes to the very beginnings of the dodecatemories, both in the equinoctial, or parallel, circle, and in the zodiac, as the prince of that art, Hipparchus, is the author (pages 104, 105). ^D Furthermore, whoever attributed the cardinal points to the middle of the signs, or to the eighth parts, and the others, all of them so divided the circles that the intersections of the equinox and the zodiac, or the contacts of the latter and the tropics, were made in those degrees of the signs which they had prefixed to the equinoxes and solstices. But as to the fact that all the astronomers who did indeed fasten the cardinal points elsewhere than at the beginnings of the signs, before the intersections and contacts of the circles, that is, the equinoxes and solstices

^A Hipparchus demonstrates in Book I, number 10, that the more southern star of those following, situated in the flank of the Greater Bear, belongs according to the legitimate division of the signs—which assigns tropical and equinoctial points to the beginnings of the signs—to the 25th degree of Leo, while the preceding ones in the same flank [are] in the 25th degree of Leo, lacking a little of a third; but according to another method, which establishes the cardinal points in the middle of signs, he places the former in the tenth degree of Virgo, and the latter in the eighteenth. Thus, the extremity of the tail of the Greater Bear, by common division, is in the fourth degree of Libra; according to the latter method, and Eudoxus, it is in the nineteenth.

Again, in number 12, he writes that the very last and brightest [star], which is at the tip of the tail of the Lesser Bear, is situated in the 18th degree of Pisces; but as Eudoxus divides the zodiac, in the third degree of Aries. Therefore, Eudoxus and other ancients anticipated the beginnings of the signs. There is an error in this passage of Hipparchus, which we have removed by a most certain conjecture. For it reads, both in the printed copies and in the manuscript codex: «O Eudoxus divides the zodiacal circle according to the 3rd degree of Aries,» for which we have rightly judged that we should write instead: «As Eudoxus divides the zodiacal circle according to... etc.,» which the sense manifestly requires. The eighteenth degree of Pisces is the third of Aries, if you begin counting the sign of Aries from the fifteenth degree before the intersection. ^B These things bear witness not obscurely that the equinoxes and solstices were never located by the ancient astronomers elsewhere than in the mutual intersections and contacts of the circles, which they attributed to the eighth or fifteenth part of the signs; nor were those eighth or other parts counted from the equinoctial or solstitial points. This, I see, pleases Scaliger and most others, and is taken everywhere as certain; for hence they think that Sosigenes and Julius Cæsar placed the cardinal points on the eighth day of the Kalends of their year, so that the eighth parts of the signs, in which all the ancient craftsmen thought the equinoxes and solstices to happen, might fall on the Kalends themselves of the succeeding months. I understand that this is said by many, from which we ourselves have not sometimes recoiled. But that this is by no means true is gathered from all the preceding argumentation. For those who once felt thus did not place the eighth parts after the cardinal points of the signs, but in the cardinal points themselves; while they placed the beginnings of the signs at the eighth degree before [them]. ^C And regarding the Julian year, the matter will be clear if one wishes to estimate its form from Ovid, Columella, Pliny, and others, by whom the ratio of that year is expressed. For they place the ingress of the sun into the dodecatemoria at about the eighth day before the solstices and equinoxes; nor has it been heard of thus far that a civil equinox or solstice was deferred by Sosigenes or Cæsar to the Kalends of the following months. Which was absolutely necessary if either the ancients had been accustomed to such craftsmen, or if they had wished to transfer their examples into their own year.

Regarding this approach of the sun to the signs, Servius, most ignorantly, says in his Commentary on the Second Georgics that the time was not fixed the same by all: "One must know," he says, "that all astrologers disagree on the rising of the stars according to the reason of the climates: but this disagreement does not proceed beyond seven days; for there are seven climates themselves. Hence it is that some say the sun comes to each sign on the fifteenth day of the Kalends, others on the fourteenth, others down to the eighth; nor does anyone proceed further." These are the most empty nonsense of an unrefined mind. ^D To finish what remains to be explained concerning the Julian year, which days were established by the decree of Julius Cæsar, or Sosigenes, as the start of the cardinal signs in the Julian Calendar is not as easy to say as I see it is commonly taken. For most think that the vernal equinox was established by Cæsar on March 25th; the summer solstice on June 24th; the autumnal equinox on September 24th; and finally the winter solstice on December 25th, all on the eighth [day before the] Kalends. Thus it is gathered from Columella, Book IX, Chapter 14, and Book XI, Chapter 2; and Pliny asserts this clearly in Book XVIII, Chapters 25 and 28. In this way, the interval from the vernal equinox to the summer solstice is 91 days (excluding the other term), from the solstice to the autumnal equinox 90, from the autumnal equinox likewise 90 to the winter solstice. Hence to the vernal equinox, 90 days. Thus the days of the whole year are totaled at 365. Yet these very intervals of the cardinal points not only Varro, but — what is surprising — Pliny himself, in that 25th chapter of Book XVIII, has divided in a far different way. To start with Varro: here in Book I of *De Re Rustica*, Chapter 28, speaking of the Julian year, that is, of the "civil days which now are," he says: "from the vernal equinox to the solstice he counts 92 days; hence to the autumnal equinox, 96 days; from this to the winter solstice, 89 days. Thence to the vernal equinox 85 days." Three days are missing to complete the year. Now indeed, if the vernal equinox is placed on the 5th day before the Kalends of April, that is March 25th, and 90 days are added, the calculation ends on the 7th day before the Kalends of July, June 25th; then with 96 days added, the equinox will fall on September 29th; and the winter solstice, with 89 days added, will fall on December 26th; there will remain 88 days to complete the year. But Varro counts 45 days from the winter solstice to Favonius, and 40 days from Favonius to the vernal equinox: which, collected, make no more than 85. But the interval from the summer solstice to the autumn equinox seems erroneous; which, against the consensus of all others, is finished in 96 days; then also the other, from the winter solstice to the vernal, which is shorter than is just. But look, Varro confuses things again, who in the same chapter attributes 91 days to the vernal season, 94 to the summer, [au]

autumni xc, hiemi lxxxix; which temperate seasons indeed begin before the cardinal points themselves: spring from Favonius, which begins to blow from the 8th day before the Ides of February until the 9th day before the Ides of May; summer from then until the 8th day before the Ides of Sextilis; autumn from this day until the 10th day before the Ides of November; the remainder he assigns to winter. If you calculate these intervals one by one, excluding the prior limits, you will find that for the former, 91 days correspond, for summer 90 days; for autumn 95 days; for winter 89 days. Thus, Varro is not in the least consistent with himself.

Pliny, indeed, is no more consistent with himself, and his text is held to contain a most manifest error. "The hinge," he says, "of the seasons is established by a fourfold distinction of the year through the increase of light. This is increased from the winter solstice, and is equalized with the nights at the vernal equinox, in 90 days, 3 hours. Then it exceeds the nights until the solstice by 93 days, 12 hours, as far as the autumn equinox. And then, ^B equalized in day, it proceeds from there to the winter solstice in 89 days, 3 hours." In these words, the definition of the interval which pertains from the summer solstice to the autumnal is missing. Therefore, we ought to read after "12 hours," in this manner: "and from there in 90 days, 11 hours until the autumn equinox." For the three intervals expressed here produce 272 days, 17 hours. With that subtracted from 365 1/4 days, the remainder is 90 1/2 days. Wherefore, it was according to the mind of Pliny that Julius Caesar described these annual intervals.

From the vernal equinox to the solstice, 93 days, 12 hours. From the solstice to the autumnal equinox, 93 days, 12 hours. From the autumnal equinox to the winter solstice, 89 days, 3 hours. From the winter solstice to the vernal equinox, 90 days, 3 hours. Having noted these things, if the vernal equinox is set on March 25th, adding 93 days, the calculation ends on June 26th. From here, after 90 days, the autumnal equinox is conjectured to fall on September 26th, and the winter solstice on December 24th, or 25th, so that from there to the vernal equinox the remaining days are 90. Thus, by two days in the summer solstice and the autumnal equinox, Pliny was inconsistent with himself. I would believe that the civil summer solstice was fixed by Sosigenes on June 24th, and the equinox on September 24th, and the winter solstice on December 25th: so that they might fall on the eighth day before the Kalends of the four cardinal signs. ^C In the Calendar which Luca Gaurico published under the name of Julius Caesar, the vernal equinox is ascribed to the 7th day before the Kalends of April, the ninth day from the sun's entry into Aries, and the summer solstice likewise to the 8th day before the Kalends of July, the seventh day after the sun entered Cancer. But one must be very ignorant to persuade himself that this is Julius Caesar's Calendar, as we have demonstrated in Book VI, *De doct. temp.*, chap. XII.

Finally, if anyone wishes to know the true year's cardinal points in the first Julian year, he may learn from the following table; in which we have also conjectured the mean entries of the sun into the signs of the zodiac from the Diagram, Book I, page 31.

Table of the mean and true entries of the sun into the cardinal signs in the first Julian year.

| MEAN CARDINAL POINTS | TRUE CARDINAL POINTS | | :--- | :--- | | Vernal equinox: March 22, 23, 47' | March 22, 23, 47' | | Summer solstice: June 24, 21, 11' | June 24, 23, 3' | | Autumn equinox: September 24, 4, 39' | Sept. 24, 23, 54' | | Winter solstice: December 23, 12, 6' | Dec. 25, 11, 11' |

From this it appears that Sosigenes wished to express the mean entries of the sun into the signs rather than the true ones: which he achieved almost everywhere, except in one, the winter solstice. Nevertheless, most writers, while they re-read the cardinal points of ancient astronomers established at different times, have through carelessness transferred them to the Julian year. Furthermore, Sosigenes himself seems to have been little consistent ^D in defining this matter for himself. For in three commentaries (says Pliny, Book XVIII, chap. XXV), although he was more diligent than others, he did not cease to doubt, correcting himself. Therefore, he bound the cardinal points to different days, from which that variety among writers in establishing the equinoxes and solstices in the Julian year seems to have stemmed.

CHAPTER VI.

On the false opinion of Scaliger concerning the solstices of the ancient astronomers. Against whom it is demonstrated that they neither thought the midday sun constantly occurred under the tropic, nor that the solstice occurred in the entire zodiacal sign. Geminus explained.

The discourse introduced by us here causes us to remember a certain comment of Scaliger, which is read in his Notes on Manilius (page 157), and in a certain letter to Mamert Patisson, which is the fourth of the first book of his recently edited letters. "There," he says, "at the very roots of astronomy (those are the words of the letter), he believes that this was the opinion of the ancient Greeks—of Eudoxus, Meton, Cleostratus, and Euctemon; and lastly down to Eratosthenes and Hipparchus—that the meridian sun always occurs under the tropic, and the day is eternal. Likewise, that the solstice does not occur at the point of Cancer or Capricorn, but in the entire zodiacal sign." I do not remember reading the former of these in the latest edition of Manilius: but the latter exists in the Notes to Book I of the *Isagoge*, where he treats of the *Antiscia*. But both are not only ridiculous, but are also falsely attributed to those ancient astronomers. For neither of the two, concerning the perpetual light under the tropic, can stand, unless we wish to believe that those ancients considered that parallel to be outside the horizon—however great it is—by…

virtue of assuming such a position for the sphere that the further one approaches the equinoctial, the greater the part of the summer tropic that would descend below the earth, and the smaller the part that would emerge, until one reached a place where that circle is divided equally by the horizon. It is therefore absurd to persuade oneself that either Eudoxus, or his contemporary Meton, or anyone else who might lay claim to the title of astronomer, was so foolish as to believe that there was perpetual day on the border of Egypt; for Syene, which is situated under the tropic, is located in that region. Nor can it be comprehended by any reasoning that the sun, when it arrives at the tropic, makes perpetual light without night, unless we think that it stands immobile there; which cannot be defended as something those astronomers suspected, unless we wish to assume that they thought there was no night interrupted by day in Greece as well, and where they were. Wherefore, to be silent for the moment about the others, certainly concerning Cleostratus, Meton, Euctemon, Eudoxus, and indeed even the more ancient mathematicians whose mention survives, no one can think such a thing without the utmost absurdity.

