Commentary on the Phenomena of Aratus and Eudoxus by Hipparchus of Bithynia

and low, those below, when in Capricorn; and those in the middle and equal to both, when in Aries or Libra.

On the Zones

3. There are five zones in the heavens and on earth. Of these, only two are inhabited: one situated between the Arctic Circle and the summer tropic; another between the winter tropic and the Antarctic. The others are uninhabitable: two on account of cold, those under the Arctic and the Antarctic; and one on account of heat, that under the equator, which is called the Torrid Zone. We dwell near the summer tropics; and we infer that, having this as our inhabited world, we have on our right ^A the zone uninhabitable due to cold towards the north, and on our left the torrid zone. For if we lived under the winter tropics, the torrid zone would be on our right, and the cold zone towards the south would be on our left. Some, among whom are Panaetius the Stoic and Eudorus the Academic, say that the torrid zone is inhabited, due to the temperature of the air resulting from the Etesian winds being more violent there, and from the atmosphere of the great sea mingling the exhaled cold with the tempering heat. Those who inhabit these zones are called *perioikoi* (dwellers around), *antoikoi* (opposite dwellers), *antichthones* (counter-dwellers), and *antipodes* (opposite-footed). *Perioikoi* are those who inhabit the same zone, because they live around the same region; *antoikoi* are those to one another who inhabit the zone under Capricorn and those who inhabit the zone under Cancer; *antichthones* are those who live on the summer or winter tropic. ^B Above, the same are also called *antichthones*; *antichthones* because they are above and below; and *antipodes* because they stand vertically relative to one another. To speak briefly, the *perioikoi* have the same hours, nights, and days relative to each other by turns. The *antoikoi* have their days the same, but not their seasons. The *antichthones* have their seasons the same, but not their days. The *antipodes* have neither their days nor their hours the same. Yet in this regard the *antichthones* also differ among themselves, for those among the upper ones who have long days, those below have shorter days. The cause of this is the inequality of the circles. The whole rotates around itself daily, and by hours; just as the Ascraean [Hesiod] says: ^C

*Delighting in the circular madness of the sphere.*

He calls the sphere "sphere," as Homer calls evening "evening"; and "circular" because of the spherical form; and "madness" the constant, circular motion. The heavens are carried from the eastern points to the west; but the sun and the remaining planets [are carried] in the opposite direction, that is, from the west to the east; so that there is a double motion for it, one as they come, and one as they are borne, just as on a wheel, and the ant, and the ship, and the one inside it, having a direction contrary to its movement, provide an example. The Creator has made this so that the whole being borne along might not be shifted by having an intense, single-inclined motion; but being pulled back, and diminished in its intense momentum by the counter-pull of the planets, it might receive a steadier impulse for its motion. As the myths play, these stars were turned back, like the dinner of Thyestes, and remained wandering in their course. But one who interprets the sphere must move it from east to west, taking the eastward motion as that facing the mover himself. ^D

HIPPARCHUS OF BITHYNIA ON THE PHENOMENA OF ARATUS AND EUDOXUS THREE BOOKS. BOOK ONE. HIPPARCHUS OF BITHYNIA ON THE PHENOMENA OF ARATUS AND EUDOXUS ENARRATIONS THREE BOOKS, TRANSLATED BY DIONYSIUS PETAVIUS. BOOK ONE.

1. Hipparchus to Aeschrion, greetings. I received great pleasure from your letter, when from it I understood [your] studious [zeal] through [your] letter, your persistence in the philosophy of the fixed stars to purge away the errors that had crept into [it] from the books and authority of Eudoxus and Aratus, of whom the former is the prince up to this day [of] astro—

^A of learning and intimacy. For you have shown me a greater skill in the investigation of natural matters and matters concerning those things said by Aratus in his risings, and so much the more so, in that you have been occupied with the business of life on account of the death of our most venerable brothers. Concerning the other matters, I will explain my own judgment to you after this; but concerning those things said by Aratus in his *Phenomena*, I have now set myself to write to you, pointing out everything in general that is said well or ill by them, from which all things will be clear to you, as well as the questions you posed.

The investigation of Aratus' *Phenomena* has been undertaken by many others, but the mathematician of our own time seems to have written on them most accurately and diligently of all ^B. But to explain the meaning of that poet's verses is, in my judgment, not a task of great importance or worthy of [great] care and attention. For this poet is simple and concise; and furthermore, he is easy to understand for those who have even a moderate grasp of things. However, to grasp with the mind what is written by him concerning celestial matters, and to recognize which things are said in agreement with the evidence of apparent phenomena and which are said contrarily; this seems to be by far the most useful thing of all, and one especially worthy of mathematical expertise. Wherefore, since I perceived that in most things, and those the most important, Aratus deviates ^C from the phenomena as they appear in reality, and that not only the others but even Attalus himself was involved in almost all the same errors, it seemed good to me, both to consult your zeal for learning and for the common good, to commit to this book those things in which I have perceived them to have erred. I do not undertake this with the intention of gaining the fruit of some empty opinion from the criticism of others; for I judge that to be vain and ignoble; nay, on the contrary, I judge that thanks ought to be given to all those who have chosen to labor privately for the common good; but [I do it] so that you and the other studious ones ^D may not stray far from the truth in the contemplation of celestial matters; which merit [the] error [that] happens to many. For the grace of poetry lends a certain credibility to what is said; and almost all who have commented upon this poet bolster what is said by him. Eudoxus had more experiencedly recorded the same arrangement concerning the phenomena as Aratus.

The work of Hipparchus

^A His poetic work is considered trustworthy through the agreement of so many mathematicians. Although it is perhaps not fitting to criticize Aratus, even if he happens to err in some points—for in following the treatise of Eudoxus he wrote his *Phaenomena*, though not having observed them himself, and being one of those who profess to offer a mathematical judgment on celestial matters, yet failing in those very matters.

Apart from the things misunderstood in the *Phaenomena* by both Eudoxus and Aratus, and the one who joined them in writing on their settings, I have recorded for you the true rising and setting in company with the twelve zodiacal signs of each of the fixed stars; so that, by following each of them accurately, you may also test the appearances of all the others among these. And I clarify not only the rising or setting, but also which stars of each set of stars ^B rise or set first and last, and which of the other stars reach the meridian; and in how many equinoctial hours each of the fixed stars rises or sets with the twelve signs themselves. Above all, I also clarify which stars define all twenty-four hourly intervals. For because each of these contributes to many useful theorems in mathematics, I believe it is easy for you to understand.

^C II. That Aratus followed the account of Eudoxus regarding the *Phaenomena*, one might learn in greater detail by comparing the words of Eudoxus for every subject with his poetic verses; but it is not useless to briefly mention it here, since the matter is called into doubt by many. Two books on the *Phaenomena* are attributed to Eudoxus, which are almost entirely in agreement with each other, except for very few things. One of them, therefore, is titled *The Mirror*, the other *Phaenomena*. Aratus composed his poem with the *Phaenomena* in view. In this very treatise, Eudoxus writes as follows regarding the Dragon: "Between the Bears is the tail of the Serpent, which raises that small star above the head of the Great Bear; it has a turning at the head of the Little Bear, and is stretched out under the feet; then, having made another turning there, it again turns back and has its head in front." And Aratus, as if paraphrasing these things, says:

But here it measures out one, at the end of the tail: The other, however, the coil circumscribes. For it, indeed, the tip Of the tail rests at the head of the Helicopter ^D Bear. In the coil, however, Cynosura holds its head. This, indeed, around Itself is turned, and reaches even to its foot. Then it turns back again, recurring.

Concerning Boötes, Eudoxus says: "Behind the Great Bear is Arctophylax." Aratus says: *Behind Helice he is borne, like to one driving,* *Arctophylax.......* And again Eudoxus says: "Under his feet is the Virgin." Aratus says: *And with both feet beneath shall you observe the Virgin of Boötes......*

Concerning the "Knee-bound" [Engonasin], Eudoxus says: "Beside the head of the Serpent is the Knee-bound, having his right foot above the head." Aratus says: *He has the tip of the right foot of the winding Dragon.* From this, indeed, that which we intend becomes especially clear. For each of them has erred; for the Knee-bound has his left foot, not his right, upon the head of the Dragon. ^B Eudoxus says that the Crown is situated under the back of the Knee-bound. Likewise Aratus: *The Crown is near his back; but observe the uttermost* *Head near the head of the Serpent-bearer;* concerning which Eudoxus also says: "Near his head is the head of Ophiuchus."

Concerning the position of the Great Bear, Eudoxus writes thus: "Furthermore, below the head of the Great Bear are the Twins situated; below the hind feet, the Lion; and before the forefeet of the Bear is a star; but a brighter one is under the hind knees, and another under the hind feet." Aratus also says: *Below its head, indeed, are the Twins, and in the middle the Crab lies;* *Beneath the hind feet the Lion shines brightly;* *And concerning the mentioned stars:* *Such a one is borne before its feet, beautiful and great;* *One under the shoulders, one also from the loins descending,* *Another under the hind knees.*

Concerning the Charioteer [Auriga], Eudoxus writes: "Opposite the head of the Great Bear are the shoulders of the Charioteer; who is situated obliquely, extending his right foot above the feet of the Twins, common to him [that is] at the tip of the left horn of the Bull." Aratus also says of him: *Helice's highest head* *Opposite rolls;*

^{C D} [Regarding the phrase "right foot of the winding Dragon":] It was the intention of Aratus that the foot rests upon the Dragon, and not the left, just as the scholiasts of Germanicus and Festus Avienus—apart from Hipparchus—have interpreted him; of whom the latter gracefully [expresses it]: *...and then the imprint of the right foot treads upon* *The prone temples of the spotted Dragon.* The scholiast of Germanicus says: "He is depicted with the right foot extended against the Dragon," which had been expressed in the verses obscurely as: *For leaning on his right knee, and stretching his arms in different directions...* ...but it could be reconciled to the true position if, resting on his right knee, he extended his left [foot] to the head of the Dragon. The Greek scholiast of Aratus, having noticed this error, wrongly attempted to excuse the poet. For he referred [the text] not to the foot, but to the Dragon, who is called "more rightward," that is, further north; since if we turn our gaze to the west, the arctic pole will be on our right. But these are trifles. Indeed, the true meaning is clear from Eudoxus, which, having been advised by Hipparchus, Hyginus corrected in Book II, chapter "On Engonasin." Although this was not so much an error as a oversight of Eudoxus, as number 7 [in his commentary] teaches.

And again: ..... The extremity of the left horn, And the right foot lying near the Charioteer A single star occupies.

Regarding Cepheus, Eudoxus says: "Under the tail of the Little Bear are the feet of Cepheus, forming an equilateral triangle toward the tip of the tail; the middle of it is at the bend of the Serpent that passes through the Bears." But Aratus says: As much measure is extended for him from the tip of the tail Unto both feet, as from foot to foot it extends. But from the belt you might look, Seeking first the bend of the great Dragon.

Both are for the most part mistaken. For the interval between the feet of Cepheus is less than either interval to the tail.

Again, regarding Cassiopeia, Eudoxus says: "Before Cepheus is Cassiopeia; before her is Andromeda, having her left shoulder above the northern Fish, and her belt above the Ram: unless the triangle lies between; and the star which she has in her head is common to her and that which is in the belly of the Horse." But Aratus says: To her, unhappy, rolls along, not very great, Shining at night, the all-lamented Cassiopeia; and a little later: For there, too, rolls that sad image Of Andromeda, constellationed under her mother. And again: ... and a common star shines, Of this one at the navel, and of that one at the uttermost head. And again, regarding the Ram: ... yet through the belt of Andromeda you might infer; for little indeed is supported beneath it. And further: And let the left shoulder of Andromeda be The mark of the more northern Fish; for it is very near to it. ^B

Regarding Perseus, Eudoxus says thus: "By the feet of Andromeda, Perseus has his shoulders, extending his right hand toward Cassiopeia; and his left knee toward the Pleiades." Aratus, however, says of Andromeda: Both feet indeed roll within the bridegroom Perseus: which indeed are always carried upon his shoulders. And again: And his right hand is stretched toward the couch Of his father-in-law's throne; and a few lines later: And near his left knee, in a cluster, all the Pleiades are carried; nor does a very large space contain them all.

Regarding the Bird, Eudoxus says: "At the right of Cepheus is situated..." ^{C D}

^A the right wing of the Bird; and by the left wing are the feet of the Horse." Aratus also sang thus concerning the Bird: *At the right hand* *Of Cepheus, extending its pinions' right tips:* *To the left wing the Horse's hoof is inclined.* But since there are not a few other things which seem to have been taken almost verbatim from Aratus, these few will suffice for us, lest we be too lengthy.

III. Furthermore, the very distribution of the stars shows sufficiently what we wish to prove. For Eudoxus, just as Aratus, first recorded those stars which are situated to the north of the zodiac, and after these he listed those situated to the south. Thus, Aratus recounted the risings and settings of the other constellations along with the twelve zodiacal signs in the same manner as Eudoxus. Now, concerning the stars which are carried along the summer and winter tropics, as well as those along the equator, Eudoxus writes thus: "In the summer tropic are the middle of Cancer and those [stars] which pass through the middle of Leo in terms of longitude; a little above the Virgin are the neck of the adjacent Serpent, the right hand of the Kneeler, ^B the head of Ophiuchus, the neck of the Bird, the left wing, and the feet of the Horse; then the right hand of Andromeda, and that which is between the feet of Perseus, his left shoulder, [and] his left leg; likewise the knees of the Charioteer and the heads of the Twins. Then it meets back at the middle of Cancer." Aratus, however, taking his beginning from the extremities, speaks as follows: *In it are carried both heads of the Twins.* *In it are set the knees of the seated Charioteer;* *The left leg and left shoulder of Perseus are therein;* *And Andromeda’s right hand, above the elbow,* *It contains; its palm is placed further north,* *But the elbow is inclined to the south.* *The horse’s hoofs, and the Bird’s neck* *Are there, with the head and the Ophiuchus’s bright shoulders,* ^C and so forth.