^B Another head of this claim is less uninitiated than that one, yet it is refuted more validly. For if Meton, Eudoxus, Calippus, and others before Hipparchus had judged that the solstices occurred during whole dodecatemoria, and not in a specific portion of them, I do not think they would have reported those very solstices as observed by themselves at specific moments of the days—as Meton, who noted that the solstice happened on that day which corresponded to our 25th of June; and as Calippus and the others whose decrees were noted in the calendars; just as one may see in Geminus and in the book of Ptolemy on the fixed stars, which we published in Greek. For Calippus, says Geminus (p. 15), placed the summer solstice in the first part of Cancer; Euctemon placed the winter one in the first part of Capricorn; Eudoxus, in the fourth. Truly, as Hipparchus asserts, Eudoxus set the hinges in the middle of the signs, that is, at the 15th degree, which we discussed in the chapter above. But if they believed the solstice was spread over the whole dodecatemorion, they would not have fastened it to specific days only, such as the first, fourth, or eighth from the ingress of the sun into a sign. Hipparchus, in book II, teaches, according to the opinion of Aratus, that the solstice occurs in the first part of Cancer, and that this was the opinion of the ancient mathematicians, either of all of them or of the greater part. "In this turning, therefore, it holds the beginning of Cancer. And by almost all the ancient mathematicians, or by most, the zodiacal circle was divided in this way." He excepts Eudoxus, who "places the tropical points in the middle of the signs." Ptolemy in Book III (p. 62 of the Greek edition) writes that the observations made by Meton and Euctemon would be more useful for denoting the true circuit of the sun, if they had not been delineated in a more general—that is, a cruder—manner, and if, moreover, the observation of the solstices had not been more troublesome and difficult. These words of Ptolemy clearly prove that this conjecture of Scaliger is most vain.

I had almost omitted what greatly concerns the matter, from the same Hipparchus, whom we just mentioned (book I, p. 18). For he demonstrates against Attalus that the equinoctial circle and the tropics lack breadth according to the opinion of the ancients; and that the equinoxes or solstices do not occur in different parallels: which he proves from the fact that they frequently assert that the zodiac touches the tropics "at one point," in one point, that is to say, it touches the tropical circles. To this, if the circles had breadth, the equinox, for example, would extend over many days: which the senses themselves refute. For equinoxes are distinguished by the eyes more easily than solstices. But truly the same reasoning prevails regarding the solstices, that they occur "exactly" and "by nature" on only one day, because the contact of the circles happens in only one point.

A single witness is cited by Scaliger for the credibility of this divination—Geminus: who in Chapter I refutes the opinion of certain ones who thought that Cancer and Capricorn were not joined with any sign, that is, that there was none which rose and set in the same place as either of them. Geminus refutes this, because it would follow that the turnings occur in the whole of Cancer: which is not the case; for they happen "in one point only, in theoretical argument." But it does not follow from that argument of Geminus that such was the opinion of Meton, Eudoxus, and astronomers of that kind. Indeed, as regards Eudoxus, that he was foreign to this error, besides those things which we related a little earlier, Geminus himself clearly signifies in Chapter VI on the months, where he censures a certain popular opinion of those who think the Isia among the Egyptians falls during the winter turnings of Eudoxus: which he proves to have happened 120 years before. Therefore, Eudoxus defined the winter solstice by one specific day.

And to touch upon even more ancient times, certainly Hesiod, most famous in the science of astronomy, who flourished in the century after the destruction of Troy, did not judge that either solstice occurred in the whole of the dodecatemoria, and over about thirty days on either side. For he writes in Book II of the *Works*, that Arcturus rises 60 days after the winter solstice: which passage we shall weigh later. Then, in the same book, he says that autumn begins on the fiftieth day after the summer turnings:

*Ηματα πεντήκοντα μετὰ τροπάς ηελίοιο,* *Ες τέλος ἐλθόντος θέρεος καματώδεος ὥρης,* *Ωραῖος πέλεται θνητοῖς πλόος.*

*Quinquagesimo die post solstitium,* *Cum ad finem venit æstatis laboriosa tempestas* *Tempestiva est mortalibus navigatio.*

^A These things are both sufficient and necessary to convince one of the falsity of Scaliger’s opinion, so that one might not rashly accuse those ancient astronomers of such great stupidity, especially Meton, Euctemon, Eudoxus, and finally the others up to Eratosthenes and Hipparchus.

CHAPTER VII.

^B But so that the opinion of the ancients concerning the cardinal points may be more clearly illustrated, and since many things pertaining to the same subject, not unworthy of knowing, are to be explained in passing, that passage of Geminus must be explained more accurately. Setting forth a fourfold order and position of the signs, Geminus (pg. 6) calls that the fourth which is said to be *kata syzygian* (by pairing); he teaches that this consists of those signs which rise from the same place and set in the same place: or those which are enclosed by the same parallels, such as Cancer and Gemini, Capricorn and Sagittarius, and the others which are at an equal distance from one or the other of the solstitial points. In this he criticizes the ancients, who believed that Cancer had no *syzygia* with any other, nor did Capricorn, but that both were *monachoi* (solitary) and *azygoi* (unpaired): since Cancer rises and sets more northerly than all signs, and Capricorn more southerly. For there is nothing that deflects toward the north or south as equally as these two. And so, except for those two, they arranged the remaining ten as follows:

^C *Pairing of signs according to the ancients.* Cancer—Unpaired Gemini and Leo Taurus and Virgo Aries and Libra Pisces and Scorpius Aquarius and Sagittarius Capricorn—Unpaired

*Pairing of signs according to Geminus.* Gemini—Cancer Taurus—Leo Aries—Virgo Pisces—Libra Aquarius—Scorpius Capricorn—Sagittarius

In both diagrams, this distinction is perceived: that the former determines the pairings of the ancients among those signs which are at an equal distance from the whole tropical signs, whereas in the other, the *syzygia* are signs equidistant from the tropical points themselves. Geminus refutes the ancients, because it follows from their reasoning that the solstices take place in the entire dodecatemory of Cancer. For since they are paired signs—those which make their risings from the same place and set in the same—as Gemini and Leo are, it is necessary that the days be equal in them, that is, the segments of the parallels above the horizon are the same: which cannot happen otherwise than if they are at an equal distance from the solstitial point. But the matter is otherwise; for the extremity of the Twins (Gemini) is the solstitial point itself; whereas the Lion (Leo) is sixty degrees distant from it. He says that the same thing is shown more clearly in Libra and Aries, which used to form a pair, yet Libra rises and sets much more southerly than Aries. Thus Geminus.

But I am persuaded that the reasoning of the ancient mathematicians was far different from what Geminus thought, and that they were not correctly criticized by him. For they did not hold that the cardinal points were at the very beginnings of the signs, but in the middle—that is, they placed them at the fifteenth degree: which Hipparchus asserted to have been the opinion of Eudoxus, concerning whom we treated more fully in Chapter IV. And even if it were not Eudoxus’s, it was certainly the opinion of those ancients who arranged the paired signs among themselves in the way that Geminus writes. For in this way it will be most true, as those ancients thought, that Libra and Aries were *syzyga* (paired) signs, because they were equidistant from either solstice, that is, from the fifteenth degree of Cancer and Capricorn. Then it follows that Scaliger (In Manil., pg. 157), whom we mentioned in the preceding chapter, concluded wrongly from that opinion of the ancients which Geminus reports and disapproves; for he falsely suspected that those ancient ones established the *tropas* (turnings) and solstices within entire periods of thirty degrees, not at any specific point—that is a false suspicion, and he had no cause why this invention should please him so much that he should reproach the mathematicians for their ignorance. Truly, this is a wonderful portent of error, that Eudoxus is accused of it by the same man—indeed, that Eudoxus is asserted to be the author of it. In this, there is a manifold *aprosexia* (lack of attention). For if Eudoxus wrote that the summer *tropas* occur at the fifteenth degree of Cancer, and the winter ones at the fifteenth of Capricorn (being in the middle of the signs on both sides), and Scaliger thinks this is proven by the testimony of Eudoxus himself before Hipparchus; with what logic, I ask, is it consistent that the *tropas* were established by him in the whole sign? Furthermore, if the prince of astronomers Eudoxus felt this way, then it did not enter the mind of Meton and other more ancient ones who preceded Eudoxus—a thing which, however, Scaliger recklessly pronounced generally about all antiquity. Therefore, let that foul stain of opinion which he dared to inflict *akritos* (indiscriminately) upon Eudoxus and the ancient astronomers be erased from all memory of literature. But neither should Geminus’s criticism delight us; on the contrary, we both can and deservedly ought to defend those ancients against it.

Thus, Scaliger played with impunity in explaining and translating the *antiscia* of the ancients from the same source of error, which, consistent with what we have adduced for their opinion, may be accommodated to a truer sense. That this may be done briefly, the matter must be repeated from a little higher up.

From the most vain theory of the *apotelesmatikon* (astrological works), the dodecatemories of the zodiac have various *scheseis* among themselves, or *schematismoi*, which are commonly called aspects. From which we shall select only those in this place,

which pertain to our business, having called upon the authorities of Ptolemy in the *Tetrabiblos* (Book I), Paul the Alexandrian, Manilius, and Firmicus. Therefore, signs are either *oikeia* ^A (familial), or *cognata* (kindred); or *asyndeta* (inconjunct), and alien. The former are said to be those which are bound to one another by some aspect (*schematismos*) or by *oikeiosis* (familiarity); the latter are those which have none of those which the practice of astrologers has admitted. An aspect is either *kata diametron* (by diameter), as Aries and Libra, or *kata trigonon* (by triangle), or *kata tetragonon* (by square), or *kata hexagonon* (by hexagon), concerning which Geminus writes in Chapter I, and to which we have observed some things in the Notes on the same. A second kind of *oikeiosis*, according to which some signs are *prostassonta* (commanding), and others *hypakouonta* (obeying), which both Paul the Alexandrian and Manilius understand under the common name *akouonton* (listening). The third kind of *oikeiosis* is of the *blepontes* (those that see each other). Let me treat of ^B these latter two.

Ptolemy calls the signs *prostassonta* and *hypakouonta* those that are at equal distance from the same [point], or that are configured at either of the equinoctial points, because they rise in equal times and at equal parallels. "Those which have a figure or connection at an equal interval from the same or from either of the two equinoctial points: because they rise in equal times and at equal parallels." The zodiacal circle is cut in two by the equinoctial line at the equinoctial points. Hence one semicircle is called northern, having six boreal signs, which are Aries, Taurus, Gemini, Cancer, Leo, and Virgo; ^C the other, the southern, is endowed with the same number of signs, which are Libra, Scorpius, Sagittarius, Capricornus, Aquarius, and Pisces; the boreal signs are *prostassonta*; but the austral ones are *hypakouonta*. Ptolemy offers the cause of this matter: because in the boreal signs the days gradually increase, while in the other they are curtailed. For that reason, they ought to command, and the others to obey, by the decree of a most foolish art. In this manner we shall arrange those signs among themselves:

| Imperantia | Signa | Auscultantia | | :--- | :--- | :--- | | Aries | | Pisces | | Taurus | | Aquarius | | Gemini | | Capricornus | | Cancer | | Sagittarius | | Leo | | Scorpius | | Virgo | | Libra |

For these signs are *isanafora* (rising in equal time), and *isoparallela* (of equal parallels), because they are equally distant from both equinoctial points. They have equal, I say, parallels—not the same, as Camerarius translated. For that is suitable for the signs that "see" each other, which are equally distant from the tropical points: concerning which Ptolemy deals in the same place. Therefore, the second kind of *oikeiosis* is of those which are called *bleponta* (seeing), and *isodynamounta* (having equal strength). These are of such a kind that they are equally distant from one or the other solstice point. Furthermore, they are said to see each other because they render days equal to days and nights equal to nights; then ^D because they rise from the same parts of the horizon and set in the same. And these are the *syzyga* (yoked) signs, which we explained above from Geminus, such as Gemini, Cancer, Taurus, Leo, and the rest, about which we have said some things in the Notes on Geminus. *Asyndeta* and *apallotriomena* (inconjunct and alien) are called those signs which possess no connection with one another through any aspect from those aforementioned. Thus Ptolemy.

But Manilius and Paul the Alexandrian explain "listening" and "seeing" signs differently. For among them, the pairs of "seeing" signs consist of those signs which are equally distant from the whole tropical signs such as Gemini, Leo, Taurus, Virgo, and the rest; [alt-version omitted] which are described in the other schema of the *syzyga*, according to the ancients, as Geminus interpreted their mind. And so Cancer and Capricornus are *ableptoi* (blind) and *monachoi* (solitary), and they do not view other signs, but only themselves.

Again, they establish *imperantia* and *auscultantia* signs as those which are equally distant from the equinoctial signs, such that the former are boreal, the latter are austral. Therefore, Aries and Libra are outside the lot, and they neither listen to each other nor to others; but they are solitary and *monozona* (single-zoned), while the others are *homozona* (same-zoned). These may be viewed in the following table.

| Imperantia | Signa Manilii et Pauli | Auscultantia | | :--- | :--- | :--- | | Taurus | Aries *azygos* | Pisces | | Gemini | | Aquarius | | Cancer | | Capricornus | | Leo | | Sagittarius | | Virgo | Libra *azygos* | Scorpius |

Therefore, Aries has no commerce of commanding or listening, but it sees Libra, just as Libra sees Aries. "Aries is its own counsel: as is fitting for a prince, it listens to itself, and sees Libra," says Manilius. Taurus sees Virgo, and commands the Pisces; the Pisces see Scorpius, and listen to Taurus, and so for the rest. But Demophilus, describing the *prostassonta* and *hypakouonta* in the same way as Manilius and Paul, differs in this one thing: that he establishes Aries as commanding Libra, and Libra as ^D listening to Aries.

Julius Firmicus, Book II, Cap. XXXII, makes the "seeing" signs the same as the Ptolemaic ones and the *syzyga* of Gemini, and he professes that he is describing them from Ptolemy, Antiochus, and Dorotheus of Sidon, and calls them *antiscia*, namely, because they cast shadows that correspond in equal measure, and make them alternately. For in Gemini and Cancer the nights are equal, but in inverse order: indeed, the beginning of one coincides with the end of the other. The beginning of Gemini makes days and nights equal to the days and nights at the end of Cancer. Thus the beginning of Taurus corresponds with the end of Leo; the end of the former with the beginning of the latter. Thus they are called *antiscia* in the sphere, not only because they cast shadows into different parts, but also because

they have them equal in an alternating and contrary way; for our *antocci*, when it is winter for us, have a shorter shadow; but we have the longest: conversely, however, when we have summer, the shadows are shortest for us, and longest for them. Furthermore, the preposition ἀντὶ sometimes signifies equality, as in ἀντίθεος, which Achilles Tatius noted on Aratus's *Phenomena*.

In this theory of the *antiscia*, and in this passage, that most great man [Scaliger] erred monstrously, to use the words of his imitator, who expressed nothing from this except arrogance and rash confidence. For in his *Manilian* notes, he boasts that he was the first of all to explain the *antiscia* of the ancients, which had been unknown until then (pp. 155 and 159), and that he taught all the mathematicians what they did not know. Therefore, he says that the *antiscia* to the ancients were those signs which are equidistant from the four cardinal points; that is, both the *audientia* [those that hear] and the *videntia* [those that see]. Moreover, since the same ancients believed that the equinoxes and solstices were situated at the full dodecatemories [signs], of thirty degrees each, it happened from this that they also made those *audientia* which are equidistant from Aries or Libra, and those *videntia* which are equidistant from Cancer and Capricorn. These are completely alien from the truth. It is false that the ancients called any signs *antiscia* which were distant by an equal space from the whole cardinal signs, since they fixed the cardinal points to the very beginnings of the signs. Furthermore, in the *oikeioseis* [affinities] of the *antiscia*, only the solstitial points had a place, not the equinoctial; nor the whole dodecatemories of Cancer and Capricorn, but those very points of the solstices. Scaliger produced no other argument for this most vain opinion than the passage from Firmicus (book II, ch. XXXII), which he interpreted most poorly. The words of that writer are: "The *antiscia* are handed down to us by the teaching of the Greeks. For I would not have anyone suspect that this treatise does not exist among the Greeks. For if Ptolemy follows no other method than that of the *antiscia*—and Antiochus, when he says that Libra does not see Aries because of the earth, which is in the middle; he touches upon the theory of the *antiscia* as if through a mirror." To these, Firmicus adds a description of the *antiscia* from Dorotheus of Sidon, like the one we rendered earlier, namely, in which signs are equidistant from the tropical points: which is the unique and most true definition of the *antiscia*, known to antiquity. ^B But Scaliger, from those words of Firmicus, gathers first that the *prostassonta* [commanding] alone, and the *hypakouonta* [obeying], are called *antiscia* by Firmicus: then that the *antiscia* of Antiochus are falsely confused with those of Ptolemy, since they are different; for the *antiscia* of Antiochus are those of the ancients, in which comparable signs are removed equally from the entire cardinal dodecatemories, as are Aries and Libra. These are Scaliger's words. In these, he errs totally, both from the truth of the matter and from the mind of Firmicus. Firmicus calls only those signs *antiscia* which Ptolemy calls *bleponta* [seeing], not [the] *imperantia* [commanding], namely only those which are equally distant from the solstitial points; nor are those things which Antiochus argued different from the *antiscia* of Ptolemy or Firmicus. Firmicus says that Antiochus made obscure mention of the *antiscia* in those words in which he said the Ram does not see the Balance because of the earth that is in between. By which, certainly, he was signifying that it is another sign that the Ram sees, that is, the Virgin. What is more absurd than this Scaligerian reasoning, that the Ram and the Balance are said by Antiochus to be *antiscian* signs—that is, *videntia* [seeing]—which, as we have taught from Ptolemy, cannot see one another because of the earth interposed? If they are *bleponta*, of which kind the *antiscia* alone are, they certainly ought to see one another. He was quite blind and too hasty when he read this passage of Firmicus, as he did not perceive the clear conflict with his own opinion. And yet, Scaliger triumphs frequently, having, as he says, been the first to explain and disclose the *antiscia* of the ancients, in which he saw absolutely nothing at all.

Lastly, to return the discourse to the *videntia* and *audientia* signs of Manilius and Paulus Alexandrinus, it is probable that this theory of theirs, which establishes such pairs of signs, and which are distant by an equal space not from the cardinal points, but from their entire dodecatemories, flowed from that opinion of the ancients which we declared above; which had ascribed the same points not to the beginnings of the signs, but to their midpoints. Thus, indeed, both the commanding and obeying signs are as equidistant from the equinoctial points as the *bleponta* [seeing signs] are from the tropical points; but only these latter should be named *antiscia*. On these, see the disputation of the Mirandulan, book VI against the astrologers, ch. XII.

CHAPTER VIII. On distinguishing the risings and settings of the stars, of which mention is made among the authors: which matter is instructed by certain rules and examples; Theophrastus, Varro, Pliny, Columella, Ptolemy, and others are either illustrated or corrected; what is the admission of the temporary and the late. The place of Genesis is explained.

Those risings and settings of stars which are computed from astronomical tables, such as we described at the end of the first book, are the true ones, and accurate, and not those that are clearly apparent, even the heliacal ones; for in this latter kind (for regarding the others the matter is explored, that they can by no means be discerned by sight) the extreme limits of appearance are collected; that is, the very moments in which they are thus first or last seen, so that they cease to be seen beyond them. Wherefore, because they then happen closer to the horizon, and are usually still hidden by intervening mists and vapors, the same times are rarely expressed for them by writers, which the method of the tables exhibits; but those risings and settings are referred to a little before or after. And those things are to be recalled to memory which we handed down in the third chapter of this book from Geminus (ch. XI, p. 28); that true matutinal risings and settings, or non-apparent ones, are prior to the *phainomenois*, that is, the apparent ones; on the contrary, that apparent vespertine [settings] happen before the true ones: which the thing itself teaches, and the examples which we have cast into the table demonstrate. For there, heliacal risings, or matutinal apparent [risings], are later than the cosmical ones, and heliacal settings, or vespertine apparent [settings], precede the acronychal, or true vespertine ones. Then in vespertine risings and matutinal settings, from which...

discourse on the rising and setting of the stars.

far distant from the heliacal [risings], the same thing happens, as we declared in that chapter. For when the sun, being carried by its own motion against the impetus of the first sphere toward the rising parts of the sky from the setting, leaves a star behind once it has overtaken it, and strives more and more into the consequent. ^A Thus it happens that, when it is positioned in the east and looks directly toward the west—which is the true cosmic setting—it still hides the star with its own rays and does not allow it to be seen; later, when it has moved further away, we look out for it as it gradually sets before its rising, which happens over the following several days. Conversely, when the sun is in the west, having the diametrically opposed star, which is the true evening rising of the star, it subsequently proceeds to hide it and gradually creeps toward it. Therefore, several days before that time of opposition, the star had already followed the setting sun with its own rising, which they call the apparent evening rising.

Hence, among those writers who followed the same position and observation of the sky, the ^B phases of the stars are noted for several days before or after the true risings and settings: because they generally followed the apparent ones. And because these do not happen on a single day and at a single moment, they are therefore usually repeated during the same times and spread over several days. But in designating these, many speak obscurely and perplexingly; they signify neither the times of the risings and settings nor the species clearly, and they hardly offer the reader a suitable handle for any conjecture. Therefore, use and judgment are especially needed to discern those things for which either no or very meager evidence is provided for predicting the sort of phase. Added to this is the diversity of places and regions in which those ^C risings and settings took place; the authors of this variety, having often taken no account of the fact that things observed in other places and at other times were not composed from the same parapegmata, mix them up with one another; this makes the investigation of these matters tedious and almost inextricable.

But so that, in inquiring into these things, beginners might hold to a certain path and rule as far as possible, this—which we noted a little while ago—should be observed, namely that apparent phases rather than true ones are employed by the writers; then also that the apparent morning risings and settings ^D are later than the true ones; whereas apparent evening risings and settings are earlier than the true ones: these things being known, I say, we shall achieve what we want by a certain method. First, therefore, it is fitting to search for the point of the zodiac at which the proposed star arrives above and below the horizon, from our table, or, if it is not contained therein, from the method of the canons. Next, if a certain time of year is defined by the author, compare the degree of the ecliptic rising or setting with it in the Julian Calendar, and observe in it the celestial month to which that degree belongs. If the day is expressed by the author, and it agrees with the degree you have found, you will understand it to be the cosmic rising or acronychal setting. But if it is in the opposite part, if the time has been declared only in a general way, one must guess from the context of the discourse, with the caution that from two nearby risings and settings, you should choose the apparent one rather than the true, unless both—which is rarer—have been grasped by the writer; for then it will have to be observed which is prior to the other, from those things which we prescribed a little above.

If the rising or setting is conceived in any way, a conjecture about the time must be made by gathering the species of the rising or setting itself from the author’s words; afterward, the point of the zodiac rising or descending with the star must be sought in the Calendar; finally, one must deliberate, just as above, whether the time is true or apparent. In those stars which our table contains in the eighth chapter of the previous book, the expressed moments of all risings and settings lighten this labor. But because, as was said in the immediately preceding chapter, apparent risings and settings are not yet clearly calculated by the astronomical method which we pursue there, therefore the risings and settings which are indicated by the authors are to be ascribed to the same, just as they anticipate or follow, by a small interval, the rising and setting of their own kind noted in the table.

Since, however, writers have drawn what they report about the stars from various parapegmata—that is, Italian, Greek, and Egyptian, or those of intervening regions—sometimes without any distinction, there is need for judgment in discerning these things, and in the stars which we have described, the calculation must be attempted for both positions of the sky, Roman and Alexandrian: the account of the remaining tracts will be established in one way or another from these.

Thus, in the centuries before or after the Julian edition, with a few things usually subtracted there, and here things added to the days corresponding to the Julian time, we shall investigate the risings and settings of the stars. In all of which, excessively accurate diligence is idle, nay, even foolish, since not even those authors whom we strive to follow thought so much was to be required of themselves in that matter.

These things are prescribed too dryly and with little utility unless their use is opened up by examples: which we shall try here in a few cases as a specimen for others. We shall speak about Sirius and the Pleiades more fully in the following chapters, as intended. Therefore, we shall refrain from examples of these for the moment. Theophrastus in Book IV of *Historia plantarum*, ch. 12, assigns [the cutting of reeds] to Boedromion: nor does he indicate whether he is speaking of the rising or the setting. *The cutting was wont to be done in season, up to the time of Antigenides, when they used the tibia more simply, under Arcturus, in the month of Boedromion.* However, that it ought to be understood as the rising is suggested by the degree of Virgo, at which, in the Julian century, it was raised above the horizon, namely 14.

Moreover, the 26 days of Parthenon are noted in the Calendar on September 21; but in the age of Theophrastus, it happened some days earlier. In conclusion, we know that Boedromion was the third lunar month from the solstice. Our Ptolemy compares the rising of Arcturus to September 26 and October 3, correctly.