Concerning the winter tropic, Eudoxus likewise says: "In it are the middle of Capricorn, the feet of Aquarius, the tail of the Whale, the bend of the River, the Hare, the feet and tail of the Dog, the stern and mast of the Argo, the back and chest of the Centaur, the Beast, and the sting of the Scorpion; then it joins through Sagittarius back to the middle of Capricorn." Aratus speaks thus: *Another, in the opposite south, cuts the middle* *Of Capricorn, and the feet of Aquarius, and the tail of the Whale.* *The Hare is in it; but the Dog does not take away* *A very large part; but as much as his feet occupy. In it too is the Argo,* *And the great shoulder-blade of the Centaur; in it also is the sting* *Of the Scorpion, and the bow of the swift Archer.*

In the same way, Aratus has translated by imitation those things which are situated on the equatorial circle. ^D Beyond these things, Aratus establishes the same position of the world as Eudoxus. For Eudoxus, in that book,

^A which he titled *The Mirror*, says that the tropic is cut in such a way that the segments have the same ratio to each other as five has to three.

IV. That Aratus, in composing his *Phenomena*, followed Eudoxus in everything ^B, I consider I have sufficiently demonstrated through the things said before. But now we shall demonstrate in what points both of them, and those who have subscribed to them—among whom is Attalus—have erred. We shall also immediately set forth where each of them errs individually. And it must be premised that Attalus agrees with almost everything said by Aratus regarding celestial matters, as if they were explained consonant with the phenomena, with the exception of one or two things, which we shall indicate in what follows. He speaks, at any rate, in his proem in this manner: “For this reason, therefore, we have sent you the book of Aratus, amended by us, together with its explanation, having made each detail consonant with the phenomena and consistent with what was written by the poet.” And again, he says subsequently: “Perhaps some will inquire by what reasoning we are persuaded to say that the amendment of the book has been made consistently with the purpose of the poet. And we furnish as the most necessary cause the agreement of the poet.” Since Attalus holds such an opinion, it must be judged ^C that whatever things said jointly by Aratus and Eudoxus we demonstrate to disagree with the phenomena, those same things are also written erroneously by Attalus.

V. First, then, Aratus seems to me to be ignorant of the inclination of the world, thinking that in the regions about Greece it is such that the longest day has the same ratio to the shortest as five has to three. For he speaks thus regarding the summer tropic:

This, being divided into eight parts in all, Five revolve above the earth, And three are beneath.

It is, however, agreed by all that in the region about Greece, the gnomon has this ratio to the equinoctial shadow which four has to three. Therefore, in that place, the longest day ^D is 14 and 3/5 equinoctial hours, or thereabouts. And the elevation of the pole is approximately 37 degrees. But where the ratio of the longest day to the shortest is as five is to three, there the longest day is 15 hours, and the elevation of the pole is approximately 41 degrees. It is clear, therefore, that it is not possible for the aforementioned ratio of the longest day to the shortest to be in the regions about Greece, but rather in the regions about the Hellespont. Although Aratus, not putting forth a judgment about such matters of his own accord, wrote this, but in this also followed Eudoxus; if he had written it of his own accord, without having clarified in what regions this inclination of the world exists, he might perhaps have deflected the blame in this respect. Attalus, however, is unquestionably worthy of censure, for he writes explicitly in Greece

^A that the ratio of the longest day to the shortest is as 5 to 3. For after he had brought forward the verses of Aratus concerning the summer tropic, he immediately added this: "By this he clearly declares that he has worked out the whole of his task in the regions of Greece. For among those people, the ratio of the longest day to the shortest night is as 5 to 3."

Furthermore, one might even more greatly wonder how he failed to notice that Eudoxus wrote differently in another work, asserting that the segment of the tropic which is above the earth has to the one that is hidden below the earth a ratio as 12 to 7. Philippus and many others wrote in agreement with him, and nevertheless they described the risings and settings of the stars exactly as if they had observed them in the provinces of Greece. Thus, the ratio escaped them due to the inclination of the place. We, however, passing over this error of theirs, have examined their whole study in relation to the horizon of Greece. For it does not befit a lover of truth, but rather one who is vainly curious, to spend all his time in convincing them of their false hypothesis and in refuting those very points, but rather to see if they can be accommodated to observations made in Greece... Let there be applied, therefore, to this consideration, the horizon of Athens; where the longest day is 14 hours and 36 minutes, and the altitude of the pole is about 37 degrees.

Concerning the northern pole, Eudoxus is mistaken, writing as follows: "There is a certain star ^B that remains always in the same place, and this star is the pole of the world." For no star is situated at the pole itself; but the place is empty, and three stars lie adjacent to it, with which the very point of the pole forms a shape roughly quadrangular: just as Pytheas the Massilian also says.

[VI.] In accordance with these things, there is a common error of all regarding the determination of the position of the Dragon; for they think that its bend occurs around the head of the Lesser Bear. For the brightest and leading stars in its quadrilateral—of which the more northern one is, according to them, above its head, and the more southern one on its front feet—are situated almost parallel to the tail of the Dragon. Therefore, these things are falsely written: "But it holds its head in the coil of Cynosura; and this head ^C rolls by it." Eudoxus wrote similar things. But Aratus makes a particular blunder of ignorance concerning the Dragon: first, in saying that the Bears are carried on either side of the coil. For they are on either side of the tail, and not of the coil. For being turned opposite to one another, and as it were lying parallel, the tail of the Dragon is stretched out in length between them; and the coil encompasses the Lesser Bear, but is separated far from the Greater Bear. For the same reason, also the expression "and bent around" is said incorrectly. For it would be true if they were placed on either side of the coil.

^A Moreover, he is ignorant concerning the Dragon, writing thus:

Oblique is its head; but it seems quite To incline towards the tail of Helice; and quite in a straight line Are the mouth, and the right temple, to the end of the tail.

For it is not the right temple, but the left, that is in a straight line with the tongue of the Serpent ^B and the tip of the Great Bear. For to say that he assumes the head of the Dragon to be turned backwards, and not turned towards the interior of the world, as Attalus says, is entirely implausible. For all the stars are arranged in relation to our view, and as though turned towards us, unless there is some tracing of them. Aratus himself makes this clear through many examples. For whenever he describes the right or left part of an asterism, he agrees in all instances with the hypothesis previously mentioned; and otherwise, this hypothesis is artificial and forced. In addition, what he wrote concerning the left foot of the Kneeler, ^C about which we shall speak later, will help to refute this error.

Regarding the position of the head of the Dragon, those around Eudoxus and Aratus agree in their claims about the phenomena; but Attalus disagrees. For Aratus, following Eudoxus, asserts that it appears on the always-visible circle, saying thus:

That head swims here, where the extremes Of sunset and sunrise meet one another.

But Attalus says that it is a little further to the south than the always-visible circle, so that it disappears under the horizon for a short time. That Attalus differs from the phenomena may be reasoned thus: for the star which is at the tip of the Dragon’s mouth is 34 degrees and 36 minutes distant from the pole; ^D its southern eye is 35 degrees; the southern temple is 37 degrees. But the always-visible circle in the regions around Athens, where the gnomon is one-third of the equinoctial shadow, is about 37 degrees distant from the pole. It is clear, therefore, that the head of the Dragon is always carried in the visible region, with only its left temple situated upon that [circle]; and not, as Attalus says, being further south, setting and rising in a short time.

VII. Furthermore, concerning the Kneeler, Eudoxus and Aratus seem to me not to have been ignorant, but rather to have overlooked something, when they say that his right foot is placed upon the middle of the head of the Dragon. Attalus, however, seems to me to have transposed this hemistich against the intention of the poet, writing thus:

...above the middle of the head

and turning the head of the Dragon outside the world; so that the right part of the head itself comes to be at the foot. For indeed, all the constellations [are turned towards the interior of the world]

and are placed by all, and by Aratus himself, and it is written in all the books:

^A ... *Middle, indeed, above the head* *The extremity of the right foot holds the crooked Dragon.*

Furthermore, since Aratus wished to explain to us the figure and position of the "Kneeler" [Ingeniculus], he ought properly to have signified which of his feet lies upon the head of the Dragon. For he does not mention the head of the Dragon without cause, except that we might follow the position of the Kneeler by it; which he is accustomed to do in the case of many others. Just as when writing of the Kneeler, he commemorates his other parts thus:

*By the back he approaches the Crown; but his head mark,* *Observe, near the head of the Serpent-bearer.*

Item, concerning the Lyre he says: *He approaches it with his left knee.*

And as concerning Perseus: *And near his left knee, all the Pleiades* *Are borne along.*

And again: *And to him the right [hand] is extended upon the couch* *Of Cassiopeia’s throne.*

And as he says concerning the Swan: *... at the right hand* *Stretching forth the right extremities of the wings of Cepheus.*

So, in the case of many others, when describing the nearby stars, he indicates whether they lie to the right or to the left. ^B That this error of the foot by Eudoxus and Aratus was a matter of neglect, not a mistake, is apparent from the remaining things which each of them reported about the Kneeler. For concerning the Lyre, Aratus says:

*He placed it, he says, before the unknown image,* *Transferring it into the heaven: and upon his legs the winged* *Knee approaches it upon the left.*

Furthermore, the leg near the Lyre is placed upon the head of the Dragon. Again, speaking concerning the rising of the Kneeler, he says:

*... they bring only the Claws* *To the right leg, as far as its knee,* *Always kneeling; and always approaching the Lyre.*

The other leg toward the setting is the one that rises first, and this does not lie upon the head of the Dragon. It is clear, therefore, that he refers to that one as the left. ^C Consonant with these, he sang concerning the rising of the Lion:

*... But he, kneeling,* *Sitting, while now other parts; then his knee and left foot* *He does not yet withdraw, while the Ocean is surging.*

From all these things it is apparent that he says that the left leg reaches down to the head of the Dragon.

^D VIII. After this, Aratus writing privately concerning the Ophiuchus...

^B in a way that suggests he is ignorant of the magnitude of his stars. For having said that the stars in the shoulders of the Ophiuchus are bright, such that they might be discerned even in a full moon, he adds:

... But the hands are not much equal; For a thin luster spreads here and there.

But the stars that are in the hands of the Ophiuchus are common to the Serpent, just as Aratus himself says: Both are worn out by the Serpent.

But the stars in the Serpent, to which the Ophiuchus is attached, are not inferior in brightness to those in the shoulders; rather, those in the shoulders are much brighter. Hence one might well wonder how Attalus says they are sufficiently bright.

IX. Next, Aratus speaks concerning the Claws: But they are destitute of light, [or "reproachable"] and by no means [20] illustrious.

Attalus says that Aratus calls them "reproachable in lights" not because the stars in the Claws are small, but because there are only four of them [4] which do not fulfill their appearance; and that he calls them "by no means illustrious" because they are not similar to one another. ^C But it does not seem to me that he calls them "reproachable in lights" and "by no means illustrious" for that reason, but rather because they are not bright. For even in their heliacal risings, he speaks thus about them:

Nor may the approaching Claws, weakly shining, Pass by as enfeebled.

He adds, therefore, immediately: ... since the great sign of Bootes Rises in a throng, marked by Arcturus.

Suggesting that we are able to take note of the Claws by means of Arcturus, but not easily by themselves because of their smallness; for as he is accustomed in most instances to call faint stars "thin" [tenuous] and "by no means illustrious."

X. In what follows, they seem to me to be entirely ignorant concerning the Bear: Eudoxus says thus: "Below the head of the greater Bear ^D lie the Twins; in the middle, the Crab; below the hind feet, the Lion." And Aratus:

Beneath her head are the Twins; beneath her middle is the Crab; And beneath both feet, the Lion shines clearly.

^A To this, Attalus and all the others subscribe. That they are mistaken, however, is manifest from the following. For the head of the Great Bear, according to the opinion of the aforementioned men, is the more northerly star of the two leading stars in the quadrilateral; but situated on the forefeet is the more southerly of those same stars. That the aforementioned star, according to them, lies on the head, is made clear by the fact that they say the star located at the tip of the Dragon’s tail is set upon the head of the Bear. For no other star lies near the one at the tip of the Dragon's tail, except for the more northerly of the leading stars in the quadrilateral; for the one at the tip of the Dragon's tail occupies the third degree of the Lion, as if on a parallel circle, while the aforementioned star in the quadrilateral occupies a little less than the third degree of the Lion. That the more southerly of the leading stars in the quadrilateral lies on the forefeet, Eudoxus makes clear by saying thus: "Before the forefeet of the Bear there is a shining star." Then Aratus: "Like that which is borne before her feet, both fair and great." ^B For only one shining star precedes the more southerly of the leading stars in the quadrilateral, which is shown even today on the forelimbs. And to speak generally, all the ancients used to configure the Bear only out of seven stars. But what we have said becomes clearer in the case of the Little Bear. For it is agreed that its head and feet are placed in those four stars which surround the quadrilateral; for no other bright stars lie adjacent to them, as they do to the larger quadrilateral, such that they might deform its head and feet, which the coil of the Dragon surrounds, as the same author asserts: "In the coil, Cynosura has her head; and winding about her, it reaches even to her feet." ^C Since these things are so, how is it possible for the Twins and the Crab to lie beneath the Bear, if indeed the head and the forefeet are located in the third degree of the Lion? Therefore, only the Lion should be set beneath the Bear. For the star in her hind feet, on which is the more southerly of the following stars in the quadrilateral, occupies less than the twenty-fifth degree of the Lion. But in total, if it were the design to designate any constellations throughout the entire Bear, one ought to have placed the Virgin beneath it, or rather, indeed, a part of the Claws. For the star at the tip of the Bear's tail, which is the last of the seven that are toward the east, according to the circle parallel to the equinoctial, occupies the fourth degree of the Claws; I mean this in such a way that the tropical and equinoctial points are located at the beginnings of the signs. But if these aforementioned [(55)] stars lie in the middle of the signs, as Eudoxus ^D [alt-version omitted]

^A says, one should not place the Lion under the hind feet of the Bear, but the Virgin. For the more southerly of the following stars in the series, according to the aforementioned division of the zodiac, holds the tenth degree of the Virgin; and the more northerly one, about the sixteenth degree of the Virgin. But the Crab should have been placed at the head and the fore feet. For the leading stars in the series will occupy, according to the aforementioned division, the eighteenth degree of the Crab. It is clear also from what has been said, and because beneath the whole Bear, according to Eudoxus, there must lie the Crab, and the Lion, and the Virgin, and the Claws. For the star at the tip of the tail of the Bear occupies, according to the same division of the zodiac, about the nineteenth degree of the Claws.