^B Pliny (lib. XVIII, c. XXVI) asserts that the same star Arcturus makes its evening rising on the 7th before the Kalends of March, but Columella on the 9th before the Kalends. In our table, the acronychal rising of Arcturus occurs at the 14th degree of Pisces, that is, the 14th of Ichthyon, which corresponds to March 5 in the Calendar. Truly, as has been said often, the true evening rising, which the table provides, is later than the apparent one. Therefore, the star was observed rising a few days after the setting of the sun, until it reached its true rising. But Firmicus, lib. VIII, cap. XIV, writes that Arcturus rises in the fifth part of Sagittarius: which is most false. Some read that the acronychal setting happens in that part: for which he imprudently substituted the rising. The acronychal setting in the Julian century used to happen in the 4th part of Sagittarius, but the heliacal rising in the 11th part of Scorpio. Furthermore, the 11th day of Scorpionis is noted in our Calendar as the day before the Nones of November: around which day it is placed by Pliny and Columella, that is, a few days earlier, as is clear from the Calendar which we have fashioned from both of them and Ovid, since the apparent evening setting precedes the true one. Finally, Columella lib. IX, cap. XIV, writes that Arcturus rises fifty days after the Dog-star: which is true concerning the heliacal rising. Sirius rose for Caesar in the 8th of Leontonos, that is, August 11, and Arcturus in the 27th of Parthenonos, an interval of fifty full days.

Polybius lib. I writes that the Romans crossed from Sicily into Africa between the rising of Orion and Sirius, during a stormy tempest. He understands by both the heliacal rising. For Sirius in the 8th of Leontonos was starting to rise at the beginning of August, Orion a little after the solstice. Therefore they sailed in the month of July. Thus Hesiod circumscribes the time of harvest and threshing by the rising of Orion:

.. Εὖτ’ ἂν πρῶτα φανῇ μένος Ὠρίωνος. When first the strength of Orion begins to appear.

The bright star in the chest of the Lion sets on January 27, as Columella writes, and Ovid on the 24th. In our table, the same star sets in the 3rd of Hydronos in the morning, exactly as Ovid reports, January 25. Wherefore it is to be understood as the cosmic setting. But Columella asserts that the bright star in the chest of the Lion rises on the 9th before the Kalends of August and the Lion rises in the midst on the day before the Nones of August. Which cannot be accepted concerning the heliacal [rising]; which in the 18th of Leontonos, August 12, began to appear at first, it can be referred to the true and cosmic [rising]. And yet Pliny lib. XVIII, cap. XXVIII, says, "On the 3rd before the Kalends of August, the royal star in the chest of the Lion is submerged for Caesar in the morning." These words demonstrate the morning setting, which occurs in the 3rd degree of Aquarius, January 24. Therefore the passage of Pliny is faulty, and it must absolutely be read "emerges," or "is emerged," that is, it rises with the sun.

Geminus places the setting of the Lion consistently in the 2nd of Aquarius. Ptolemy writes that the king-star of the Lion sets on the 6th before the Kalends of February, or January 25. But the Greek [text] edited by us establishes its setting in January, or the 22nd of Tybi; and likewise the 6th of Mechir, or February. The 6th of Mechir agrees with the last day of January.

Among the Hyades, there is the most brilliant one, which, placed in the eye of Taurus, is called by the Romans the Palilicium star. Hesiod reports the setting of the Hyades at the same time when the Pleiades and Orion set; and he writes in the second book that it is opportune for plowing:

Αὐτὰρ ἐπὴν δὴ Πληϊάδες θ’ Ὑάδες τε, τό τε σθένος Ὠρίωνος Δύνωσιν, τότ’ ἔπειτ’ ἀρότου μεμνημένος εἶναι.

Theophrastus says that Orion rises at the beginning of "opora," and sets at the beginning of winter, where he takes "opora" for the summer already inclining, some days after the solstice is finished. In our table, it makes the heliacal rising of the bright star of Orion's foot in the 18th of Carcinonos, July 12. ^C But in the age of Theophrastus, and at Athens, it used to happen earlier. Truly, after the day of the heliacal rising calculated from the tables, the same morning risings are reported as apparent. Therefore this rising was propagated up to the beginning of "opora." But the morning setting of the same bright star occurred in the 5th of Scorpionos, October 29; in the 12th of Scorpionos, November 5, the middle belt sets; the right shoulder in the 21st of Scorpionos, November 14. Therefore it is true that Orion set at the beginning of winter. The things reported about the rising of Orion by Ovid, Columella, and Pliny also agree, as when Ovid and Pliny assert that the belt rises on the 6th before the Kalends of July. For the middle star of the belt in Egypt rose heliacally in the 4th of Carcinonos, at Rome on the 17th; but before this, another star rises in the same belt.

^D This signifies the morning setting or cosmic [setting]. For in our table, the Palilicium sets in the morning in the 9th degree of Scorpio at Rome, that is, November 2, the day on which Columella writes that the head of Taurus makes its setting, as does Geminus from Calippus. But in Egypt, the morning setting used to happen in the 11th degree of Scorpio, November 4. Furthermore, the same Columella says that the Hyad sets in the morning on November 21, and also that Rhapsode under the name of Ptolemy edited by Leonicus. For our Greek [text] throws the morning rising of the Hyades into November, or the 16th of Athyr. According to Geminus, the setting of the Hyades occurs on the 27th of Scorpionos, from Euctemon; from Eudoxus, on the 29th, which in the age of Julius Caesar corresponded to November 20 and 22; but in the age of Euctemon and Eudoxus, those days preceded them. This is the apparent morning setting of the Hyades.

^A Since the true setting comes after, it extends for some days; just as the true evening rising is later than the apparent ones, which are often repeated in the Fasti for many days before it. The true evening rising of the Hyades at the time of July corresponded to the 21st of Scorpius, or November 14, following the true morning setting. But an apparent evening rising preceded it: which the Greek parapegma of Ptolemy places on the 6th of November, or Athyr. Geminus, however, places it on the 22nd of Zygon, in the age of Eudoxus; Pliny, book XVIII, chapter XXXI, says that the Hyades rise in the evening on the sixth day before the Kalends of November, at that same apparent rising. Soon, however, he says to Caesar that the Hyades rise with the sun on the day before the Kalends of November. False. For that happens at the time of spring. He wrote, or should have written, "when the sun is setting." Pliny, in book XVIII, chapter XXVI, reports the same Hyades star setting in the evening according to Caesar's calculation on the 15th before the Kalends of May, that is, the 26th of Crionos, on which day the heliacal setting of that star falls according to our calculations. Ptolemy, in the edition of Leonicus, says the Hyades emerge on the 6th of April. Nay, they were submerged at that time and were setting with the sun, which they finally did on the 17th of April. Hence, in the same author, they are said to be hidden in the evening on the 12th, 15th, 16th, and 17th of April. For the apparent morning rising of the Hyades began in the Julian Fasti on the 11th of Didymonos, June 4. Whence Ptolemy, as edited by us in Greek, must be corrected, who says that the bright star of the Hyades sets in the evening on June 4, which is false. Therefore, he immediately says of June: έῷος, "in the morning." Geminus is no less to be corrected, who sets the evening rising of the Hyades on the 30th day of Tauronos. Instead of this, the morning rising must be substituted; which he soon after, following Eudoxus, sets on the 5th of Didymonos. ^B Ovid and Columella write that Capella, which is in the back of Auriga, rises on the Kalends of May. Pliny, on the 8th of the same month. This is true in Egypt concerning the heliacal rising, which falls on the 9th of Tauronos. At Rome, however, it is the 15th of Crionos, April 5. Our Ptolemy exhibits the morning rising of Capella on March 29 and April 18. Geminus, following Euctemon, on the 9th of Tauronos.

Ovid says that the Dolphin rises in the evening on the 4th of the Ides of June: "The sailor sitting in the ship will see the Dolphin, he says, When the humid night has risen with the pulsed day." Pliny and Columella agree. Our table also agrees exactly. For it makes the bright star of the tail of the Dolphin rise acronychally there precisely on the 16th of Didymonos, which is the 4th of the Ides of June.

Columella and Ovid have written that Lyra, or the Harp, sets in the evening on January 21 and 23. This is a heliacal setting, not acronychal, as is noted by some. For the heliacal setting of Lyra happens on the 6th of Hydronos, January 27.

Columella, in book XI, chapter II, is the author that the Eagle sets in the evening on the 5th before the Kalends of January. Pliny, in book XVIII, chapter XXVI, on the 3rd before the Kalends, in Attica and neighboring places. They speak of the heliacal setting; which happened at Rome on the 11th degree of Capricorn, that is, January 1; at Alexandria on the 5th degree, the 6th before the Kalends of January. The Greek Ptolemy says the Eagle sets in the evening on December 27, or the 27th of Choeac, and the 30th. The same happens to Geminus on the 7th of Capricorn, with Euctemon as author. Eudoxus reported that it rises in the morning on the 26th of Toxonos. Thus, in our table, its heliacal rising falls on the 28th of Toxonos, which is December 21. The Greek Ptolemy, December 25 or Choiak 25. The Rhapsodist published by Leonicus erroneously has the evening rising of the Eagle on the 11th before the Kalends of January. For this happens on the 9th degree of Gemini, June 2, to which both Columella and Pliny assent, as well as Ovid, and indeed the Rhapsodist himself.

Varro, book II of *De Re Rustica*, chapter II: "The best time for mating (he speaks of sheep) is from the setting of Arcturus to the setting of the Eagle." Also Pliny, book VIII, ch. XLVII: "Mating for all (is) from the setting of Arcturus, which is the third day before the Ides of May, to the setting of the Eagle, that is, the 13th before the Kalends of August." This place, which is generally corrupted, is to be read thus. They understand in both cases the cosmic or morning setting; for Arcturus began to set at the 4th degree of Gemini, that is, May 28, at Rome; at Alexandria, on the 13th of Tauronos, that is, May 6. The Eagle also sets in the morning at Rome on the 27th of Carcinonos, that is, the 12th before the Kalends of August. Both of them assign this single time for the mating of sheep. "Afterwards, the conceived lambs are weak," says Pliny: "which the ancients called 'cordi'." But that there was another time, and indeed in the opinion of some more convenient, the same Pliny soon indicates in these words: "Many prefer winter lambs to spring ones: because it matters more that they should be strong before the solstice than before the winter; and (that) this animal alone is usefully born in the winter." Virgil, in Book II of the *Georgics*, among the praises of Italy, reckons this, that there: "Twice the flocks are pregnant." To which Servius thinks that the following from Eclogue II pertains: "Milk is not lacking for me in summer, nor in the cold." Wherefore it is the conjecture that there was one lambing time in the summer and another in the winter, not only in Italy, ^D but also in the East, as in Syria and Mesopotamia. In Genesis chapters 30, 41 and 42, this double mating is signified: of which one is called timely, the other late. Therefore, Jacob placed the peeled rods in the troughs during the more mature and timely (one), so that varied and spotted flocks might be born, which had fallen to him as wages; because from that former lambing, stronger and more robust beasts were born. In the late one, he did not place the rods, so that the beasts born from it, which were weaker, might belong to Laban. Concerning which passage Jerome in *Traditions* and Augustine, Question 95 on Genesis, assert that the flocks were pregnant twice in Mesopotamia, as also in Italy. "But the nature of the Italian and Mesopotamian sheep is said to be one," says Jerome. But in the consti-

contention over the season of both breedings, authors vary. For some think the "timely" [breeding] is that which occurs in the spring, and that the "late" is the autumnal. Thus Aben Ezra and other Hebrews, whom Munster, Fagius, and Mercer follow, and among our own, Pererius and Delrio. Others, on the contrary, judge the timely breeding to have occurred in the autumn, and the late in the spring. Thus Vatable. Nor does Saint Jerome think otherwise in his *Traditions*, if we diligently attend to his words: "If ever the sheep and goats were mounted in the early season, because the spring offspring is better, he would place rods before them, that a variegated brood might be born." The spring offspring is that which is born in the spring. This, therefore, must have been conceived at the beginning of winter or the end of autumn. For sheep carry their young for five months, or 150 days; as Aristotle is the authority in Book VI of *History of Animals*, and Pliny in the place cited.

That I should favor this latter opinion rather than the other is primarily due to the fact that the words "timely" and "late" are used elsewhere in Sacred Scripture in the manner that this opinion defends. As when early and late rain is spoken of in Deuteronomy 11:14 (Heb. *moreh*, *yoreh*, and *malkosh*). Regarding which passage R. Solomon interprets *yoreh* as the rain which, falling after sowing, irrigates the land and the crops, but *malkosh* as that which comes toward harvest. Aben Ezra agrees with this, as does David Kimhi in chapter 2 of Joel, verse 24, where both rains are mentioned, and Kimhi says the timely one occurs in the month Marcheswan, and the late one in Nisan. The Chaldean in the same place compares the late one to Nisan.

The origin of both appellations, I think, was twofold. The first and most ancient flowed from the very nature of things and from the use and convenience of rustic labors. For those are wont to be called timely which happen early and at the very beginning; late, which happen later and toward the end. All rustic work begins with plowing and sowing, and ends with the harvest. Therefore, the rain that comes at the very time of plowing and sowing deserves to be called timely and mature; that which comes a little before harvest, late. The second cause is sought from the beginning of the civil year, which the Jews started from the autumn and Tishri. Therefore, those things that happened at the beginning of the year were rightly called timely; those that happened when the year was declining, late. If these things are true, then surely the timely and late breeding was used by the same Jews in no other sense than that by which it is agreed among all that the rain is named and distinguished. It is therefore fair to understand the timely breeding as autumnal, and the late as vernal or aestival.

Moreover, in other respects, and due to the conveniences of different kinds, it could be called timely, or *proïmon*, because it happens early; and late because it happens when the year is already declining, since, as Eustathius observes in his commentary on the beginning of Book II of the *Odyssey*: "The year is a kind of small day: of which spring is the morning, because of the temperate weather at that time; summer is like the middle of the day; autumn is like the late afternoon; and winter is like the evening, which looks gloomy toward the sunset and beyond." A small year is the day. Its nature is as the morning because the air is temperate; the midday is like the summer; the afternoon is like the autumn; and the evening, with what follows, is like the winter. These points have been discussed somewhat more fully on account of the setting of Arcturus and the Eagle. And so much for the use of the method and the examples: since their treatment was intended to be proposed as an imitation for beginners, it will also be useful in subsequent books and disputations.

CAPUT IX. Concerning the rising and setting of the Pleiades, those things which have been handed down to memory by the ancients are explained. The passage of Virgil concerning them is inextricable. Most authors have been explained or corrected.

The preeminent observation among the ancients was that of the Vergiliae [Pleiades], which the Greeks call *Pleiades*: so much so that the year was called *pleion* by them, as Theo reports in his *Commentary on Aratus*. Lycophron indeed takes the word *pleion* for a year, in these words: *Eis pente pou pleiōnas imeirōn lechous*, "Longing to lie [there] for about five years." This also Hesychius has, although he brings forward another cause for this appellation: *Apo tou pantas tēs gēs tous karpous symplērousthai*, "Because all the fruits of the earth are full [at the time] of their turning." They are situated on the back of Taurus, six in number, says Geminus. Hyginus places them between the extremity of the body of Taurus and the tail of Aries; Aratus near the left ^B knee of Perseus, which word interpreters have received in various ways.

*Agchi de oi skaiēs epigounidos ēlithen pasai Plēiades pherontai.* Cicero: *At propter laevum genu omni ex parte locatas Parva Vergilias tenui cum luce videbis.* Avienus: *Pleiades femoris pariter sub fine sinistri Perseus protollit.*

Hipparchus in Book I of his *Phenomena* denies that they are near the left knee of Perseus. And so some have referred *epigounida* to the whole leg. See Tohen. The same Hipparchus reproves Attalus because he said there were six, when they are seven in number, as Aratus also sang; but that one scarcely appears. Theo adds that they form a triangle, the base of which looks toward the sunrise; nor is it contained in a large space: since it occupies one degree in length, and in breadth one-half and one-eighth, that is 37 1/2 minutes. Their middle one, which is also called the bright one of the Pleiades, is of the third magnitude; the others are of the fifth and sixth. Thus, although they are small, they were nevertheless believed to have the significations of great things. Cicero: *Hae tenues parvo labentes lumine lucent, At magnum nomen signi clarumque vocatur.*

For they distinguished the beginnings of summer and winter, and the times of harvests and plowings: so that no star is more famous among authors, or more frequent

^A than the stars of this cluster; and indeed, for the purpose of illustrating them at this point, we shall explain two things: one regarding the time of their rising and setting, and the other regarding the division of the year which the ancients assign to them. For there are just as many chapters in the confused hotchpotch of the Plinian commentator into which we shall inquire a little later.

Regarding the rising and setting of the Pleiades, the verses of Hesiod’s *Works* are trite but not to be omitted: Πληϊάδων Ατλαγενέων ἐπιτελλομενάων Ἀρχεσθ᾽ ἀμητοῦ· ἀρότοιο δὲ δυσσομενάων. Αἰ δή τοι νύκτας τε καὶ ἤματα τεσσαράκοντα Κεκρύφαται· αὖτις δὲ περιπλομένου ἐνιαυτοῦ Φαίνονται, ταπρῶτα χαρασσομένοιο σιδήρου. When the Pleiades, born of Atlas, begin to rise, Begin the harvest; but the plowing, when they set. For truly, for forty nights and days They are hidden; but again, as the year revolves, They appear, first when the iron is sharpened.

That here the matutinal rising, *phenomenon*, or solar, is signified, and the *dusis eoa*, or cosmic setting, not even children are ignorant of. In Hesiod’s age, that rising occurred in Taurus. The Vergiliæ are many stars: one of them is brighter than the rest, of the third magnitude. In the time of Hesiod it set heliacally in the 4th degree of Aries, 8'; it rose in the 11th degree of Taurus, 4'. But the first star toward the west made its heliacal setting in the 0 degree of Aries, 51'. The interval between the setting of the first of the Pleiades and the rising of the brightest is 40 degrees. Rightly, therefore, does Hesiod sing that the Vergiliæ are hidden for forty days. Now the Sun entered Aries by its motion in the time of Hesiod on March 31. Indeed, in the year of the Julian Period 3714, the true place of the Sun at the beginning of Aries was at Athens on March 31, at 1 hour, 24 minutes past midnight. Therefore, it entered Taurus on April 30. Accordingly, the bright star of the Pleiades rose on the 11th day of May. The last of the Pleiades rises to the east on May 16, at which time the harvest began in Greece.

Their matutinal setting occurred in the 19th degree of Libra, but it is *aethe,00* (invisible), and not observable. Therefore, around the beginning of Scorpio, an *epikatadysis phainomene* (visible setting) occurs, at the beginning of November. For the autumnal equinox during that same time falls at the beginning of October. Then, therefore, the time of plowing and sowing draws near, which Virgil expressed in these verses: Before you, let the Atlantides be hidden, And let the star of the burning Crown depart from Gnosus, Before you commit the due seeds to the furrows, etc.

By *Eoum*, he understands the matutinal setting, not, as Servius thinks, the heliacal one, who also ignorantly says that the Vergiliæ are not seen to begin in the month of November: as if they were obscured by the rays of the sun situated in Scorpio.

Virgil also mentions this same rising and setting in *Georgics*, Book IV, where he speaks of the double harvest of honey: They collect the pregnant offspring twice: two times of harvest: When the Pleiad shows her honest face to the lands, And has repulsed the despised rivers of Ocean with her foot. Or when the same, fleeing the star of the watery Fish, Descends in gloomier mood into the wintry waves of the sky.

Here he describes two times for harvesting honey: one after the rising of the Pleiades, in the spring; the other in autumn, after the matutinal setting: concerning which ^B Aristotle follows in *History of Animals*, Book IX, chapter 40, which is also Book V, chapter 22; he denies that honey is made before the rising of the Vergiliæ. But why does he say that the Pleiad, in setting, flees the Fish? Servius and the other interpreters I have seen understand this to be the southern Fish, into whose mouth Aquarius pours water; whence it is also called "watery." But this Fish rises at the time when the Pleiades set. Yet that is false. For at the moment when the Pleiad is situated in the matutinal setting at the elevation of the pole under which the poet wrote, the mouth of the southern Fish is little distant from the lower meridian; and in that position it is very close to that which Ptolemy calls the *eon promesouranema* (rising and culminating). The other fishes also have their rising and setting before the Vergiliæ. Therefore, it must be asked in what sense the Pleiad is said by Virgil to set while fleeing the fish; which, unless it is used concerning some star that is present, is not customary. For thus Quintus Calaber rightly writes in Book V that this same Pleiad sets fleeing Orion: ...And he was like a tempest, Dreadful, heavy with baleful squalls, Which brings to sailors a portent of shivering fear, When the Pleiad descends into the streams of the unwearied Ocean, Cowering beneath the famous Orion.

For the Pleiades precede Orion in their matutinal setting. But I truly do not see that they are said to flee the fishes, especially the southern one.

Varro, Columella, Pliny, and others write that the rising of the Vergiliæ occurs after 44 or 48 days from the vernal equinox. Varro in Book I, chapter 27, appoints 44 days; others say forty-eight; Columella in Book IX, chapter 14 (who, however, in Book XI, chapter 2, wrote that they rise on the Nones of May, that is, on the 44th day from the equinox); Pliny in Book XVIII, chapter 25. Whether this be understood of only the brightest and greatest of the Pleiades, or of the whole asterism, it is not true. For its heliacal rising at Rome occurred in the last part of Taurus, on the sixtieth day and more from the entry into Aries: that is, on the 20th day of May. But if this is to be understood of the entire asterism, that star of the Vergiliæ which pertains most to the east among the three brighter ones rose heliacally in the first Julian year in the 5th degree of Gemini, that is, over sixty-five days from the equinox. But this truly happened in Meton’s age in that position of the sky which is at Athens. For in the 4283rd year of the Julian Period, which is nearest to that in which Meton observed the solstice, the heliacal rising of the bright one of the Pleiades fell in the 18th degree, 46' of Taurus, which in that age corresponded to about the 15th day of May. The vernal equinox occurred in the year we mentioned, on March 27, at 0 hours, 28 minutes at Athens. The entry into Taurus by motion corresponds to April 26, at 18 hours, 56 minutes. Thus the sun held the 18th degree, 48' of Taurus on that night which intervened between the 14th and 15th of May, that is, on the 48th day after the equinox.

^D To this time, this interval of 48 days between the equinox and the matutinal rising of the Pleiad ought to be referred: not to the Julian age, nor to the location of Rome, but to that of Greece. And since the most famous,

and everywhere propagated, Metonic cycle of nineteen years had been—

^A and it is from the sixth part of Taurus that the Pleiads rise." (Although it is one thing to rise in the sixth part of Taurus, another for the Taurus of the Pleiads to take up the sixth part of itself; for this is the sixth part of the sign, which is five degrees. But Firmicus conceived it as the sixth degree.) Nor are the obscure words of Pliny, book II, chapter XLVII, to be understood otherwise: "For the rising of the Vergiliae is given to this (Favonius) in as many parts of Taurus, six days before the Ides of May." Where he says there are as many parts as there are days before the Ides of May. As it is true that in the age of Hesiod in Boeotia the heliacal rising of the bright Pleiad occurred around the sixth of the Ides of May, yet not in the sixth part of Taurus, but in the eleventh or twelfth; so it is false that this happened in Italy, Greece, or Egypt in the age of Pliny. Thus, many things are said here and there by authors in a confused manner, which must be measured by our method. According to Geminus, the Pleiad rises for Euctemon on the thirteenth day of the Taurones, from which the beginning of summer is also sought. But according to Eudoxus, the Pleiads make their rising on the twenty-second day. We, at Athens, in the time of Meton, find the heliacal rising of the bright Vergiliae in the 19th degree of Taurus, and indeed that of the last Pleiad in the 24th degree, 53'. Between these two is the later observation of Gemini. In the book inscribed to Ptolemy, concerning the fixed stars, the rising of the Vergiliae is placed on April 1st, then the 10th before the Kalends of May, that is, April 22nd, then the Nones of May, and the 4th of the Ides, and the 3rd of the Kalends of June. Thus, that writer, according to his custom, inserts partly false things, and partly things belonging to other times, into the same Myconus.

^B the Metonic cycle having been added by Cecropian art: And it settled in their minds, clever Greece held fast the matter Immediately, and sent the discovery into the long years.

Wherefore, although many things have been changed and innovated in astronomy and the distribution of the seasons by Hipparchus and those who followed him, skilled in celestial matters, that ancient Metonic calculation nevertheless remained among the common people, and indeed in the administration of rustic affairs, just as Columella testifies in book IX, chapter XIV. Of which kind he seems to be the rising of the Vergiliae defined by a space of forty-eight days after the equinox. And since this, as has been said, pertained to the site of Attica in the age of Meton, Roman writers rashly dragged it to the site of Italy and their own age. I had almost overlooked Ovid, who in his Fasti conjectures the rising of the Pleiads to be on the 11th of the Ides of May, which is the thirteenth day, and the fiftieth from the equinox, and, proceeding from the ingress into Aries, which he establishes on the 15th of the Kalends of April, the fifty-seventh. Theon, in his Commentaries on Aratus, asserts that the Pleiads rise on the 25th of the month Pharmuthi: which falls on the 20th day of April, ὅτε τοῦ θερίζειν καιρὸς ἐν Αἰγύπτῳ (when the time for harvesting is in Egypt). He adds that this happens fifty-two days after the equinox, and that the sun is then in the 17th part of Taurus. We, at the site of Alexandria in the age of Theon, that is, in the year of Christ 360, observe the heliacal rising of the bright Pleiad in the 25th degree of Taurus. The equinox was then on March 20th: from which, the calculated 52 days end on the 5th of the Ides of May, that is, on May 11th, the 16th of Epiphi. But the one which is on the extreme cusp toward the east had its heliacal rising in the 29th degree, 55' of Taurus, around May 17th. And so he speaks not of the heliacal, but of the cosmic. Again, in the age of Hesiod in Boeotia, this same last of the Pleiads to the east made its heliacal rising in the 17th degree of Taurus, that is, at 16, 7: and thus the words of Theon are to be taken in that miscellany of scholia, which distinguishes neither times nor the site of regions, provided they pertain to the heliacal. Manilius, book V, writes that the Vergiliae rise in the sixth part of Taurus; for thus his words are to be interpreted:

Taurus, as it is lifted headlong to the adverse rising, Leads the Pleiads, struggling to the airs of light, With the sixth part of itself.