XI. Again, Aratus, speaking about the Charioteer, brings up these points:

It seems to me, however, that he disagrees with the appearances also in these points. For only the feet of the Charioteer appear at the same time as Taurus; but the rest of his body rises with the Fishes and the Ram. And he himself says in what follows:

But the Kids, and the palm of the left foot, with the Goat ^C Are borne along with Taurus.

But whatever he says is borne along with Taurus, these things rise at the same time as the Ram, according to him; for he denotes in this way the simultaneous risings of all the stars; for example, the beginning of the sign being on the horizon, which stars appear risen near the horizon. The right shoulder and the right hand rise long before the left foot. It is evident, therefore, that according to Aratus himself, only those parts at the feet rise with Taurus; the rest of the body, and the left ^D [side]...

I cannot praise Hipparchus, who wrongly refutes Aratus. For he does not say that the whole Charioteer rises with Taurus, but since he has his feet at Taurus, he is to be thought of as speaking about these very parts, so that the meaning is, as interpreted by Theon, that whatever parts of the Charioteer ascend with Taurus do not set at the same time. For of those things that rise together, the more northerly ones, because they have a greater arc of their parallel circle above the horizon, precipitate more slowly toward the setting; but the more southerly ones set more quickly. But Hipparchus objects against this explanation, that even those things which are at the feet of the Charioteer rise later and set earlier than the corresponding parts of Taurus. But this is not true in all cases. For some things rise together on both sides. And indeed Hipparchus is mistaken; whose speech means this, that no part of Taurus ascends at the same time as a part of the feet of the Charioteer. It is no less false what he says, that the feet of the Charioteer set entirely before Taurus. This is refuted even by the authority of Hipparchus himself, who in book III, number XV, says that Taurus sets with the part of the zodiac which is from the twentieth degree of the Ram to the twenty-sixth of Taurus, and that the last part to set is that which is at the extremity of the left horn. But this same author in the first book and number XI says that the right foot of the Charioteer descends with the twenty-sixth degree of Taurus. Therefore, the whole of Taurus sets before the feet of the Charioteer.

^A And yet not even this is helpful to him; because he does not speak of the whole, but that of the parts of the Charioteer that arise with it, the Bull sets earlier. For this also is false. For the parts situated at his feet not only do not fall behind the Bull, but even descend first. At any rate, the parts at the right foot of the Charioteer descend with the twenty-first degree of the Bull. If, therefore, he were writing in accordance with the phenomena, as Attalus supposes, it would have been much better and more remarkable to say that the tip of the Charioteer's foot, having risen later, descends first, rather than to assert this—that having risen at the same time, it descends later.

^B XII. Following these, all have fallen into error concerning Cepheus, affirming that his feet, with that star which is at the tip of the Bear's tail, form an equilateral triangle, as Aratus also says: 106 Equal to it a line from the tip of the tail extends To both feet, which is stretched from foot to foot. For the side measuring the interval between the feet is smaller than either of the others, so that an isosceles triangle exists, and not an equilateral one.

Regarding this, Aratus speaks thus concerning the Lyre: He placed it (says Hermes) before the unknown image; and it is situated to the East of the Kneeler. ^C Nor should anyone respond here that Aratus calls those things situated to the East "first" in the masculine gender. For on the contrary, he frequently calls those situated to the West "first." Immediately, therefore, after speaking of the Ram, he brings in those about the Fishes, and says: those that also precede it.

These things written by Aratus concerning Cassiopeia are no less false: ...not very many By night appearing in the full moon, Cassiopeia: For not many and frequent stars illuminate her. For the majority of those shown in her are brighter than those in the shoulders of Ophiuchus—which he nevertheless says are visible even in the full moon, speaking thus: ^D (57) Hipparchus draws his argument to the effect that the feet of the Charioteer precede that part of the Bull in their setting, with which they had risen, from the fact that the star which sets last in the Charioteer's asterism, namely, that which holds the right foot, is depressed with the twenty-seventh degree of the Bull. There is no force in this argument, unless it signifies this: that three degrees of the Bull remain which have not yet set, when the feet of the Charioteer have already finished their setting; which complete their setting with the twenty-seventh degree of the Bull. There is, in the right and southern foot of the Charioteer, a certain star, placed directly above the extreme tip of the northern horn of the Bull, of which Hipparchus speaks. In his age, this was situated at more than the twenty-second part of the dodecatemorion of the Bull; it rose with about its third part, and set with the twenty-seventh part of the same, as we have discovered from our tables entirely in accordance with the mind of Hipparchus. Therefore, that reasoning proceeds in no other way than as I have said. And yet, the fallacy of Hipparchus in this matter is manifest, confusing the asterism of the Bull with its dodecatemorion. The Bull, I say, with whose twenty-seventh degree the right foot of the Charioteer sets; this, which is a dodecatemorion in the zodiac of the Bull, Hipparchus imprudently confused with the starry figure of the Bull, about which Aratus wrote. For if he were speaking of the asterism alone, he would not only act absurdly, in dividing the asterism into thirty degrees, but he would also contradict himself; as one who in book three, number XV, taught that the whole figure of the Bull sets before that very foot of the Charioteer. But see concerning this error of the great man what is discussed below in column 1347.

^A Such are the bright shoulders lying beneath that head; they are visible, and even under a full moon they would be apparent.

And they are, indeed, almost more brilliant than those in Andromeda, except for those in the head and the one following those in the girdle, concerning which he says: "Do not think overmuch to examine the night, so that you may see it the better. Such is its head: such are its shoulders on both sides, and the extremities of its feet, and all the girdles."

Again, Eudoxus is found to be mistaken concerning the head of the Great Bear. In the one work which is inscribed *Phaenomena*, he speaks in this manner: "Under Perseus and Cassiopeia, not far off, is the head of the Great Bear. The stars between them are dim." And in the other, which is inscribed *Mirror* [Enoptron], it is written thus: ^B "Behind Perseus and near the haunches of Cassiopeia, separated by no great space, lies the head of the Great Bear. But the stars between are dim." For the head of the Great Bear does not lie toward Cassiopeia and Perseus, nor is it at a small distance from them. For Cassiopeia is at the 14th degree of Pisces; Perseus is at Aries; but the head of the Great Bear, according to Eudoxus, is attributed to the 16th degree of Leo. It would be nearer to the truth, therefore, to say that Perseus and Cassiopeia are located at the tip of the tail of the Lesser Bear. For the last and brightest star of this one is situated at the 18th degree of Pisces; but as Eudoxus divides the zodiacal circle, it is around the third degree of Aries.

XIII. In regard to Aries, also, Aratus seems to me to have fallen into ignorance, claiming that it cannot be seen during the full moon on account of the smallness of its stars; and that its position must be marked out partly by those stars which are in the girdle of Andromeda, and partly by the triangle adjacent to it from the north. For these are his words: "The paths of Aries move swiftly there." And a little later: "It is itself languid and obscure, so that it may be seen ^C by observers during the moon; but one might nevertheless judge it by the girdle of Andromeda, for it is set a little below it." And again: "And there is also another sign set near it, shaped like a Delta, similar to both sides in equality; the third is not so, but it is very easy to find, for it is bright above many." To these, the stars of Aries are a little further south. But there is no need to mark out Aries from these. For the three stars situated in its head are brighter ^D than...

[these]. Furthermore, that which is situated in its front feet is well-known. These statements by Aratus are also false:

"But those that are still further ahead; furthermore, in the southerly regions, the Fishes..."

For both are not further south than Aries, but only one of them. For of the stars in the rostro of the more northerly Fish, those which are a little further south than the one following those in the belt of Andromeda are distant from the northern pole by 70 degrees; the one preceding those in the tail is distant from the northern pole by 78 degrees. Moreover, of the stars in Aries, the one situated more northerly on the rostrum is distant from the pole by a little less than 78 degrees; likewise, the more northerly one in the tail holds the same position. But all the stars that are contained in the whole body of Aries are south of these. It is therefore clear that one of the Fishes is more northerly than Aries. ^B

In the passages concerning Aries, Attalus is also ignorant, speaking as follows: "Observing that Aries is neither accurately outlined, nor endowed with bright stars that might be clearly visible even when the moon is waning, he attempts to clarify the position of these [stars] through the adjacent stars, and through those that move in the same circle as it." For besides the fact that it possesses bright stars—those in the head, as we said, and those in the front feet—it also seems to me that he is altogether mistaken, assuming that the poet has made the position of Aries clear by means of stars that are carried in the same circle as it; for this reason, he makes this observation. But, explaining what follows Aries, he adds this:

"In the middle, it grazes the vast heaven: where the tips of the Claws, and the belt of Orion, rise."

XIV. In the following verses, Aratus is ignorant when he speaks about Perseus: ^C

"Near to his left knee, all the Pleiades are carried."

For the left knee of Perseus is far from the Pleiades. But Attalus says that the word "near" (ἄγχι) is not used for "near" (ἐγγύς), but for "very near" (ἐγγυτάτω). He thinks that the poet intends to say that the left knee is situated closer to the Pleiades than the rest of the stars. But he does not say this. For the two bright stars in the left foot of Perseus, and furthermore those in the left shin, are much closer to the Pleiades than the left knee.

It is also false, as stated by Aratus, that the Pleiades consist of only six stars, indeed: ^D

"...seven, he says, they are explicitly called, Though only six appear to the eyes..."

But this escapes him. For if anyone directs his eyes on a clear and moonless night, seven stars are seen to be contained in that constellation. Hence, there occurs that...

mirari, quemadmodum Attalus ea quæ de Vergiliis dicta sunt, enarrans, hoc erratum præterit, quasi in eo recte ille sensisset.

Pālin te ^A Aliud Arati in sequentibus erroris caput, ubi de Cygno disserit:

'Αλλ' ὁ μὲν ἠερόεις· τὰ δέ οἱ ἐπιτετρήχηνται Αστρασιν οὔ τι λίην μεγάλοις, ἀτὰρ οὐ μὲν ἀμαυροῖς.

Verum is quidem, ait, obscurus: alæ autem ei asperæ sunt stellis haud adeo magnis: neque tamen imbecillis. Habet enim Cygnus cum plures lucidasque stellas: tum eam, quæ in cauda est, splendidam in primis, et ei propemodum æqualem, quæ lucida est in Fidicula.

XV.

Σῆμα δέ τοι κείνης (59-60) ὥρης, καὶ μηνὺς ἐκείνου Σκορπίος ἀντέλλων εἴη πυμάτης ἐπὶ νυκτός. Ἤτοι γὰρ μέγα τόξον ἀνέλκεται ἐγγύθι κέντρου Τοξευτής· ὀλίγον δὲ παροίτερος ἵσταται αὐτοῦ Σκορπίος ἀντέλλων· ὁ δ' ἀνέρχεται αὐτίκα μᾶλλον. Τῆμος καὶ κεφαλὴ Κυνοσουρίδος ἀκρόθι νυκτὸς Ὕψι μάλα τροχάει· ὁ δὲ δύεται ἠῶθι πρὸ Ἀθρόος Ὠρίων· Κηφεὺς δ' ἀπὸ χειρὸς ἐπ' ἰξύν.

Περὶ δὲ τούτου ὁ Ἄτταλος προενεγκάμενος, αὐτίκα γράφει ταυτί· «Τὰ μὲν οὖν λοιπὰ μετρίως εἴρηκεν ὁ ποιητής· τὸ δὲ περὶ τοῦ Κηφέως ὁμολογουμένως ἠγνόηκε, φήσας αὐτὸν δύεσθαι κατὰ καιρὸν τοῦτον. Οὐ γὰρ δύσιν, ἀλλ᾽ ἐκ τῶν ἐναντίων ἀνατολὴν τότε ποιεῖται. Καὶ τοῦτο δι' αὐτῶν τῶν ποιημάτων φανερόν γίνεται. Τῆς μὲν γὰρ δύσεώς φησιν αὐτὸν ἄρχεσθαι, καθ' ὃν καιρὸν αἱ Χηλαί, πρὸς τῇ ἀνατολῇ οὖσαι, μέλλουσιν ἀναφέρεσθαι. Πάντα δ' αὐτοῦ δεδυκέναι τὰ μέρη, τὰ δυνάμενα δύεσθαι, ὅταν ὁ Σκορπίος πρὸς τῇ ἀνατολῇ γένηται.» Δοκεῖ οὖν μοι ἀγνοεῖν ὁ Ἄτταλος, φάσκων τὰ μὲν περὶ τῆς κεφαλῆς τῆς μικρᾶς Ἄρκτου, καὶ περὶ τοῦ Ὀρίωνος ὀρθῶς εἰρηκέναι τὸν Ἄρατον· περὶ δὲ τοῦ Κηφέως διημαρτημένως. Τοὐναντίον γὰρ περὶ μὲν τοῦ Κηφέως εἴρηκε συμφώνως τοῖς φαινομένοις· περὶ δὲ τῶν ἄλλων, διαφώνως.

XVI.

Ortum solis in Sagittario positi hæc verba respiciunt, quando Scorpius ante lucem oritur. Ridicule proinde Solinianus Exercitator de occasu solis explicat, propterea quod ἀκρόθι νυκτός de ineunte nocte dicatur; quo nihil ineptius dici potuit. Huic ergo silentium indicet Hipparchus, qui de extrema nocte, uti necesse erat, interpretatus est.