To which Firmicus assents, book VIII, chapter VII: In ^C (For in the Greek there is no mention of the Pleiads, as we observe in the Notes.) But that he says it rises on the Kalends of April is evidently a hallucination either of the author or the interpreter; for he placed its setting on the third day after: which, in any case, precedes the rising.

Concerning the setting of the Pleiads, there is no less variety among writers; for some define the matutinal setting as 48 days after the autumn equinox. Thus Pliny, book XI, chapter XVI, where he also predefines the day as the Ides of November, from which the 48 days counted backwards end on September 27th. Therefore, they are to be counted after the equinox of Sosigenes, which Pliny placed on September 26th. But the same Pliny, book II, chapter XLVII, says that the Pleiads set 44 days after the autumn equinox, and that this happens on the Ides of November. In this way the equinox will correspond to September 28th or 29th. Yet the same author also repeats this in chapter XXV of book XVIII, by the prescription of Caesar. Columella, book IX, chapter XIV, reports that the Pleiads set 40 days after the equinox. Varro, book I, chapter XXVIII, [says] 30 days. To these, Pliny, book XVIII, chapter XXV, handed down that the matutinal setting of the Pleiads occurs according to Hesiod when the autumn equinox is completed: but according to Thales on the 25th, Anaximander the 29th, Euctemon the 48th. From all these, that opinion of Varro agrees most with Julius Caesar, if it is about the true, non-apparent matutinal setting. For we find this in the 3rd degree, 17' of Scorpio. Thus also at the time of Thales, that is, in the year of the Julian period 4113, the same true matutinal setting [was] in the 24th degree of Libra ^D

^A in comparison to, rather than with regard to, the exact risings and settings, the ancient mathematicians based their parapegmata on the argument that, as Theon reports in his *Aratea*, they publicly displayed their parapegmata with predictions of tempests, winds, and other things of that kind, which they had foreseen would happen throughout the whole year. The words of Theon are worthy to be recorded here: "The astronomers after Meton also placed tablets in the cities concerning the revolutions of the sun in the nineteen-year cycles, that in each year there will be such a winter, such a spring, such a summer, such an autumn, and such winds; and many things useful for the needs of men." But all these things are not wont to be observed at the very moments of the astronomical risings or settings, but some time before or after.

This is a point which is excellent. Truly, as has been demonstrated above from Geminus and Ptolemy, the acronychal rising and the true matutinal setting differ from the apparent ones. How many days are interjected between both, no one, so far as I know, has explained; but that there is an interval of some days, both reason itself and experience convince us. Wherefore, Anaximander is to be understood regarding the apparent setting of the Pleiades, and Thales regarding the true setting. In Hesiod, the ratio is not clear. For the brightest of the Pleiades in his age had its matutinal setting at the 18th degree, 47' of Libra. Perhaps the suspicion is not slight that Pliny, through inattention, may have taken the matutinal setting for the heliacal one. For this occurred almost at the equinox in the age of Hesiod. Indeed, concerning the three brighter ones, which lean toward the west, he placed the heliacal setting in the 1st degree of Aries, that is 0, 51'; the one situated on the eastern cusp in the 2nd degree, 13', and the most brilliant of all in the 4th, 8'. See how beautifully this mode of reasoning ^B corresponds to this. For regarding the matutinal setting, it is a very false notion. Moreover, in the time of Meton, and therefore in the time of Euctemon, the true matutinal setting of the Pleiad corresponds to 27th degree, 44' of Libra, to which it is necessary that some margin of space be added up to the *phainomenon*, of which there are also some degrees of apparent setting. For gradually, as the sun moves further away from the opposite region of the sky, the star is visible both at rising and at setting; and this occurs continuously for several days. For Geminus in chapter XI writes that true matutinal risings and settings are prior to the apparent; conversely, in vespertine ones, the apparent are prior to the true. Therefore, the apparent matutinal risings and settings, which the Greeks call *proanatolai* and *kataduseis heōs phainomenas*, more often follow the true ones, as long as the star preceding or following the sun's rising falls within a moderate interval. Thus also, before the vespertine rising and setting of the stars, many apparent ones occur; until the star follows the sun, which is concealed by a small space, with its own rising or setting.

^C What cause, finally, can be brought forward for that variation, which we also generally perceive in the age between authors of the same region and the region itself: while one prescribes other times for the rising or falling stars, and extends the day, so that they seem at times to depart somewhat from those limits which we have established by means of triangles according to astronomical rules and method. This happens because those writers, who set out to record the memory of events or to treat matters concerning the common use of life, describe these things with a popular scale, and with the judgment and estimation of the senses and the common people, not by a refined and subtle method. Wherefore, in all that time, which follows the *akribeis* (exact) rising and setting of the stars by a moderate space or precedes the vespertine ones, some choose one set of days and others another, on which they pronounce that the stars rise or set, especially when more vehement *episēmasiai* and notable changes of the air occur, which, based on an ancient opinion handed down by our forebears, were wont to be attributed to those certain stars. Regarding their effects and *episēmasiai*, ^D since the ancient mathematicians had a regard for these rather than for the exact risings and settings in their parapegmata...

Geminus in his parapegma reports from the description of Callippus that the Vergiliae (Pleiades) set in the 16th part of Scorpio. But Eudoxus in the 19th; Euctemon in the 15th, whereas Democritus had previously established it in the 4th. The book on the significations of the inerrant stars, which is attributed to Ptolemy, ascribes several days to the matutinal setting of the Vergiliae, namely October 19, 23, 27, and the Kalends of November, the 7th, 11th, and 13th of the same month, which settings can be reconciled with those astronomical decrees mentioned above by Geminus, so that they are understood not as true settings, but as apparent, in the manner we proposed just now. Indeed, in the age of Julius Caesar, the true matutinal setting of the Pleiades took place in the 4th part of Scorpio. From this time, after ten or fourteen days have intervened, the apparent setting will occur on the 44th or 48th day from the equinox. Both of these are imputed by Pliny most especially to Sosigenes and Julius Caesar.

At the same time of autumn, before the matutinal setting, the vespertine rising of the Pleiades occurs: to which, indeed, diverse days have been set by Geminus and Ptolemy. Geminus says that Euctemon established it in the 5th part of Libra, Eudoxus in the 10th. And that this is to be taken as the *alēthinē* (true) setting happened in the age of Hesiod. For then the Vergiliae were rising in Greece in the 10th part of Libra *akronychōs* (at sunset): however, in the time of Thales, in the 16th, in the same position of the region. But while Meton was living, in the 19th, and finally in the age of Julius Caesar, in the 23rd. And these are the *alēthinai* (true) and *akronuchoi epitolai* (acronychal risings), which, of course, the apparent ones precede. Moreover, these occur more frequently over repeated days. From which each one has taken for himself certain times, by which he might say that the Pleiades rise a little after the sun has set. In the Latin book of Ptolemy, that same rising is noted on the Kalends of October, and on the second day, the ninth, and the twelfth. The author of this book may have written thus about the true rising, who thought the sun entered Libra on September 19th; from which the Kalends of October is the thirteenth day, the ninth is the twenty-first, the twelfth is the twenty-fourth. Which last corresponds to the Julian acronychal rising, while the others correspond to the age of Meton and others. These things [are] from the author of that.

^A false persuasion regarding the entry of the sun into the eighth sign before the equinoxes, not absurdly suspected; otherwise they could be referred to the visible acronychal rising.

There follows the evening setting of the Pleiades, which Geminus says Euctemon placed in the 10th degree of Aries; Eudoxus and Democritus in the 13th. I find that in the time of Thales their heliacal setting occurred in the 10th degree of Aries; but in Meton's time in the 13th: which is sufficiently consistent. Democritus added that thereafter they remained hidden for forty days: which we have demonstrated to have been true in the time of Hesiod. Furthermore, in the time of Thales the heliacal setting occurred in Aries 10, the rising in Taurus 16: an interval of thirty-six days. But this occurred in one of the bright stars of the Vergiliae [Pleiades]: for the one farthest to the east had its heliacal rising four or five days after that, so that it is most true of the whole constellation that it remained hidden for as many days. Behold, in the time of Meton the heliacal setting of the bright Pleiades fell on the 13th degree of Aries, the heliacal rising of the last one to the east on the 25th degree of Taurus: an interval of 42 days. Thus, in one of the bright stars of the Vergiliae in Rome in the time of Julius Caesar, you will find the same thing: for the heliacal setting occurred in the 18th degree of Aries, the rising in Taurus 30: a difference of 42 days. The Latin book of Ptolemy ascribes to April 2 the evening setting of the Vergiliae, which day is the nineteenth from the false entry of Aries which he supposed. Ovid placed it on April 2: who also assigns the beginning of Aries to the 15th before the Kalends of April, from which the second of April is the sixteenth day. These do not poorly agree with the astronomical setting of the bright star of the Pleiades. Thereafter he writes that the rest of the Vergiliae set on April 12. This also consistently, as we have already said. But Pliny, lib. XVIII, cap. XXVI, says that in Attica the Vergiliae are hidden in the evening on the third of the Nones of April, and the same in Boeotia on the day after; but for Caesar and the Chaldeans on the Nones. Columella, lib. IX, cap. II, says that on the eighth of the Ides of April, which day is the sixth, the Vergiliae are hidden in the evening; but on the tenth before the Kalends of May they rise with the sun: which they call a cosmic rising. Finally, it does not seem that this should be overlooked in this matter: that the beginning of the day is popularly accepted not only from the rising of the sun itself, but from the dawn itself, or the increasing morning twilight; just as the end is sometimes accepted from the setting of the sun, sometimes from the clearer twilight. Thus Aratus described the *prokatadysin* of Orion, as Theon explains: *The Orion, all together, sets before the dawn...* that is, before the dawn. Hence, just as each star precedes another's beginning or follows its end, so also its rising or setting were accustomed to be established at different intervals. Furthermore, Godefridus Vendelinus, a man very learned in these disciplines and worn out by the use of celestial observations, taught us that it was observed by him, partly in the province of Marseilles, partly in Belgium, in summer and autumn days, when the air is most serene, that a certain vapor lies on the horizon to a height of about 17, or 18 parts, so dense that through it the brighter stars do not shine, unless they are some degrees above the horizon; the Pleiades, indeed, often hide in that very 17th degree; which he confirms he observed not once in autumn. From this, a star is said to rise or set in a new way, when it first emerges from that vapor or is hidden in it. For these reasons, that variety among authors in designating the rising and setting of the stars is sought. For these apparent risings and immersions happen up to twenty days after the true ones.

CAPUT X.

The Vergiliae made themselves most illustrious in the sky, because mortals were once accustomed by their observation to distinguish the annual weather, as well as the times of harvest and sowing. For the morning rising of the Pleiades, that is, the heliacal, gave the beginning of summer and harvest; but the morning setting, [that of] winter and sowing. Thus they divided the year in a twofold way. Hesiod is a witness that this was done of old in Greece in those verses which we mentioned in the previous chapter. Then countless Greeks and Latins proceeded to write the same thing thereafter. Wherefore Theophrastus in the book *De signis pluviarum* writes that the Vergiliae divide the year in two in these words: ^C «They divide the year in two by the setting and rising of the Pleiades: for from the setting until the rising is half of the year.» The rising and setting of the Vergiliae divide the year in two. For from the setting of them until the rising, it is half a year. Varro follows this same [thought], lib. I *De re rust.*, cap. XXVIII; and explicitly Pliny, lib. XVIII, cap. XXIX, where he says that summer begins with the rising of the Vergiliae, winter with their setting, encompassing in a six-month space between them the harvests, vintages, and the ripening of all things. But Aratus: ^DFor they, however few and dim, are yet named In spring and autumn; Zeus is the cause of their turning, Who commanded them to signify both summer, And the beginning of winter, and the approaching time of plowing. Cicero: At a great name of a sign, and famous it is called, Because both the beginnings of summer are bright, And, revealing the rising of the coming winter time, It warns mortals to entrust seeds to the lands. But that the Vergiliae do this at their morning rising and setting, Aratus sang; Cicero does not express it. But Festus Avienus rendered this with his own interpretation: For if the Vergiliae lift themselves from the deep, Days to ply curved sickles in the yellow fallows. If they hide their flames in the sea, [It is] time to cut the earth with a pressed plow. This bipartite distribution of the year is to be accepted conveniently and broadly, not precisely and rigidly. For the annual space is not exactly divided in two by their rising and setting. Which can be gathered from Hippocrates.

“They divide the year into four parts, which most people know best: winter, spring, summer, autumn. And winter from the setting of the Vergiliae [Pleiades] until the spring equinox; spring from the equinox until the rising of Arcturus; autumn from Arcturus until the setting of the Vergiliae.” ^B In this quadripartite division of the year, the segments are not equal, but the measure of summer and winter is far greater than that of spring and autumn; for the latter are finished in no more than forty days. In the age of Hippocrates, that is, of Meton, the morning and heliacal rising of the Pleiades occurred in the 19th degree of Taurus, the rising of Arcturus in the 25th of Virgo: an interval of four signs and 6 degrees. Hippocrates assesses the summer segment at this much; but to the spring season, no more than thirty-six days are allotted. Again, the evening and true setting of the Pleiades took place in the 28th degree of Libra. Thus, from the rising of Arcturus to the setting of the Pleiades, there are 33 degrees in total. Finally, from the setting of the Pleiades to the spring equinox, there is an interval of almost four signs. And if we employ the apparent setting of the Vergiliae, not the true one, not much will have been subtracted from this winter interval. Such divisions of the year, therefore, were established more for the senses and for the vicissitudes of the air and sky than for the proportion and equality of the parts. Which we may show is the case for the single star of the Vergiliae: its heliacal rising in the age of Meton fell in the 19th degree of Taurus; its setting in the 28th of Libra: an interval of 5 signs, 9 degrees; from its setting to its rising, 6 signs, 21 degrees. But if we wish to estimate the intervening days, since in the time of Meton the true ingress of the sun into Taurus at Athens occurred on April 26, at the 17th hour, 57th minute, and it entered into Libra by true motion on September 28, at the 20th hour, 10th minute; furthermore, the heliacal rising of the Pleiades fell on the 15th day of May; and the morning setting occurred on October 26: the interval between them is 165 days. Which differs from half the year, that is, 181 days, 18 hours, by almost 17 days. ^D Thus, in the time of Hesiod, in the year 3714 of the Julian Period, since the vernal equinox occurred on March 31, at the 1st hour, 24th minute at Athens: the true ingress into Taurus was likewise May 1, at the 4th hour, 18th minute. Also, the autumn equinox [was] October 2, at the 17th hour, 33rd minute at Athens; the interval between the 10th of May, on which the 11th degree of Taurus and the heliacal rising of the Vergiliae fell, and the 20th of October, to which the 19th degree of Libra and their heliacal setting corresponded, is 163 days. Which is far from half the year, namely by 20 days.

In the first Julian year, finally, the sun entered Gemini by true motion on May 24, at the 11th hour, 54th minute, at Rome, where the heliacal rising of the Vergiliae occurred at the beginning of Gemini. But it entered Scorpio on October 25, at the 5th hour, 53rd minute: the fourth degree of which, into which the morning setting falls, is reached on October 28. The difference between both is 157 days, which stands apart from half a year by almost 26 days. This variety of the gradually increasing interval arises from the precession of the equinox, as well as [from] the eighth sphere, progressing in consequence with the stars, and then the change of the sun's apogee.

CHAPTER XI.

There is another star after the Vergiliae, in which we shall also test the use of our method; and we shall weigh the passages of writers concerning it a little more accurately; [this] is Canicula, which the Greeks call Sirius: which name is extended more broadly among the ancients, for it sometimes also signifies the sun. As in Hesiod, *Works*, where he describes the autumn season thus: “For then indeed the star Sirius Goes slightly above the heads of suffering men By day: and possesses more of the night.”

All interpreters agree on this point, that Sirius here is the sun, because of *seiriazein*, which is “to shine”: and you cannot interpret it otherwise in this passage, contrary to what a learned man thought. For the parallel that Canicula describes does not have unequal segments above the earth and below it in different seasons of the year: which the poet sings about Sirius. Hesychius [says]: “Sirius, the sun, and the star of the Dog.” The same teaches that it is used by Archilochus for the sun, and by Ibycus for all the stars. The Egyptians called this Sothis (says Horapollo, book 1, cap. 3), to which they also attributed the primacy of the stars, and from its rising they were accustomed to take a conjecture about the state of the whole year. “For the effects of this are felt most broadly on earth,” as Pliny says (book 2, cap. 40); “but especially, because by its rising the vapors of the sun are thought to be ignited.” “The seas and lands feel this,” as the same man says, “and many wild beasts too. Nor is the veneration for it less than for the stars described as gods.” But Geminus, in chapter 14, in a long and learned dissertation, refutes this common error of those who think that the state of nature is changed by the rising or setting of any star. For stars are not endowed with greater power than others: nor are they to be thought to excite any storms by their rising or setting. But the cause of these vicissitudes lies with the sun: when the rising or setting of certain significant stars occurs in their seasons, it pleased [the ancients] that these be used as signs for marking and designating them. And Geminus asserts this especially regarding the rising of Canicula, which, since it falls at that time of the year in which more vehement heat exists, [his text continues]

to the heliacal rather than the cosmic rising. In the first year of the Julian calendar, the cosmic rising of Sirius occurred at Rome in the 22nd degree and 48th minute of Cancer; about the 16th of July; the heliacal rising in the 7th degree and 43rd minute of Leo; about the 2nd of August. In the passing year 1630 of Christ, the cosmic rising falls in the 7th degree and 16th minute of Leo; the heliacal in the 20th degree and 30th minute of Leo, about the 12th of August. Thus the beginning of the dog days has deviated from the heliacal rising, and will henceforth always retreat further. The ancient age was ignorant of this *metaptosis* (shifting) of the starry sphere, and therefore they constantly held to the risings and settings once designated by their ancestors; and they treated the heliacal and cosmic risings promiscuously, and those which were proper to certain places they applied to others without any distinction. To these heads, nearly all that variety which occurs in ancient writers on this matter can be referred.

Most writers place the rising of Sirius at the moment in which the sun enters Leo. But since it was a common opinion that the solstices and equinoxes occurred in the eighth parts of the signs, they anticipated the beginnings of the dodecatemories by as many days before the true ingresses. The solstice of Julius Caesar was fixed on the twenty-fourth day of June. Therefore, on the 15th of the Kalends of July, or the 15th of June, the sun was thought to enter Cancer. But it was thought to enter Leo after thirty-one days, on the 15th of the Kalends of August. Pliny, book II, chapter XLVII: "The star of Canicula rises in the most ardent time of summer, with the sun entering the first part of Leo: which is the 15th day before the Kalends of August." Also in book XVIII, chapter XXVIII, he says Canicula rises twenty days after the solstice. If the solstice is on the 6th of the Kalends of July, the entry into Cancer occurs on the 16th of the Kalends, which is the 17th day of July. Varro, book I, chapter XXVII, counts twenty-nine days from the solstice to the rising of Canicula; Columella, book IX, chapter XIV, thirty days; others, as Palladius, book VII, tit. IX, record that Canicula rises on the 14th of the Kalends of August, which is the 19th day of July: which also Ptolemy, ^C edited by us in Greek, mentions among others. For he places the rising of Canicula on Epiphi 21, that is, July 15th, and Epiphi 25, which is July 19th, and Epiphi 27, July 21st: on which day Censorinus also writes that it rises in Egypt, chap. XXI.

That Canicula by its rising intensifies summer heat was not only believed by the ancients, but has become pervasive in the usage of all mortals today and in common speech. But since the rising of stars is twofold, apparent or heliacal, and true, which is also called cosmic, that great power of increasing heat and accomplishing other things used to be attributed to the heliacal, not the cosmic rising, as we reported just before from Geminus: which other writers also teach us, who demonstrate that prognostications of future events were wont to be sought from the aspect of Canicula when it rises. Thus Homer, *Iliad* X, describing the rising of Sirius:

*"Which goes forth in the summer season; and its rays are clearly seen ^D shining among many stars at the dead of night,* *Which they call by the name of Orion's Dog;* *It is most bright, but it has been made an evil sign."*

He understands the heliacal rising, which happens at the end of summer, which he calls *oporan*, in the dead of night, as Eustathius rightly explains. Although Theon, in his commentary on Aratus, seems to ascribe those huge heats to the cosmic rising. But after a longer space of years has elapsed, after that star has had its progression *eis ta epomena* (toward the following [signs]), all that *episemeia* (indication) has evidently moved from the heliacal to the cosmic rising.

And the greater part, as I have said, of the Ancients who wrote after the Julian calendar was established, assign the rising of Canicula first to the ingress of the sun into Leo; as Varro, as Columella, as Palladius, as Manilius, as Firmicus, and others: who handed down this opinion to posterity as if it had been transmitted by hand. In which all the more recent ones are most mistaken. For neither in the age of Julius, nor of Constantine—when Firmicus flourished, and Manilius a little later, as some are of the opinion—did the heliacal rising of Sirius, of which they speak, fall into the first part of Leo at Rome. For in the first year of the Julian calendar, Canicula rose cosmically at Rome with the 22nd degree and 48th minute of Cancer, and heliacally with the 7th degree and 43rd minute of Leo. But at Rhodes in the same century its cosmic rising fell in the 16th degree and 48th minute of Cancer; the heliacal in the 1st of Leo. That which [he records] there as having happened in his own age...

Geminus testifies to, and before him Hipparchus. From this, our conjecture regarding the age of Geminus is confirmed. For we showed in Book II, *De doctrina temporum*, chapter VI, that he flourished in the sixth century of the City, from the fact that he reports the *tropai* (solstices) of Eudoxus as occurring 120 years before he was writing: about which we have treated more accurately in our *Notes on Geminus*, page 19.

I return to the rising of the Dog Star (Canicula). Our method exhibits this as agreeing precisely with the calculations of Geminus. But Pliny and the others, who wrote that it rises in the first part of Leo around the 15th or 20th of July, were moved by that false persuasion which, as we showed above in the fourth chapter, crept into them wrongly through the preposterous imitation of the ancients. This was the first of their errors. To this another was added: while the true and cosmic rising of the Dog Star occurred at Rome around the time conceived by them, the heliacal [rising] did not occur in Italy, but in Egypt at the same time; these men applied to the Italian [horizon] what had been adapted by the Alexandrians and Egyptians to their own region and published in their writings. The cosmic rising of Sirius in the first Julian year occurred at Alexandria in the 12th degree, 27th minute of Cancer, around July 7th; the heliacal [occurred] in the 26th degree, 9th minute, that is, about July 20th. Wherefore, regarding what they write about the time of the canicular rising, if the discussion is about the Italian position of the heavens, it refers to the cosmic [rising]; if the Egyptian method is being considered, it is the heliacal that must be noted. Columella, who places the rising of the Dog Star thirty days after the solstice and in the eighth part of Cancer, has fallen into the truth inadvertently. For thus the ratio is reduced to the seventh part of Leo. But common error carried him away in defining the time; for because he bound the solar entrance into Cancer to about June 17th, it follows that the entrance into Leo is ascribed to July 18th, and the rising of the Dog Star to July 23rd or 24th, at about the seventh part of Leo. In this, however, his reasoning fails him. For the heliacal rising of the Dog Star falls around that time on the Kalends of August or shortly thereafter. With no less hallucination did Pliny think that the Dog Star rose heliacally on the twenty-third day after the solstice, when in reality it rose cosmically on the same number of days after the solstice in the age of Julius Caesar.