^A That these signs are not fitted to the rising of Sagittarius, but to the rising of Scorpio, the poet himself demonstrates. For since the sun is positioned in Sagittarius, this Sagittarius himself cannot be seen; and since he wished to explain the signs of this time—which must be perceivable by the senses to be signs at all—before the sun’s rising, while the night is still present and the stars are visible, he says, "Let the sign be Scorpio rising at the end of the night." It is therefore reasonable that he proposes the remaining signs to us while it is still night, if indeed they are to be signs. This is clear also from the fact that Aratus himself says of the Bear:

*Then too the head of Cynosura at the end of the night,*

as though it pertains to the outermost part of the night; and of Orion:

*...but he sets at the break of dawn.*

This is before the daybreak, and by no means, ^B by Zeus, before the sun is already rising at the beginning of this time. Attalus was misled because, to the words spoken concerning Sagittarius,

*...but he ascends soon higher,*

he joined "then the head of Cynosura," and what follows. Yet even if this were granted to him, not even so is what Aratus said tolerable, as Attalus thinks: that at the rising of this [Sagittarius], the head of the Lesser Bear runs very high. For when it is borne very high and culminates, it is so far from Sagittarius rising that Aquarius does so. For the head of the Lesser Bear, according to the circle parallel to the equinoctial, occupies the end of Scorpio. While this is culminating, in the zodiac the third degree of ^C Sagittarius culminates; when this is culminating, in the region of Greece, and wherever the longest day is of 14 1/2 equinoctial hours, the 17th degree of Aquarius rises. Therefore, when the head of the Lesser Bear culminates—which is the same as saying, "it runs very high"—at that time Scorpio does not begin to rise, but more than half of Aquarius has already risen, along with the whole of Scorpio. From these things, it is evident that this is not said tolerably by Aratus, as Attalus claims, but that it disagrees with the appearance of the phenomena by more than three signs.

That indeed Orion does not set entirely when Scorpio begins to rise, as both Aratus affirms and ^D Attalus agrees, but rather when Sagittarius rises, this is made manifest by these facts. For in the regions around Greece, where the longest day is 14 1/2 hours, his left foot begins to set when the 7th degree of Taurus is setting; and lastly his right shoulder sets when the 24th degree of Taurus is setting. And if one must add the *collorobum* (the club) which he bears in his right hand, it occurs with the last part of Taurus.

It is clear, therefore, that if it sets with Taurus, the whole of Orion does not set when Scorpio is beginning to rise, but rather when Sagittarius is rising. ^A That the remaining things said about Cepheus are in accordance with the phenomena, and do not disagree as Attalus assumes, can be made clear through these points. His parts which are south of the always-visible circle begin to set when the 10th degree of the Claws [Libra] is rising; or, as some say, it is possible [they begin to set] at the 13th degree of the Claws. ^B It is clear, therefore, that while Scorpio is rising, the two parts of Cepheus must have set. But Attalus was mistaken in saying that Cepheus does not set, but rather rises from the opposite parts, having accepted the poet’s intention—as I have already said—and having assumed that Aratus meant that while Sagittarius is rising, both Orion and Cepheus set.

XVII. Apart from what has been said, both are ignorant—that is, Aratus and Attalus, who agrees with him—as to why Cepheus sets at the belt: ^C *Grazing the earth; and all those parts near the head* *Dipping into the Ocean: these it is not permitted [to set]; but those parts* *The Bears themselves prevent, the feet, and knees, and the loins.*

For in the regions around Greece, Cepheus does not set down as far as the belt, nor even as far as the shoulders. For only the stars situated at his head set, while the shoulders are carried in the always-visible segment, neither rising nor setting. ^D For the bright star in the right shoulder is distant from the pole by 35 degrees, while the bright one in the left shoulder is distant from the same pole by 34 degrees and 15 minutes. Where the longest day is 14 1/2 hours, there the always-visible circle is distant from the pole by 36 degrees; but at Athens, by 37 degrees. It is clear, therefore, that the bright stars situated at the shoulders of Cepheus are always carried further north than the always-visible circle, or, as some say, they are in the hands of Cepheus, depending on how one measures his body, which has no stars. And the error becomes much greater if we assume the inclination of the world itself. For where the longest day is...

^A 15 hours long, there Cepheus is carried whole within the Arctic circle.

Besides this, Aratus has erred regarding the constellation of the Argo, when he writes that whatever belongs to it from the prow to the mast is devoid of stars, expressing it in these verses:

And partly dim, and starless to the very Mast from the prow it runs, in the rest all shining.

For the bright stars which are situated at the cutting of the ship—of which the more northern one is on the deck, and the more southern one on the keel—deviate much toward the east.

XVIII. Following these, Aratus, having passed through the remaining southern stars of the zodiac, adds these:

These, indeed, in small space, and in small light ^B posited Between the Mast and the Whale are rolling, Faint ones falling under the flanks of the Hare.

In these lines he seems to have made a slip (for this is how it must be spoken), assuming that the anonymous stars are situated between the Mast and the Whale. For it is agreed that they should be placed between the River and the Mast. For Orion is turned toward the south of the Hare. And to the south of this are still situated the anonymous stars—which the Mast of the Argo succeeds to the east. Furthermore, from the left foot of Orion, the River reaches toward the west as far as the Whale; but after this, having turned toward the east, it turns back again towards the south and the west. But Aratus himself says that the Whale is situated ^C

A little above the lying starry River.

It is clear, therefore, that the stars lying under the Hare must be placed between the River and the Mast. And Eudoxus, indeed, feels as we do, for he speaks thus in one book: "Under the Whale the River lies, beginning from the left foot of Orion. Between the River and the Mast of the Argo, under the Hare, is a place not large, containing faint stars." And in the other book he writes thus: "Between the Mast of the Argo, under the Hare, there is a small region containing faint stars." But Attalus did not mention this slip of Aratus, thinking that it was truthfully reported by Aratus; yet he rebukes him, as if he were not acting correctly and knowingly in ^D describing these verses:

But in moderate space, and likewise set in moderate brightness, In the middle of the Steering-oar, they roll between the Whale, Lying under the flanks of the Hare, Lacking a name. For they are not like limbs Scattered upon a finished image: such as many Moving in order walk along the same paths With the turning years; which some men who are no longer Among the living observed, and thought to call everything by name, Figuring them in groups. For he could not utter The name of all things distinguished one by one, nor learn them. For many are everywhere; moreover, those of many are equal.

^A Having brought these points forward, Attalus adds: "In these verses the poet struggles rather unhappily, falling into the same line of thought repeatedly, and being unable to express his meaning clearly and without ambiguity. For he wishes to point out that the stars situated between the Whale and the Rudder, below the Hare, are not counted in any constellation, but are nameless. For since there were many stars, and some were similar in magnitude and color, the first who arranged the stars and assigned names to each according to their groupings could not have recognized them ^B if they were scattered, unless he had first selected from the crowd those which, when gathered together, could form a certain image, and thus applied names to them."

But to me, it appears to be the exact opposite: that Attalus has not grasped the poet's meaning, and not only this, but that he has failed to explain clearly and has interpreted rather foolishly the meaning of the verses he proposed to clarify; whereas Aratus, however, has expressed it masterfully. For he intends to say that there are nameless stars situated between the Rudder and the Whale, beneath the Hare, which are few in number and small in size. They are not positioned in such a way that animals or some constellation could be formed from their location, like the rest of the stars which some of the ancients assembled into forms, ^C though he did not dare to assign a form to every single one. For since there were many stars, scattered individually, he could never have grasped them in any one particular image, or figured them in groups. For this reason, it seemed good to him to take those stars that were near one another and gathered together, and to comprise them in certain names and to fashion them.

XIX. Next, Aratus speaks concerning the Altar: *But beneath the burning sting of the great monster* *The Scorpion, near the south, the Altar hangs;* *Which you will perceive rising for only a small amount of time;* *For it rises opposite to Arcturus.* ^D *And the paths of Arcturus are indeed very lofty,* *But it returns more quickly beneath the evening sea.*

In these lines, it seems to me that Aratus is mistaken, assuming that the Altar is as far from the south pole as Arcturus is from the always-visible circle; and Attalus, likewise, by agreeing with him, is also mistaken. For in explaining the meaning of the verses we have mentioned, he says as follows: "In his discourse concerning the Altar, he says that it is situated near the never-apparent circle..."

^A pole, having the same relation as the star called Arcturus has toward the visible pole. Hence he says that the motion of the Altar above the earth is short, while that of Arcturus is long." But they form a false judgment by claiming that Arcturus is as distant from the northern pole as the Altar is from the southern. For, in the first place, the stars that are in the Altar are not on this same equidistant circle; but many are much more southerly than others, and some are more northerly. Then, even if we pass over this and make the comparison with the most central of the stars in the Altar, the statement is not correct even then. For Arcturus is distant from the northern pole by 59 degrees; but the bright star in the middle of the Altar ^B is distant from the southern pole by 46 degrees. Arcturus is therefore much further away [from the pole] than the Altar is; and it is further not only than the Altar, but even than the Scorpion itself, under which the Altar lies; excluding those stars that are positioned in its chest and forehead, and additionally the one vertebra that is the first after the chest. For the second vertebra after the chest is distant from the southern pole by 59 degrees, just as Arcturus is from the northern pole; but the remaining ones are less distant than this; and the most southerly of them is distant by 52 degrees and 20 minutes.

XX. Furthermore, when Aratus had written about the Altar, that whenever it is seen from the north to be obscured by a cloud, then one must expect the south, he immediately adds the following regarding ^C the Centaur:

*But if from the western sea the Centaur’s shoulder* *Should be far off—as much as the former—and a light mist* *Should hide it; and besides, if it should create such signs* *With the most splendid Altar at night, you must not by any means* *Watch for the south, but rather look for the east wind.* *You will find that star lying beneath two others.* *For its parts that resemble a man lie below the* *Scorpion, and the horse’s tail beneath them the Claws hold.*

In these matters, first of all, it is impossible to assert which shoulder of the Centaur he designates. For neither is the one distinguished from the other as a separate constellation, but both culminate at the same time. Hence the poet's words can be applied to one of the two as well as to both. But if the shoulder of the Centaur is equally distant from the east ^D and the west—which is what the word "western" signifies; and this occurs when it is culminating—then the east wind should be expected, not the south. For the shoulders of the Centaur are not a little distant from one another, from east to west.

But to leave these matters aside, in this point also he is utterly ignorant, saying that the human parts of the Centaur lie beneath the Scorpion, and the equine ones beneath the Claws; yet he refutes this himself from the position of that same asterism, though he thus mixes the dodecatemoria once again with the stellar signs. For he says the last of all is situated in the head, in the 29th degree of Virgo, which is in the right shoulder in the 6th degree of Libra; and the more southerly of the hind feet is in the 13th degree of Virgo. Therefore, the human parts cannot lie beneath the Scorpion, nor the equine ones beneath the Claws. Indeed, all those positions refer to the equinoctial or the parallel; and thus Virgo, the Claws, and the Scorpion are equinoctial dodecatemoria, not stellar forms, about which alone Aratus speaks; but even so, his reasoning does not hold.

^A For the Centaur lies almost entirely under Virgo, except that the right shoulder, the right hand, and the front legs of the Horse are stretched out under the Claws. Indeed, the star situated most prominently in the head occupies the 29th degree of Virgo; the one on the right shoulder occupies the 7th degree of the Claws; and the one further south in the hind legs is distant about 13 degrees from Virgo. How, then, is it possible for the parts of the Centaur resembling a man to lie under the Scorpion, and the horse-tail parts under the Claws? Attalus passes over this point too, as if his words were well-spoken.

Following these [comments], he is also ignorant regarding that which follows from him: "And it seems to be always stretching its right hand Opposite the rotating Altar."

For between the right hand and the Altar not only the whole Beast lies, but also most parts of the Scorpion. For the right hand is situated around the parts of the Claws; but the Altar [lies] under the lowest parts of the Scorpion: as Aratus himself says: "And beneath the burning sting of the huge monster Scorpion, near the south, the Altar hangs."

XXI. Next, Aratus speaks thus regarding the tropics, the equator, and the zodiacal circle: "They themselves are widthless ^B and fitted to one another All; but in measure two answer to two."

Since it is written in two ways, some saying "They themselves are widthless," and others "They themselves are wide," Attalus says it is better [to read]: "They themselves are wide." "For indeed," he says, "astrologers suppose the tropics, the equator, and the zodiac to be wide," and [claim] that the sun does not always perform its turnings on the same circle; but sometimes further south, and sometimes further north. And that this happens, Eudoxus also says; he says, therefore, in the *Mirror* as follows: "The sun appears to perform its turnings in different places..."

^C ...but since this later reading has been adopted, so that they are "fitted to one another," this means they correspond to each other in magnitude: the zodiac to the equator, one tropic to the other tropic. But the former reading is expressed by Cicero and Avienus; and it is not a little more plausible. Attalus' reading is utterly inept. For those four circles are not "wide." Yet the same [reading] possesses a most beautiful and highly illustrative trace of ancient observation: from which it appears that those ancients perceived an anomaly in the obliquity of the ecliptic, who so explicitly thought that the solstices do not occur at the same perpetual point, but saw them now further south, ^D now further north: as did Eudoxus; as did Attalus, who even therefore attached "width" to the circles: which, indeed, he could with equal right attribute to the solar tropics as to the zodiac; and [thereby] be secure from Hipparchus’ reproach. For just as, on account of the excursions of some of the planets, certain limits are set on either side of the ecliptic, and a certain circle like a belt or band is marked out in the heavens; so, on account of the sun’s fluctuations at the solstices, and its occasional further approaches to the north, or retreats to the south, some "wide" circle can be conceived. And thus that passage of Hipparchus is wonderful and worthy of consideration.