Scaliger, in his *Notes on Manilius*, Book V (page 405), corrects his poet, who had said based on common opinion that Sirius rises in the part of Leo: "He would have done better," he says, "to have said that the Dog rises at the beginning of Cancer in the barbaric limiter. In the age of Manilius, it rose in the 8th of Cancer." Even if we concede that Manilius flourished in the Augustan age, which Scaliger thought, the Dog Star rose neither at the beginning of Cancer nor with its 6th degree. For its true rising at Alexandria happened at the 12th degree, 27th minute; the heliacal at the 26th degree, 9th minute. Pliny, however, does not differ much from its rising: he says in Book XVIII, chap. XXIX, that the Dog Star rises in Egypt on the 4th of the Nones of July. For the eleventh degree of Cancer falls on this day. Although, it seems Pliny understood this latter passage as referring to Procyon, not to the Dog Star. For in the preceding chapter, on the 4th of the Nones for Egypt, he had said that Procyon rose, or the cosmic rising of Procyon at Rome happened with the 11th degree, 0th minute of Cancer: the heliacal with the 27th degree, 54th minute of the same. But in Egypt, the cosmic happened in the 6th degree, 17th minute of Cancer; the heliacal in the 21st degree, 5th minute. Manilius, however, in Book V, and Firmicus, as Scaliger rightly corrected, wish Procyon to rise in the 25th part of Cancer: which does not agree with the age of Julius nor that of Firmicus.

There are two stars in the heavens to which the name "Dog" applies: Procyon and Kyon. The former is called Antecanis, or the lesser Dog, situated near the Milky Way, between the equinoctial circle and the zodiac; and it has two stars; one on the neck, another on the thigh, which properly is also called Procyon. The origin of this word is sought from the fact that it precedes the rising of the Dog (Sirius). The Dog, however, is a star situated to the south, below the equinoctial circle. Although it has many stars, it carries the principal one in its mouth and jaw: which they call Sirius, the Latins *Canicula*, even if *Canicula* is sometimes used for the whole star itself. Pliny, Book XVIII, chap. XXVIII, denies that the name Procyon exists among the Romans. "Which star," he says, "has no name among the Romans, unless we wish it to be understood as this *Canicula*: that is, the lesser Dog, as it is depicted in the stars; pertaining greatly to the heat." Thus Peliserius had corrected it in the margin of his codex, for which commonly it is read: "But it is greatly pertaining." He says that Procyon pertains to the heat, "because," he says, "it indicates a star known among all, which we call the rising of the Dog." And consequently, it announces that intense heat: indeed, it even contributes to it in part. Hence Horace, Book III, Ode 30:

..... *Procyon already rages,* *And the star of the frenzied Lion,* *As the sun brings back the dry days.*

Unless, perhaps, someone wishes to confuse Procyon with Sirius in Horace, because this first star of the constellation of the Dog appears before the others, and so before the whole Dog itself. For thus Galen, in Book I of his *Commentaries on Hippocrates' Epidemics*, [writes]: "For the Kyon (*Canis*) is the whole constellation; but that which is on its jaw is Sirius, which one might rightly name Procyon, not the Kyon." He says that Sirius is called *kyon* by some, which is the name of the whole star; but that it could be named Procyon more correctly than *Canis*. This passage of Galen, as well as almost everything else about *Canicula*, Salmasius stole for his *Solinian Miscellany* from the twelfth book of the second volume of our Bisciola's *Subsecivae*, chapter II; and he did not even name the author from whom he had learned these things, which is his custom. Whether Pliny always took Procyon for *Canicula*, as the *Exercitator* thinks, we will say in chapter I of the seventh book.

That the Dog Star excites excessive heat at its rising, as writers assert, [so too] at its setting it stirs up cold and frosts inimical to crops. Manilius, Book I; Pliny, Book XVIII, chap. XXIX; Columella, Book XI, chap. II: "The day before the Kalends of May the Dog hides in the evening; it signifies a storm."

We shall ^A relate the words of Pliny for the sake of correction, because they are faulty. He narrates that the Robigalia were established on the 7th day before the Kalends of May: "Which, after nineteen days from the vernal equinox, during that four-day period, by various observation of nations, on the 4th day before the Kalends of May the Dog sets, a star powerful in itself and to which it is necessary for the Dog-star to precede." He says that from the 5th day before the Kalends of May to the 4th, this whole four-day period is decisive for the crops: and he counts nineteen days from the vernal equinox. The vernal equinox is assigned by Pliny to the 8th day before the Kalends of April, from which the thirty-second day is the 6th day before the Kalends of May. Therefore it should be read: "after thirty-one days." The same Pliny, from Varro, reports the setting of the Dog-star to the tenth part of Taurus. This agrees with the opinion of that age, which represented the entry into the zodiacal signs on the eighth day before the cardinal points. In order, therefore, that the sun may enter Taurus on the 11th day before the Kalends of May, its tenth part will fall on the 4th day before the Kalends, on which day Ptolemy, as published by us in Greek, noted the setting of the Dog. Our tables render the heliacal setting of Sirius at Rome at 5 degrees, 31 minutes of Taurus. The sun approached this in the age of Julius Caesar on about the 3rd day before the Kalends of May. Pliny, however, who noted the 7th day before the Kalends, can be reconciled by the reason of appearance after absence. For his intervals are accustomed to be wider, as we have demonstrated above. Geminus says the Dog is in the second part of Taurus for Euctemon, and in the fourth for Eudoxus.

CHAPTER XII.

It has seemed strange and not sufficiently credible to some, that it is established by the testimony of Hesiod ^B and other ancients that the timely harvest in Greece was at the rising of the Vergiliae. For their heliacal rising in the first Julian year occurred at Rome at 27 degrees of Taurus, which fell on the 21st day of May; but in Egypt, at 21 degrees of Taurus, the 14th of May. But in the time of Hesiod that rising occurred still earlier. But I shall say nothing for now about Greece and Italy; certainly in Egypt and Palestine they began the harvest long before the heliacal rising of the Vergiliae. For Theon, ^C in his commentaries on Aratus, is a witness that on the 25th day of the month Phamenoth, which corresponds to the 20th of April, with the Vergiliae rising, it is the time of harvest in Egypt. And he speaks of the cosmic or true rising, not the heliacal, which occurred in the age of Theon around that time. So that no one may consider this vain, I shall cite another witness, the Egyptian, even more suitable than the former: St. Isidore of Pelusium, who writes in Book III, epist. 110, that at that time when the Jews celebrated the Passover, the ears of corn were already seen to be ripe for harvest. "For at that time alone, the ears of corn grow heavy, and are bent down by the fruit and by the time of harvest, as if calling the sickle to themselves." Therefore, those who, because of the corn pulled and rubbed by the apostles, denied that the "second-first" Sabbath was any one of the days of the unleavened bread—a point on which most agree—relied on the reason we have opposed: that on the 15th day of Nisan, or the 20th of March, the ears could not be ripe. "For the feast of firstfruits," they say, "was celebrated on the fiftieth day after the Passover: it was celebrated, however, as soon as the first sickle was put into the harvest. Therefore, the crops could not be ripe at the feast of unleavened bread, that is, fifty days before." Against this, from the chapter of Leviticus XXIII, 10, we offer this ^D objection: that a sheaf of new fruits was offered on the day after the first day of unleavened bread; therefore the crops were already ripe. And indeed, not on the fiftieth day after were new fruits presented, but from the new fruits the loaves of firstfruits were represented. But that recent writer counters us, saying that not ripe ears, but still green ones; and not wheat, but barley, were offered. "Therefore," he says, "if the ears of the barley harvest, which were then offered, were still green during the days of unleavened bread, it is best inferred that wheat, which ripens later, could not have been ripe at that time." But that not only barley, but also wheat were ripe during the time of unleavened bread, [is]...

^A is necessary to believe if we hold the faith of the Scriptures. For Leviticus XXIII declares this not obscurely. Where, after Moses commanded in verse 10 that they should offer sheaves of the harvested grain as first fruits, he adds in verse 14: "You shall not eat bread, or roasted grain, or fresh ears from the harvest until the day in which you bring an offering from it to your God." If the crops were never ripe even for rubbing in the hands at the time of unleavened bread, he would have warned in vain against bread-making, lest bread from the new crops be made before the Omer was offered. Therefore, this is an argument that wheat was sometimes ripe [by then]. But the history of the entry of the Israelites into Palestine and the crossing of the Jordan, which is contained in the ^B book of Joshua, chapter III and the following, silences all stubbornness.

For they crossed the Jordan at the time of the harvest. "The Jordan, however," says the third chapter, "had filled its banks at the time of the harvest." Having crossed it, they were circumcised and stayed there for some time, until the wounds healed; (chap. V, 8) afterwards they celebrated the Passover, "on the fourteenth day of the month at evening." Without doubt, this was from the prescription of Moses, and therefore in the first month. He adds that they ate of the produce the day after the unleavened bread and roasted grain; and that the manna ceased when they first began to eat the new produce of Canaan. Who, from this, does not see that not only were ^C crops ripe for gathering in the first month, but also for making bread from them? Add to this the name of the month itself, which is therefore called Abib, or "of the new," on account of the new crops, of course. Add those passages of Theon and Isidore of Pelusium, which we cited at the beginning of the chapter, from which it appears that the time of the harvest began then, as much in Egypt as in Palestine.

But so that the matter may be further illustrated, two things must be proposed. The first is that the first month, or the month of the new, was by no means fixed or set at a certain time among the ancient Jews. For the masters ^D teach, along with many other reasons, that that month was accustomed to be deferred and pushed back by intercalation; namely, because the new crops were not yet mature. This is treated extensively in the Talmudic Digests, and by Rabbi Moses Maimonides. Then Aben Ezra explains the same in more detail in chapter XII of Exodus, where he writes, among other things, that nothing was stipulated by the lawgiver concerning the lunar month, but he commanded only this, that they should celebrate the Passover in the very month of the new crops. Therefore, according to whether the crops had grown slower or faster, he announced that first month later or sooner, and sometimes declared two consecutive intercalary years. Indeed, as regards that year in which the *deuteroproton* Sabbath, which is under discussion, occurred—which was the first of the [leap years], the Paschal new moon appears to have occurred on April 11, *feria* VII, and the first day of unleavened bread on April 16, *feria* VII. Therefore, the *deuteroproton* Sabbath fell on April 22, which is the fourth day from that which is pre-defined by the rising of the Pleiades and the beginning of the harvest. ^A But in that same year, the Passover was celebrated a full month earlier than the one in which Christ suffered.

Furthermore, it must be known that there is a double degree of maturity in crops. For either the harvest is ripe for the sickle, which time the Evangelist Mark signifies in chapter IV, 29, in obscure words that must be briefly explained: "But when the fruit has offered itself, at once he sends forth the sickle." The common reading is to take it as though *parado*, "has offered itself," is used absolutely; which is unusual. I would prefer to interpret it this way: "when the crops have permitted it"—that is, when they have begun to invite the reapers with full maturity. The translator of the Vulgate has expressed the thought rather than the words. Our conjecture is aided by Theophylact, who explains it thus, or perhaps reads: ^B "but when the harvest has yielded." Which you cannot explain unless we have done so ourselves. Therefore, either that full maturity in the crops is being considered; or the grain itself as well as the ear is still green, yet so that both are suitable for eating, and it can still be plucked and husked, being tender wheat, rather than parched, and able to be mown and harvested. Indeed, it is even sweeter to eat while it is still green. On that *deuteroproton* Sabbath about which we are speaking, the crops were mature not only for eating but also for the harvest. For it was the twentieth day of April. At other times, when the Passover occurred earlier, a sheaf of barley was offered, or green ears of wheat. The Scripture does not define of which type of grain the Omer consisted. Therefore, there is room for a just suspicion that it was permissible to offer either one indiscriminately, according to which one’s maturity coincided with the ^C formal day. For while full maturity suitable for the harvest was not awaited, nevertheless, the grain was not still milky when used for the Omer, but at least at the green stage. But when the Passover happened a little sooner than a bundle of wheat could be acquired for the offering, the barley harvest—being earlier—was used as a substitute.

Finally, it does not seem to have been forbidden by any law to the Jews that they should not perform the harvest, even the barley harvest, before the offering of the sheaf. Rather, that it had been done beforehand, the passage of Leviticus XXIII, 10, demonstrates: "When you have entered the land which I will give you, and have harvested the crop, you shall bring the sheaves of the ears," etc. Which, however, does not always happen, but sometimes occurs according to what we have said a little before. The same judgment must apply to Pentecost; it was not forbidden to the Jews by any regulation to eat of the new crops and the loaves made from them before this festival; those who advocate the contrary opinion take this for granted: rather, that it was lawful beforehand is declared by the history of the third and fifth chapters of Joshua, which we cited. Nor does the term "first fruits" always signify that which is the very first of all, and before which nothing else was in use; but sometimes it is used simply for any offering or thing set apart and chosen for the honor of God, as Exodus XXV, 2, and XXXV, 5 and 21; Numbers XXXI, and if they were offered, it by no means follows from this that the Jews did not consume new crops before this time. What in.