^A Verily, Attalus seems to me to display his ignorance in this matter, when he supposes that the sun sometimes has its turnings further to the south, and sometimes further to the north, and that therefore it is necessary to suppose the circles are wide. For if the sun is not carried through the middle circle of the zodiac, but deviates from this toward the north and toward the south, just as the moon does, it is clear that the shadow which proceeds from the earth also varies in the same way as they do. And since this happens, the eclipses of the moon would necessarily differ greatly from the predictions compiled by astrologers, since they assume in all their operations that the center of the shadow moves along the circle that passes through the middle of the zodiac. But they do not differ by more than two digits, and rarely, even then, very much from those most elegantly compiled treatises.

To say, however, that such great width exists in these circles is the same as asserting that they are devoid of width; ^B not to mention that it is not sufficiently certain whether it is from the motion of the sun or from the moon that such variety occurs in lunar eclipses. To these points, both Aratus and the mathematicians have pretended that only the tropic circles have width for that reason, but not at all the equinoctial. But to speak universally, I believe that all these mathematicians whom I have mentioned assigned no width to the tropic circles, nor to the equinoctial, nor to that which is always visible, nor to that which is always hidden. For it is not even possible to conceive by thought that they have any width. For it happens that each one is accustomed to be contemplated by imagining a constant line alone, and one not endowed with width.

Furthermore, when they assert that the equinoctial and the zodiac are among the greatest circles in the sphere, and that the sphere is bisected by each of them; ^C and that the center of the zodiac, the equator, the horizon, and the meridian is the same; and, moreover, that the zodiac touches the tropic circles at one point; and many other such things: by these points they signify that those circles are entirely devoid of width. For nothing from all those accounts could be correctly used if those same circles were wide; nor would the equinox occur on one day only, but on many. For the sun would make a stay of more than one day in the equinoctial circle, if it consisted of width. Then, in all the reasoning for constructing gnomonic instruments, this is applied as a foundation: that there is no width to those circles, since they are described partly from the center of the sun itself, and partly by the eye of the observer. ^D That Aratus, just like the mathematicians, conceives of those circles without any width, anyone will understand from what he wrote about the equator:

In it, however, days are equal to nights for both, When summer ends, or when spring begins.

For otherwise he would not have assigned the equinox to one day only in spring and autumn, but to more, if it had width. And it is likewise clear from those things which he sings about the tropic:

^A Of that which is measured in the main by eight, Five turn about on the upper side and above the land; Three are at the limit. For if it had width, and was divided into eight, it would be possible for the whole segments to be inclined above and below the world. But indeed, also when speaking about the zodiac, sometimes he writes thus: As much as the ray of the visual radius extends, Six times that much might run under it; but each, When measured equally, cuts off two stars. Sometimes it is thus: As much of its hollow as sinks beneath the Ocean, So much is borne above the earth; and every night, Twelve of the cycle always set; Just as many rise; and to such a length in each, Night is always extended, as much as half the circle Rising aloft from the earth, beginning at night.

He seems to my mind to define it not as having width, but on the contrary, as being without width. For the ray of the eye is straight, and it measures out six times the greatest and widthless circle, but not the one that has width; and for the zodiac, every day and night a semicircle rises and sets, with the sun being carried on a path that is widthless and through the middle of the signs; for this could not happen on one that has width. And from many other things too, it is clear that Aratus assumes the circles are widthless, in accordance with the mathematicians.

XXII. On the Galaxy, and the error in Aratus' measurement of the tropics

XXII. Proceeding next to speak about the Milky Way circle, he adds that of these two circles, two are equal; but the other two are much smaller, saying as follows: To this one in color no other circle ^B Turns; but as for their measures, of the four that exist, Two; but the two that remain are rolled around much smaller.

It does not seem to me to be well-stated, either, that the tropics are much smaller than the equinoctial and the zodiac; for they are less than them by not even the eleventh part.

Regarding the stars which lie upon each of the tropics and upon the equinoctial, Aratus writes in this fashion: Of these, one is near the descending north, And in it both heads of the Twins are borne; And there the knees of the Charioteer are set in place.

And yet the heads of the Twins are not situated upon the summer tropic. For the summer tropic is ^C indeed more northerly than the equinoctial circle by about 24 degrees; but of the Twins, the following head is more northerly than the equinoctial by 30 degrees; and the preceding one by 33 1/2 degrees. Thus far distant from it, which is 1,000,000 of the total sine, to the 91,555 sine of 66 degrees, the complement of the distance of the tropic, that is to say, as to 6905/100000. ^D

^A The one part of a single zodiacal sign is further north than the summer tropic, and the other by about a third part. Moreover, the Heniochus (Charioteer) possesses no stars upon his knees. If anyone places some faint little stars there, he does so ignorantly. For his feet lie very close to the tropic circle. The one which is on the left is 27 parts north of the equinoctial; the one on the right is... parts. Nor can it be said that the stars which we designate as being on the feet are the same ones as those he places upon the knees. For what we say is on the right foot, he also indicates is the same in these verses:

... The summit of the left horn And the right foot of the neighboring Charioteer A single star occupies.

^B Next he says:

The left shin and the left shoulder of Perseus himself.

In this, too, he departs significantly from the truth; for the bright star in the middle of Perseus's body is 40 parts north of the equinoctial. It follows that it is 16 parts north of the tropic, which is more than half of a zodiacal sign. Therefore, the left shoulder is much further north of the summer tropic. For the position of Perseus is such that the parts near his head belong to the north, and his feet toward the south, with the head inclining slightly toward the east.

XXIII. Regarding Andromeda, Aratus writes:

... She holds the middle of the right forearm above.

He is ignorant in this regard as well. For the stars on her right shoulder are further north than the tropic. Of the three stars, the one further south is more than 30 degrees north of the equinoctial. And of the three stars on her right hand, the one toward the south is 32 degrees north of the equinoctial. It is clear, therefore, from these facts that the elbow is well to the north of the tropic, and not to the south, as Aratus claims. ^C Next he says:

The hooves of the Horse, and the neck of the Swan Together with the extreme head.

What stars he placed upon the hooves of the Horse is not sufficiently clear; but regarding what he says about the Swan, thus:

... near the right hand Of Cepheus, showing the right limits of the wing, By the left wing, the foot of the Horse is inclined,

it seems that he might approach the truth. For the one at the tip ^D of the wing is further north of the equinoctial by 23 degrees. Of the Swan, the beak...

is further north of the equinoctial by 25 degrees; ^A and the one next to it, as if located in its throat, is further north of the equinoctial by 31 degrees. It is clear, then, that neither the head of the Swan nor its neck can be situated on the summer tropical circle.

Next he says:

In these lines he is completely ignorant. For of the shoulders of Ophiuchus, the right one is far closer to the equinoctial than to the tropical circle, and the left one is a third of a sign further south of the tropical circle. For the right shoulder is further north of the equinoctial by approximately 7 degrees, while the left is approximately 15 degrees. ^B

Next he says:

It seems to me that he has spoken these things in agreement with the phenomena. For of the stars in the chest of the Lion, the most southern and brightest—which some place in the heart—is a little further south of the tropical circle; and the one next to it, ^C situated toward the north, is a little further north of the summer tropical circle. And of the four bright stars in the thighs and legs of the Lion, the second one from the north, situated in the thighs, is further north of the tropical circle, while the third, situated in the legs, is further south of the tropical circle. It is clear, then, that the Lion is cut lengthwise by it under the chest and the flank. Of the stars in the Crab, of the four situated around the nebula, the one more to the south is further south of the tropical circle by not less than 1 degree; and the more northern of them is further north of the summer tropical circle by less than 1 degree. Of the two stars situated to the east around the nebula, the one further south is situated almost upon the tropical circle itself, ^D while the one further north and leaning toward the north is distant from the same by approximately 2 degrees. It is clear, then, that he has reported the matters concerning the Crab in a way that is as close as possible to the observable phenomena.

One must discern, however, that Eudoxus had recorded the things about the Crab, the Lion, the Virgin, the feet of the Horse, and also those concerning Perseus, the knees of the Charioteer, and the heads of the Twins, even before Aratus, whom we believe Aratus has followed. Eudoxus, however, asserts that the head of Ophiuchus—not the shoulders—is situated on the tropical circle; which is, in fact, itself false. Nevertheless, the head is closer to the tropical circle than the shoulders are, for it is further south of the summer tropical circle by about seven degrees. Furthermore, the Swan's neck and left wing [sit] in the tropical circle.

^A, as does the right hand of Andromeda. From this, it is evident how much each of them differs from the appearances in these matters. But Eudoxus in particular places the neck of the Serpent, which Ophiuchus holds, and the right hand of the Kneeler [Ingeniculus] in the tropical circle, which is consistent with the evidence of the appearances.

XXIV. Now, as for those things that are on the winter tropical circle, Aratus describes them thus:

Another, in the opposite south, cuts through the middle Of Capricorn, the feet of Aquarius, and the tail of the Whale. In it also is the Hare; the Dog, however, does not take up A very large part, but as much as his feet occupy; in it is the Argo, And the large back of the Centaur; in it is the sting Of the Scorpion; in it is the bow of the famous Archer.

In these matters, the rest generally agree with the appearances; but the stars that are in the sting of the Scorpion are further south of the winter tropical circle by more than 8 degrees. It would therefore be more accurate to place the middle of the Scorpion ^B on the winter tropical circle. Eudoxus, while he holds the same opinion as Aratus on other points, nonetheless says that the bend of the River is situated on the tropical circle, and that the feet of the Dog are at its tail; he also places the Beast [Fera] upon it, which the Centaur holds, but he is mistaken in this as well. For the Beast is much further south than the winter tropical circle.

XXV. Regarding the equinoctial circle, the words of Aratus are these:

A sign for it [the circle] is Aries, and the knees of the Bull are placed. Aries indeed is drawn lengthwise through the circle; Of the Bull, however, as much of the leg as appears [is] the joint.

These things about Aries are said ignorantly. For it is entirely further north ^C of the equinoctial circle, with the exception only of the star which is in its hind feet; for this star is carried on the equinoctial circle.

Aratus continues:

In the same place is the belt of the splendid Orion, And the bend of the burning Hydra; in it also is the light Crater; And the Raven is in it.

Now, the belt of Orion is indeed situated on the equinoctial circle; but the coil of the Serpent, and the Crater, and the Raven, are far further south of the equator; unless, perhaps, those parts that are nearer to the tail of the Raven approach the equinoctial.

There are also (he says) stars, not very many, ^D Of the Claws; in it are also the knees of Ophiuchus.

Of the Claws, only the bright star that is in the northern Claw approaches the equinoctial; the rest are much further south of it. The knees of Ophiuchus are further south of the equinoctial; the left one by 5 1/2 degrees, but the right one by more than 10.

Aratus continues:

Not, however, is it parted from the Eagle; but very near To Jove flies the great messenger; and near to it The Horse's head and neck are turned.

These things also approach the truth. Eudoxus, while he does not dissent in other matters, says that the middle of the Claws lies on the equinoctial, and the left wing of the Eagle, and the loin of the Horse, and furthermore the more northern of the Fishes. But neither does the Eagle touch the equinoctial, and that which is on the loin of the Horse is more northern than the equinoctial by more than 3 1/2 degrees; and indeed the more northern of the Fishes is more northern than the equinoctial by approximately 10 degrees. ^B Attalus, having omitted a detailed discussion concerning the stars that are in the circles which we mentioned above, writes as follows: "As to the places where he clarifies through which stars each of the three parallels passes, I have therefore chosen to leave out the general account, because the circles through which he says they pass cannot actually pass through those stars, as you have followed and examined them for yourself by means of a dioptra." Yet it was necessary, first of all for the sake of the other students of his doctrine, to explain, if he understood it, which stars appeared to be more southern or more northern than the summer tropic, and by how much. Then, in order for it to be understood as one thing, that circles are not drawn through the stars which have been enumerated, there is no need for a dioptra. For since some are far more southern and others are more northern, it becomes evident to one who looks up at them from that very observation, that it is not possible for the equinoctial or any circle parallel to it to be drawn through the aforementioned stars.

^B XXVI. Besides the aforementioned three circles, Eudoxus also clarifies those stars which are situated on the arctic circle; and he says that the left shoulder of Arctophylax lies upon it, and the parts above the Crown, and the head of the Serpent that passes through the Bears; also the parts above the Lyre and the right wing of the Bird; and the breast of Cepheus and the parts above Cassiopeia. Then, under the forward feet of the Great Bear and of the Lion, as far as the shoulder of Arctophylax, it is more southern than the always-visible [circle] in the places around Greece by more than 4 degrees; for it is distant 44 1/4 degrees from the north pole, ^C and the always-visible circle is 37 degrees [from the pole]. The parts above the Crown and the Lyre have been described too generally. For these do not approach the always-visible circle, but each of them is far more southern. For the more northern of the stars in the Lyre is 49 degrees distant from the north pole; and the head of the Serpent that passes through the Bears is carried more to the south, but near the always-visible circle. For the more southern of them, and the one on the left, is 49 degrees from the north pole; and the more northern of those in the Crown is 53 degrees. And the head of the Serpent that passes through the Bears is carried upon the always-visible circle. ^D [The note regarding the textual corruption follows in the Latin apparatus].

chest of Cepheus, moreover, is further south than the always-visible circle, as we have demonstrated above. The upper parts of the right wing of the Swan, and the foot of Cassiopeia, are carried upon the visible circle. For the more northerly of the stars that are in the extremity of the right wing is distant from the northern pole by 40 degrees; while the more northerly of those that are in Cassiopeia, which is situated in the feet, is distant from the same pole by 38 degrees. Furthermore, the feet of the Great Bear are carried further north than the always-visible circle. For the one of them that leads is removed from the northern pole by about 24 degrees; the following one, by about 25 degrees. Truly, therefore, he rightly pronounced that the always-visible circle passes between the Bear and the Lion.

Now, in that circle which never appears, the stars that are contained therein are not seen at all. But they are closest, he says, to it: the extremities of the water of the River, and the bottom of the Ship, and the Rudder. Next, the Wild Beast, and the Altar. Also, the right leg of Sagittarius; and the star which is seen from Egypt is contained in the same. Of these, whatever things are somehow close to the truth are to be set aside as beyond controversy. But concerning that star which is called Canopus, he does not rightly assert that it is never carried within the always-visible circle. For ^B this star is further south than those that are in the Rudder, and is bright; and it is distant from the pole by 38 1/2 degrees. But the circle that is always visible at Athens is distant from the pole by 37 degrees; in Rhodes, however, by 36 degrees. It is certain, therefore, that this same star is more northerly than the circle that is never visible in Greece, and that it can be seen above the earth, just as it is also observed in the regions around Rhodes.

XXVII. Regarding the stars situated on the colures

What is next handed down in the two books by Hipparchus concerning this requires more leisure and labor, so that they may be tested by the reliability of our own tables—the danger of which thing we have already tested in many cases, but the magnitude of an infinite and troublesome task has deterred us from working out more. For even in investigating these very stars which Hipparchus designates, and in selecting them from the lists of Ptolemy or Tycho, there is no small amount of business; and, when you have extracted something certain, an innumerable variety of risings and settings must be explained; which could break and weary even the keenest and most eager person. Here, therefore, we shall make an end of this method of commentary; the rest of the Hipparchian doctrine, which it is of the utmost importance for all to know, you will find explained for the most part in our Dissertations.

BOOK I

^A of the head of the Hydra occupy more than 10 degrees of Cancer. It is plain, therefore, that the neck of the Hydra is left much further from the aforementioned circle.

XXVIII. Regarding the Argo, what he has written is not correct. The leading star in the tail of the Southern Fish is distant from the first point by more than 23 degrees. It is therefore distant by that much from the circle I have mentioned, nor does it move upon it. The Arrow, insofar as it exists, is distant from the same circle, nor is it bisected by it. For the leading star in it is distant by one degree. Wherefore it cannot be divided in two by that circle. Similarly, the entire Swan is situated to the east of the aforementioned circle. For its leading star, which is situated on the tip of the beak, is distant by 1/2 a degree. Of the stars in the tip of the right wing, the one which is situated furthest to the west is not distant from the former by more than 1/2 a degree. Therefore, neither the neck of the Swan nor its right wing can be situated on the aforementioned circle.

^B Furthermore, the left hand of Cepheus is quite far removed from the same circle toward the east. For the stars in his head, especially the leading ones, occupy more than 10 degrees of Aquarius. The bright star in the left hand, which some attribute to the shoulder, occupies 25 degrees of Aquarius. Therefore, it is removed by an interval of almost two signs. Regarding the bend of the Serpent and the tail of the Lesser Bear, however, he pronounced correctly.

XXIX. Regarding the other colure, he says that the left hand of Arctophylax is situated upon it, and that it passes through the middle of it along its length; then the middle of the Claws along their breadth; furthermore, the right hand and the front knees of the Centaur; and after the invisible pole, the bend of the River, the head of the Whale, the backs of the Ram along their breadth, ^C and the head and right hand of Perseus.

Yet, the left hand of Arctophylax is distant from that circle by an interval of almost half a sign; nor is it situated on that same circle which passes through the equinoctial points, as Eudoxus affirms. For the leading star of those in it occupies more than 13 degrees of the Claws. He is, moreover, mistaken in that, where he says that the middle of its body along its length is cut by the aforementioned circle. For the star on the head occupies about 16 2/3 degrees of the Claws; the one on the right foot occupies about 24° 45' of the Claws; the bright star in the belt occupies about 14° 20' of the Claws; and the one in the right hand of the Centaur is distant from the aforementioned circle by about a quarter of a sign. For it occupies 8 degrees of the Claws. The head of the Whale is indeed distant from the aforementioned circle, but not by a large space. For the knot of the Fishes, which is situated after the head of the Whale, and upon its neck, occupies 3° 15' of the Ram. Nor indeed are the backs of the Ram to be placed in that same circle. They are distant from it by more than a third of a sign. For the star that is in the middle of that back occupies more than 11 1/2 degrees of the Ram.

And the right hand and head of Perseus are ^A distant from the same circle by about a third part of a zodiacal sign.

HIPPARCHUS: COMMENTARIES ON THE PHENOMENA OF ARATUS AND EUDOXUS, BOOK TWO

I. Now to the matters concerning the Phenomena of Aratus and Eudoxus ^B discussed thus far, we shall add an investigation of the rising and setting of parts of the zodiac with the stars, in order to demonstrate both those points in which both have attained the truth, and those which they have recorded that are contrary to the appearances.

First, Aratus, wishing to explain how one might infer the hour of the night from the rising and setting of the stars, expressed it in these verses: "It would not be a thing to be spurned for one observing the day To consider the parts when each of them rises. For always with one of them the Sun himself rises; You would discern these best by looking directly at them. ^C But if they should be obscured by black clouds, Or, hidden by a mountain, they should rise, Make the sure signs from those rising with them; And Ocean himself, from the very ends on either side Would supply them: for he rolls numerous things unto himself From the bottom, as he rolls each one of them."

He asserts, therefore, in these lines that we can most especially determine the hour if we observe any one of the twelve zodiacal signs rising. For he who knows in which sign of the zodiac the Sun is, and in what part of it, and because six signs rise throughout the entire night, ^D he supposed that one would easily understand the hour of the night from the rising sign. But if, on account of mountains or clouds, the rising sign is not visible, he thought that we could determine the rising sign from the rest of the stars, which are situated outside the zodiacal circle but are close to the horizon, if we notice what kind of stars rise or set together with each sign.

II. But in this he first errs, by assuming that it is sufficient for determining the hour of the night to calculate how many signs remain until the rising of the Sun. For this would be true if each of the signs rose in an equal amount of time. But since there is a great differ-

-^Aence in the risings of the twelve signs, he who uses the aforementioned calculation will be ignorant of the hour of the night. One might especially wonder how even Attalus subscribes to this. For he speaks in this manner: "In what follows he attempts to demonstrate how one might be able to discern the hour of the night by means of the stars." For since the beginning of the night is the setting of the sun, and the sun is always in one of the twelve signs, it is clear that to one who knows in which sign the sun is, and in what degree of that sign, it is easy to know, and which sign is rising at the beginning of the night, and which degree. For the degree lying opposite to the degree occupied by the sun will produce the rising at the beginning of the night. Having set this forth and recognized this, that in every night six signs arise in the east, he will know how much of the night has passed, and how much remains until the rising of the sun. »

After this, it has escaped both of them that, even if one sees the very sign risen, one is not able to calculate the hour of the night accurately in the aforementioned manner. For if each of the constellated and visible signs were completed in a single dodecatemorion of the zodiacal circle, we would fall into error only on account of the inequality in the times of the risings; but since the visible signs are not equal to the dodecatemoria, nor are they all situated in their own proper places—but some of them are smaller than the dodecatemorion, ^B and some are much larger, just as, for example, Cancer does not even occupy a third part of the dodecatemorion, while Virgo takes something away from Leo and the Claws; and the more southerly of the Fishes lies almost entirely within the dodecatemorion of Aquarius—how could it be possible to calculate the hour of the night from such a rising of the twelve signs? And when some of them are not even contained entirely within the zodiacal circle, but are much further to the north, as is the case with Leo and the more northerly of the Fishes, it is clear that the calculation of the hour from the rising of the visible signs will be ^C much more erroneous.

Therefore, as soon as the constellated Cancer has risen, the head of Leo ascends on the given horizon, along with the eighth degree of Cancer. Aratus, observing the head of Leo rising, and assuming that it is the dodecatemorion of Leo that is ascending, will be mistaken by three whole half-hours. Again, the Scorpion begins to set ^D when the thirteenth degree and a half of Aries is rising; yet it is completely below the horizon when the sixth degree of Taurus is rising; for we have demonstrated all such matters in our treatise on the co-risings. It is clear, then, that apart from the twelve signs ascending in unequal times, because the signs themselves are of unequal size and are arranged irregularly, he who wishes to calculate the hour from the rising of the visible signs will be much deceived.

^A

III. Next, therefore, let us assume this: that rising and its opposite descent are described with respect to the segments of the zodiacal circle, not to the stellated images; let us see what has been said regarding these things, whether in agreement or disagreement with what is seen in the world. In this, first, it must be understood that the division of the zodiacal circle is instituted by Aratus such that it begins from the tropical and equinoctial points, and these are the beginnings of the signs. Eudoxus, however, so divides it that those points are in the middle—those of Cancer and Capricorn, and these of Aries and the Claws. As far as Aratus is concerned, he sufficiently shows from these things that he places those points at the beginnings of his signs; for, discussing the four circles—namely, the two tropical ones, the equinoctial, and the zodiacal—he writes that three of them rise and set parallel to each other, and he says that each of them rises and sets at one and the same point; but that the zodiac performs its rising and setting in as great an arc of the horizon as extends from the rising of Capricorn to the rising of Cancer; ^B which he explains in these words:

And these indeed rise, and from the opposite side below set, All equidistantly: but each one of these has its own Orderly descent on either side and ascent. But this one [the zodiac] so much of the Ocean's water traverses, As from Cancer, when Capricorn is rising, it maximumly Is rolled toward the rising.

From these it is clear that the tropical points are constituted by him at the beginnings of the signs, the one at the beginning of Cancer, the other at that of Capricorn. Indeed, the rising zodiac passes through the arc of the horizon defined by those points at the rising of those signs. He also seems to declare the same with these verses, which he sang concerning the Lion:

Where indeed are the courses of the sun most burning. And then the fields are seen empty of ears of grain, With the sun first approaching the Lion.

For the heat is intensified about the rising of the Dog Star. ^C This occurs approximately thirty days after the summer solstice. Therefore, after as many days, according to his opinion, the sun reaches the beginning of the Lion. In that same solstice, therefore, it holds the beginning of Cancer. And by this method the zodiacal circle was divided by almost all, or the majority of, the ancient mathematicians.

But Eudoxus testifies that he places the tropical points in the middle of the signs in these words: "The second is the circle in which the summer turnings occur. In it is situated the middle of Cancer." Item: "The third, he says, is the circle in which the equinoxes occur. In it is placed the middle of Aries and the Claws. The fourth, in which the winter turnings occur. In it the [middle of] Capricorn [is placed]..."

^A This is signified still more clearly in the place where he treats of the colure circles, which are drawn through the poles and the tropical and equinoctial points, writing thus: "There are two other circles, cutting each other in two at right angles through the poles of the world. In these are the following stars: first the ever-visible pole of the world; then the middle of the Bear according to latitude, and the middle of Cancer, etc." Shortly after, he adds: "And also the tail of the southern Fish, and the middle of Capricorn." Next he writes that in the other circle passing through the poles are situated, among other things which he enumerates, the middle of the Claws according to latitude, and in the same latitude, the back of Aries.

^B IV. It must further be observed that Aratus, placing the beginnings of each of the twelve signs in the east, specifies which stars positioned outside the zodiac have simultaneously made their rising or, on the opposite side, their setting with that very sign; this is of great importance for inferring the zodiacal segment about to rise from other near-lying constellations. He demonstrates this also in the rising of the Fishes with these words. For when he had said concerning the Hydra that the parts from its head to the first coil are in the heights as Aquarius ascends, and that the rest of its body rises with the Fishes, he presently adds:

And thus the weary hands, and knees, and shoulders Of Andromeda, all severed in half; these indeed before, the others ^C Reach from the Ocean, when the two Fishes are lately Rising; both draw the right hand to him, But the rising Aries pulls the left from below.

For by the words "when the two Fishes are lately rising," he signifies nothing else than when the Fishes are beginning to rise. ^D He demonstrates this very point also regarding the Argo most clearly. For he asserts that when Virgin is rising, her entire stern rises; and that the rest of her, up to the mast, rises when the whole of the Virgin has risen. For having said before:

Not a few stars indeed does the rising Virgin Cast beneath the earth...

shortly after he says:

...the Dog, anticipating, seizes the feet of others, Dragging from behind the stern of the star-studded Argo. But it runs over the land; the mast is divided by it When the Virgin is wholly emerged from the depths.

And Eudoxus, whom Aratus has followed as his authority, in the same manner posits the beginnings of the signs in the risings in the east: so that from this also, the poet's intention is made very plain to us. These things having been previously demonstrated, let us now examine the risings and settings described by them.

V. Aratus, therefore, having posited the beginning of Cancer in the east, states that half of the Crown has set; of the southern Fish, [the portion] up to the spine of the back; of the One-Kneeling, whatever is above the belly; [and] Ophiuchus...

as far as the shoulders; and the Serpent, which Ophiuchus holds, as far as the neck; and more than half of Arctophylax. He says that the belt of Orion rises at the shoulders. Therefore, these constellations that he mentions rise in part with the Gemini and set in part opposite them. ^A But Eudoxus, recounting all that are above the earth when Cancer begins to rise, says that the One-Kneeling is entirely visible; the half of the Crown; the head of Arctophylax; the head of Ophiuchus; the tail of the Serpent that is held in his hand; the whole southern Orion; and of the southern Fish, the part towards the head.

Now, as for the Crown, the opinion of Aratus conforms most closely to the truth; for in the regions of Greece, it begins to set when the 23rd degree of Gemini is rising; and it sets completely when the 4th degree of Cancer is rising. ^B However, according to Eudoxus, it is clear that he disagrees, since according to him the beginning of Cancer is in the middle of the sign of Gemini. So that we need not constantly remark upon this, it must be held generally that, since the two do not describe the signs in the same way, the observations of what appears cannot agree with both. It must also be understood that, with few exceptions, both describe the things that pertain to the risings in the same way. For Aratus has followed the footsteps of Eudoxus. Indeed, the risings recorded by them agree more with the zodiacal division according to Aratus than according to Eudoxus, as will be clear from the details concerning them that we shall state.

For the southern Fish, the greater part ^C ought to be above the earth, and not only the part near the head, as they say. For it begins to set when the 4th degree of Gemini is rising; and it sets completely when the 18th degree of Cancer is rising.

As for the One-Kneeling, only the head has set, and the right shoulder with the hand; the left shoulder and the rest of the body are still above the earth. For when the right shoulder is setting, the 27th degree of Gemini is rising; when the left shoulder is setting, the 8th degree of Cancer is rising; and when the right shoulder is setting, those in his sides are still rising. ^D Therefore, Aratus spoke falsely when he said that the part of him from the belly to the head had already set.

Regarding Ophiuchus, Aratus and Eudoxus think correctly. For [his] shoulders set opposite to Gemini; but [the part] in his head sets when the 11th degree of Cancer is rising.

As for the Serpent, which Ophiuchus holds, only the tail is above the earth, as Eudoxus thinks, and not the head, as Aratus says. For its head sets when the middle of Gemini is rising; but the end of its tail sets when the 9th degree of Cancer is rising.

VI. They are entirely mistaken concerning Arctophylax. Asse-

For they say that it sets opposite to four signs: Aries, Taurus, Gemini, and Cancer. For Aratus, with the sun placed in the orient, says: Arctophylax sets already with the first sign, Whose four parts, except for the hand, lead him down, as if he were setting opposite to the rising of Aries. Consistent with this hypothesis are the things he writes about the beginning of the rising of Cancer: Nor would Arctophylax any longer be much in both Lesser by day, but already more so by night. For at four degrees, the Ocean receives ^B Boötes descending together. Eudoxus, however, writes as follows: "When Aries sets, the feet of Arctophylax towards the north descend, and the rest of the beast towards the south." And at the beginning of the discourse concerning risings, having gone through all things that are in setting and rising, as Cancer begins to rise, he says next: "But when Cancer rises, none of the northern constellations rise; but of the southern ones, the Hare and the foreparts of the Dog, and Procyon, and the head of the Hydra. And the head of Arctophylax sets from the northern ones." It is manifest, therefore, from the opinion of Eudoxus, that the first parts of Arctophylax set opposite to Aries, ^C and the last parts to Cancer. But Arctophylax does not set opposite to four signs, as they say, but only to two—less than half. Nor does it begin to set with Aries; but it makes the beginning of its setting as the 6th degree of Taurus is rising, and it sets entirely, except for the left hand and the elbow, as the 19th degree of Cancer is rising. One must observe that Aratus speaks in agreement with the phenomena concerning Arctophylax, even if he is entirely mistaken that it sets opposite to four signs—Aries, Taurus, and Gemini having risen—and as the Cancer begins to rise, which is the remainder ^D of the four signs, in which Arctophylax also sets, he reasonably says that not much of it is any longer captured by the horizon both above and below the earth, as used to happen when the Gemini were rising; but rather that a greater part appears below the earth and a smaller part above the earth. For "diurnal" signifies that which is above the earth of the world, and "nocturnal," that which is below the earth; and he makes this clear through many things, as he does directly in the case of Engonasin [the Kneeler], saying thus: But he, turned backward, with his other parts not yet Reaching to the lowest belly; but the higher parts are carried by night. The things, however, that follow are not spoken by him as pertaining any further to its setting itself, but as things incidental to it.

^A ... For when it is sated with light, ^B it keeps to the time of sunset, a longer portion of the night passing by. For when it begins to set together with the Claws, the sun being in them—at which time it sets—the nights are said to be "at Arcturus"; since it is carried over the earth the whole day long, because it rises together with the Virgin, and it consumes a longer time than half the night, [and] it sets together with the four signs. That it rises together with the Virgin exactly as he says, he makes clear in these words:

"Nor let the coming Claws, though faintly shining, Pass by unknown; for Boötes, a mighty sign, Rises altogether, marked by Arcturus."

VII. And not only Aratus and Eudoxus, but almost all the other mathematicians, as many as have discoursed about Boötes, have similarly fallen into error with them, thinking that it sets together with four signs. Attalus, however, asserts firmly, as we were showing, that the beginning of its setting is not with the Scorpion, but with the Claws, stating it in this manner: "For some, neither possessed of the knowledge of the phenomena, nor able to grasp the mind of the poet, have made various pronouncements concerning it. And there are some who think that it first begins to set with the Virgin, then with the three following signs; others that it begins from the Scorpion, and ends at the Waterman; some of whom you yourself have encountered, being refuted by us and changing their opinions. But in general, since the phenomenon itself confirms this, and the poet clearly says that it becomes entirely set when Leo is in the east, but begins to set when the Bull is about to rise—and the sign of the Scorpion, which is diametrically opposite to it, is situated at the setting, and the Claws have just recently set, with which Arctophylax begins to descend—I consider it manifest that all those who disagree with us on this matter are entirely ignorant of the phenomena."

It would have blessed us, indeed, if he had not been content merely to state his opinion without demonstration, asserting that those who thought otherwise were refuted by him and had abandoned their opinion, but had also committed the proof of his words to writing, so that the others who disagreed with him might also be ^D persuaded that it begins to set with the Claws, and not with the Scorpion. Since, therefore, this has been omitted by him, I do not think it useless to remind you in a few words by what lines of reasoning we think that Boötes begins to set with the Scorpion. For we have reserved the more copious discourse on this matter for our treatise on the simultaneous risings. Let it be understood now that the most southern star of those in the left foot of Arctophylax is positioned on the horizon toward the setting. But this star is north of the equinoctial circle by 27 and 1/3 degrees, of which sort of circle passing through the poles, there are 360. On account of this, the circle parallel to the equinoctial circle passing through the aforementioned star has its portion above the earth of such segments

15, less about a twentieth part, as the circle described through the poles has 24. Wherefore the half of that circumference, which pertains from the meridian to the sunset, is of the same parts 7 1/2. But that same star lies, according to the parallel circle, about the first part of the Claws. Therefore, as it sets, it must culminate, according to the parallel circle, the 21st degree and 15' of Capricorn; this degree culminating on the parallel, the 22nd degree of Capricorn must culminate in the zodiac. But when the twenty-second degree of Capricorn culminates in the zodiac, the sixth part of Taurus must rise on the given horizon; for each of the things mentioned is demonstrated through the lines in that work in which we instituted a general treatment ^B regarding such matters. Therefore, the left foot of Bootes sets as the sixth part of Taurus rises. That the left foot of Bootes sets first, is demonstrated separately in the discussion concerning him. It would also be evident from the position of Bootes itself. For Bootes, standing upright, inclines in such a way by his position that his left foot, being much further south than his head, precedes the circle drawn through the poles and his head by more than three-quarters of one sign. Regarding Orion, Aratus agrees, assuming that he rises entirely with Gemini.

VIII.

IX.

^A This ship runs above the earth, dividing the mast at its center, when the Virgin has just now fully escaped from below. Eudoxus teaches the same things as Aratus; and from this it is most of all apparent that Aratus is, as it were, transcribing what was said by Eudoxus. In other matters, then, they agree concerning the phenomena. But the Arrow does not set only with the Lion, but also with the Crab. For it begins to set when the twenty-seventh degree of the Crab is rising in the middle, and it finishes setting when the second degree of the Lion is rising in the middle. And the River flowing from Orion does not begin to set with the Lion, as those around Eudoxus say, but with the Virgin; for the leading star of it, and the most southerly, which is also the brightest, sets when the seventh degree of the Virgin is rising. He says that only the poop of the Argo rises together with the Lion, and that having been bisected at the mast, it is carried up until the whole Virgin rises. ^B Attalus, however, not being able to grasp the mind of the poet, but assuming him to mean that when the Virgin is about to rise, the poop has risen as far as the middle of the mast, says that the word "whole" in the last line is superfluous. For, setting forth the last of the aforementioned lines, he adds this: "In these, the word 'whole' has the place of a filler." For if one should transfer it to the Argo, making the statement such as: "And all the ship runs above the earth, dividing the mast at its center, when the Virgin has just now fully escaped from below," it admittedly has the force of a filler; or if on the Virgin, the same will happen, unless one accepts that he says the whole Virgin has risen, which is what he wishes to say. For if the whole Virgin has risen, it is clear that the Claws are on the point of rising. And at this time he says the whole Argo has risen, saying as follows: ^C "Nor indeed should the approaching Claws, shining faintly, pass by unnoticed, since the great sign Bootes rises entire, struck by Arcturus. But the Argo does not yet stand entirely aloft." It seems to me, therefore, that Attalus is mistaken, not understanding that the words "dividing the mast at its center" are said by the poet as an epithet, and not that it rises as far as the middle of the mast; and the following statement is such: when the Virgin begins to rise, the Dog has already risen, and the poop of the Argo. But it itself, being half-risen as far as the mast, is carried up until the whole Virgin rises. ^D X. Aratus has used this same manner of expression also regarding the Kneeler, saying as follows: "...of whom only the shin appears with both Claws; but he himself, still turned toward the head in another direction, awaits the rising Scorpion and the bow-bent Archer. For they carry him." For when the Claws are beginning to rise, he says that Bootes has entirely risen, and the Argo; but of the Hydra, only those parts toward the tail are under the earth; and of the Kneeler, the right shin alone has risen as far as the knee; the rest of his body, except for the left

hand, is still under the earth, when the Scorpion is in the east; but his left hand and head appear elevated when the Archer is rising. He further asserts that half of the Crown and the tail of the Centaur rise together with the Claws; and at the same time, on the opposite side, the entire body of the Horse and the tail of the Swan descend, as well as the head of Andromeda, the Whale from the tail up to the crest, and both the head of Cepheus and his hand and shoulders, and the greatest part of the River. In these matters, Aratus has similarly, with changed words, transferred the position of Eudoxus into his own book. ^B Now the rest has been stated correctly by them, but they are entirely mistaken concerning the Centaur. For neither its tail nor its hindquarters in general rise; rather, the left shoulder-which is much further north-starts to rise, not with the Maiden, as he claims, but with the Claws. For his left shoulder rises with the eleventh degree of the Claws. And concerning Andromeda, not only has the head set when the Claws are in the east, but both hands as well. Furthermore, the Whale does not begin to set on the opposite side when the Maiden is rising, as they think, but when the Lion is. For of the two bright stars which it has in its tail, the more southerly one sets opposite the middle of the twenty-seventh degree of the Lion; yet the remaining body of the Whale does not set entirely when the Maiden is rising, but only as far as the crest, as Aratus says. Of Cepheus, only the head sets; his shoulders lie in the always-visible segment, as we have already said. ^C And they are not only ignorant concerning this, but also concerning their claim that his head sets opposite the Maiden. For it does not begin to set opposite the Maiden, but opposite the Claws. For the more southerly of the stars in his head sets when the eighth degree of the middle of the Claws is rising.

XI. When the Scorpion begins to rise, one of the two authors says that the remaining parts of the River set, as well as the remaining parts of Andromeda, of the Whale, and of Cepheus from the shoulders to the belt, as well as the whole of Cassiopeia, except for what pertains to the legs from the feet to the knees. He also says that the rest of the Crown rises, and the tail of the Hydra, and the remaining body of the Centaur, except for the front feet; he also says that the Beast, which the Centaur holds, begins to rise, and the head and hands of Ophiuchus; and of the Serpent, which the Ophiuchus holds, the head as far as the first coil; and of the Kneeler, the rest, except for the head and the left ^D hand. But Eudoxus writes the rest in the same way; however, he notes the head of Ophiuchus as rising, and only the left hand; but the other hand, and the Beast, are above the earth and visible not when the Scorpion is rising, but when the Archer is. And while they both agree in their description of the others in accordance with the phenomena, regarding the Beast, neither does it rise with the Claws, nor is the remainder for the Scorpion.

But Aratus is moreover mistaken concerning Ophiuchus. For only his left hand rises with the Claws; his head and right hand rise with the Scorpion. ^B

XII. Aratus thinks that as Sagittarius is rising, the head and left hand of the Kneeler [Engonasin] have risen, and also the body of Ophiuchus, and the tail of the Serpent which Ophiuchus holds, and the Lyre, and the parts of Cepheus from his head down to his chest. He says that the whole Dog [Canis], and Orion, and the Hare, and the parts of the Charioteer from the feet to the belt set; and the Goat and the Kids, of which the one is on the left shoulder, the others in the left hand, and also the head and right hand set in opposition to Sagittarius; while the parts down to the feet set in opposition to the Scorpion. He says that Perseus also sets, except the right knee and the foot, and the poop of the Argo. In these matters, the others indeed agree with the phenomena; but the left hand of the Kneeler rises with the Claws, and not with the Scorpion. For even his left shoulder, being far in front of the hand, as if he were stretching out his arms, as the same [Aratus] also writes, rises with the third part of the Scorpion. Therefore, the head does not rise with the Scorpion alone. ^C

For this reason, regarding the rising of the Scorpion, he blunders in the preceding [lines], writing: *The head, and the other hand, With Sagittarius they ascend.* In which he follows Eudoxus.

No less do they differ from the appearances in the case of Cepheus. For only his head sets and rises; his shoulders and chest are carried in the always-visible segment. Besides these, of the stars which are in his head, the leading one rises with the twenty-eighth degree of the Scorpion; but the one that rises last, being more southerly than those in the head, rises with the sixth degree of Sagittarius. So that not only does the head of Cepheus rise with the Scorpion, but also with Sagittarius. But Perseus sets entirely in opposition to the Scorpion; and not, as they ^D say, the right foot and the right knee setting in opposition to Sagittarius.

They are ignorant also concerning the Argo. For it begins to set in opposition not with the Scorpion, but with the middle of the Claws. It was right, therefore, when the Scorpion was rising, to say that the poop of the Argo had set, and not when Sagittarius was rising.

XIII. Again, when Capricorn is placed in the east, they say that the whole Argo and the Fore-dog [Procyon] set in opposition to Sagittarius; and that the Swan, and the Eagle, and the Arrow, and the Censer rise together. Now the others are said by them in agreement with the phenomena; but the matters concerning the Swan are misunderstood by both, though much more by Aratus. For Eudoxus [says that] the right wing of the Swan is rising...

rises with the Scorpion, and its remaining body with the Archer; from which it is clear that according to Eudoxus the right wing of the Swan must rise with the final parts of the Scorpion, while Aratus says that it rises only with the Archer. In truth, those in the tip of the right wing of the Swan rise with the final parts of the Claws; but the one at the tip of the left wing, which is the last to rise, rises with the twenty-second degree of the Archer.

XIV. He says that when the Water-bearer begins to rise, the head and feet of the Horse rise with the Goat; and the hindquarters of the Centaur set, as well as the part of the Water-snake from the head to the first coil. But Eudoxus says that Cassiepea and the Dolphin also rise. Now, regarding what they have said in common, it almost agrees with the phenomena; ^B except that the head of the Water-snake begins to set opposite [the sun] at the final parts of the Archer, not at the Goat. And of the Horse, not only the head and feet have risen, but also the shoulders and the chest.

Some find it a matter of consideration why, since Aratus sets the beginnings of the other signs in the east, and thus explains the risings and settings of the other constellations, he assumes that the Water-bearer rises in its middle, saying thus: The Horse indeed with the mid-Water-bearer rising With feet and head is turned about. Attalus, questioning this, says it is an error, and thinks it should be written thus: The Horse indeed with the newly-rising Water-bearer. But both Attalus and the others fail to grasp the intention of the poet; and perhaps also the appearance itself. For the Water-bearer, being situated ^C from the south toward the north, has its parts regarding the chest and head falling far from the zodiacal circle into the northern region, while the parts regarding the feet are more southern than the zodiacal circle; but its middle parts lie in the zodiac. Since, therefore, the dodecamoria of the zodiacal circle are assumed to be rising, for this reason Aratus says: "The Water-bearer rising by its middle body, the Horse with feet and head is turned about"; and not the middle of the length in the dodecamorium, as both the ancients and Attalus understand it. Therefore, it seems necessary to me not to change the verse, as Attalus suggests, since in all the copies it is written in this way.

But Eudoxus is mistaken ^D regarding Cassiepea and the Dolphin. For they do not rise with the Goat; rather, Cassiepea rises with two, namely with the Archer and the Goat. For she begins to rise with the twenty-first degree of the Archer, and finally rises with the twelfth degree of the Goat. But the Dolphin rises entirely with the Archer, from its twentieth degree to the twenty-fourth.

^A XV. When the beginning of the Fishes rises, Aratus says that the rest of the Hydra and the Centaur have already set; and that the southern Fish has not risen entirely, but with a small part left over; likewise the right parts of Andromeda along its length. Eudoxus, in his first commentary, which Aratus follows, also thinks that the right hand of Perseus rises. But in the *Enoptron*, he says that the whole of it has risen, except for a small part; and that all the Hydra as far as the Crow is setting. Here, Eudoxus seems to me to differ from what is apparent only insofar as he says that only the right hand of Perseus rises with the Water-Bearer. For almost half of it rises with the Water-Bearer; indeed, the sufficiently bright star in the middle of its body rises with the twenty-seventh degree of the Water-Bearer. But Aratus is mistaken in thinking that the whole Hydra sets as the Water-Bearer rises. For the star located at the tip of the tail above the Centaur sets as the eleventh degree of the Fishes rises. Eudoxus is therefore better in asserting that the tail of the Hydra is still remaining. On the subject of the Centaur, both are mistaken. For it has not entirely set as the Fishes begin to rise; rather, its front parts are still above the horizon. For its head and its right shoulder are eclipsed as the Fishes rise. Both also differ from what is apparent regarding the southern Fish, assuming that it rises almost entirely with the Water-Bearer. For, on the contrary, the greater part of it rises with the Fishes. For the more southern of the stars in the tail rises with the third degree of the Fishes, while the bright one in its snout rises with the twenty-first degree of the Fishes. Both are entirely deceived regarding Andromeda; for she does not rise with the Water-Bearer and the Fishes, as these men say, but with the Capricorn and the Water-Bearer. For her left hand rises first, almost at the middle of Capricorn; and her last, the right hand, rises with the twenty-fourth degree of the Water-Bearer.

XVI. Concerning the rising of the Ram, Aratus writes falsely as follows:

The last line is written in this way, but it is likely that the word "ending" was placed there by error. For from the very beginning of the work, he places the beginnings of all the signs in the east, and not their midpoints or endings. For in the case of other stars, some parts set or rise as the signs are at their midpoint, others as they are beginning or ending. Whence Attalus also correctly perceived this as follows:

error. And altogether, or as it pleases him, that verse must be conformed thus: Whether it appears as Aries rises, or in Taurus, or in this way indeed: Whether it appears as Aries is ending; so that the word "ending" refers to the belt. ^B Nevertheless, he is unaware of the poet's intention even in this. For he speaks thus: We, however, believe that for this matter, both in agreement with the poet and in accordance with the phenomena, the poem should be written in this way: And the belt itself, and it might be a matter of doubt, Whether it appears as Aries rises, or in Taurus. With which it revolves in a mass. For since, when Aries is about to rise, Perseus is admitted to be visible as far as the shoulders; but at the same time as Aries begins to rise, the belt of Perseus immediately becomes manifest, because its appearance differs very little from the beginning of Aries; the poet hesitates as to whether he should posit that it becomes visible already at the beginning of Aries about to rise, or whether he should resort to what is more generally agreed upon; because, when Taurus is about to rise, the belt of Perseus is manifest together with the rest of the body. And with the poem written in this manner, both the written words will be preserved, and he would appear to be explaining ^C what pertains to the belt, not only expertly but also accurately.

XVII.

XVII.

^A Indeed, I suspect that the doubt was cast upon Attalus for this same reason for which it had earlier arisen for Eudoxus, whom Aratus used as an authority. For Eudoxus writes in his commentary on the *Appearances* that the right parts of Perseus rise with the Fishes; from which it follows that, once the beginning of Aries is posited on the horizon, only the right parts of Perseus appear above the earth according to him. But in his other book, which is entitled the *Mirror*, he asserts that the whole of Perseus, save for a little, rises with the Fishes. Therefore, since those two commentaries agree with one another in almost all things that look to the rising of the stars, but disagree in the description of Perseus, Aratus, being rightly placed in ambiguity and not knowing which side to follow, says that it is uncertain and doubtful whether the belt of Perseus also appears on high ^B with the shoulders and head when Aries is rising, or rather when Taurus is ascending, which is contained in the other work of Eudoxus. Therefore, he says that it is doubtful not because it is difficult to judge by sense perception due to the smallness of the difference, as Attalus thought, whether the belt of Perseus appears while the beginning of Aries occupies the horizon, or whether it emerges only when the head of Taurus begins to rise, but rather because he is unable to decide in either direction, since he saw that each is handed down equally.

Moreover, since there is a double reading of that passage—for in some codices [it is written one way], and in others [another]—it must be written not as Attalus thinks; for it is correctly joined with the copulative particle. For it is not necessary to separate it because the noun is placed in the plural number, since this manner of speaking is customary. ^C

XVIII. At the rising of the beginning of Taurus, Aratus and Eudoxus write that the whole of Perseus shines above the earth, and the left hand of the Charioteer, in which the Kids are situated, and his left foot; and of the Sea-Monster whatever is from the tail up to the neck; but that a part of Boötes is setting. In this they have fallen into error, when they think that only the left parts of the Charioteer rise equally with him. For his right shoulder ascends with the twenty-second degree of Aries. But the more southern of those which are in the head rises even earlier with the Fishes; so that they err in this also, insofar as they think that the Charioteer rises primarily with Aries. ^D Similarly, a double error has been committed by them regarding the Charioteer. For he neither begins to rise with Aries, as they think, but with the Fishes, nor does he ascend with Aries only up to the neck, but almost entirely, except for those things which are in the head [and those] which are bright in the edge of the shoulder blade. For that Boötes himself does not begin to rise with Aries, as they wish, but with Taurus, we have stated above.

When Gemini begins to rise, Aratus says that the feet of Ophiuchus as far as the knees are setting; but the Whale [is...]

^A begins to rise, and the first part of the River. These things have been stated by them in accordance with the phenomena.

Those points among the matters spoken of by Aratus and Eudoxus in the *Phenomena* which seemed to me useful to examine and to record are these. Next, I shall set forth the account of each of the fixed stars under a heading: with which of the twelve signs each rises together and sets together; and from what degree of the sign it begins, and up to what degree it finishes rising or setting in the regions around Greece; and in general, where the longest day is fourteen and a half equinoctial hours. The detailed proofs for these, we have arranged in other works in such a way that in almost every place of the inhabited world one may be able to follow the differences of the risings and settings. ^B

XIX. First, therefore, we shall explain the risings and settings of the northern stars of the zodiacal circle; then those of the southern ones; and last of all, those of the twelve signs themselves. I speak of the constellations, since some occupy a larger space than a twelfth-part, and some a smaller. Furthermore, some are much further north or south of the zodiac, and by a long distance precede or follow their own dodecatemoria in their risings and settings. We shall also clarify for each the sign in the zodiacal circle that is at the mid-heaven, and its degree; and in addition to these, which of the fixed stars culminate at the beginnings and endings of the risings and settings of any star; and further, in how many equinoctial hours each of the stars sets or rises. We shall clarify each of these by approximation until there is no material difference. I judge that you easily perceive that such a treatise is much more useful than those compiled by the ancients, and that it contributes to many of the theorems in astrology. ^C

Bootes rises together with the zodiacal band from the beginning of Virgo up to the 27th degree of Virgo. And while that zodiacal segment is rising, the mid-heaven is from the 27th degree of Taurus to the 27th degree of Gemini. And the first star of Bootes to rise is the one in the head, and the last is the one in the right foot. When the rising of Bootes begins, the left shoulder of Orion and the left foot culminate, preceding the meridian by half a cubit; and when it ends, the bright star on the hip of the Dog (Canis) culminates. The whole of Bootes rises in about two equinoctial hours.

When Corona rises, the zodiacal arc rises from the 27th degree of Virgo up to the 5th degree of the Claws (Chelai); the mid-heaven is from the 27th degree of Gemini up to the 5th degree of Cancer. And the first star of Corona to rise is the one that precedes the most brilliant, but the last is the more northern ^D

of those which, from the most brilliant, recede toward the east ^A and the Bears. At the very beginning of the rising, the star which is on the thigh of the Dog culminates; the last one, however, is the bright one which precedes the head of Hydra: this is higher than the two stars of Cancer and the Bear which are situated in the front feet; then, next to the stars which are around the nebula of Cancer, placed toward the west. The Corona rises in two parts of one hour.

When the Kneeler (Ingeniculus) rises, there rises with it that segment of the zodiac which is from the 12th degree of Virgo to the middle of Scorpio. It culminates from the middle of Gemini up to the 14th degree of Leo. Both of the stars of this asterism rise first, of which one is in the right foot, the other in the right knee; the last is that which is in the extreme left hand. Of the other stars, as the Kneeler is rising, the first to culminate is that which, out of the four situated at the feet of Gemini, is the second from the west; the newest is the more southern of the two in Leo, which are placed around the bright star of the loins. The Kneeler rises in a space of 4 hours and 36 minutes approximately.

XX. When Ophiuchus rises, that arc of the zodiac rises at the same time which is from the 29th degree of the Claws to the 25th of Scorpio. It culminates from the 5th degree of Leo to the 3rd of Virgo; its first stars to rise are those which are in the left hand: then those which are in the Serpent; the last to rise is the second toward the sunset out of the four which are in his right foot; the first to culminate is the bright one of those which are in the neck and breast of Leo, which is the second toward the north, and finally that which is in the head of the Raven. Ophiuchus rises in two hours.

With the serpent, which Ophiuchus holds, rises the arc of the zodiac from the 8th degree of the Claws up to the 1st degree of Sagittarius. It culminates from the middle 8th degree of Cancer to the 14th of Virgo. The first star to rise is the more northern of the leading ones, which are in its head; the last is that which is in the extreme tail. The first star to culminate is the bright one which is at the extremity of Argo, distant by the space of about half a cubit from the meridian; the last to culminate is the Vindemiator, and the more northern shoulder of Virgo, both of which stars are distant by an interval of almost half a cubit from the meridian. The serpent rises in 4 1/2 hours.

When Lyra rises, the arc of the zodiac rises with it from the 9th degree of Scorpio up to the 18th; it culminates from the middle 8th degree of Leo up to the 26th. The first star of Lyra to rise is that which lies toward the north of the most brilliant one; the last, however, is one of the two bright ones which are in its yoke, namely that which is toward the east. The first to culminate is the southern one of the two brilliant stars in the loin of Leo; the last is that which is the bright one in the tail of Leo, and that which is in the extreme left wing of Virgo, at a distance of half a cubit.

from the meridian. ^A The Lyre rises in 4/5 of an hour.

When Cygnus rises, the zodiac rises from the middle of the Claws to 22 degrees of Sagittarius; it culminates from the beginning of Leo to the middle of the Claws. The first of these, the more northerly of those in the right wing, rises. The first bright star in the heart of Leo culminates; the last is the more southerly of those under the right shoulder of the Centaur; and Arcturus also, at a distance of half a cubit from the meridian. Cygnus rises in 4 hours 24 minutes.

XXI. Of Cepheus, only the parts toward the head rise. ^B The zodiac rises with it from 27 degrees of Scorpio to 6 degrees of Sagittarius; it culminates from 9 degrees of Virgo to 21 degrees of the same. The first to culminate is the bright one in the tail of the Crow, at a distance of almost half a cubit from the meridian; the last is the left elbow of Virgo, preceding the meridian by the same amount. Cepheus rises in approximately 0 hours 36 minutes.

When Cassiopeia rises, the zodiac rises from 22 degrees of Sagittarius to 12 degrees of Capricorn; it culminates from 11 degrees of the Claws to 3 degrees of Scorpio. The first to rise is the bright one on her throne; the last is that in the head. ^C The first star to culminate is the more southerly of those under the right shoulder of the Centaur, with Arcturus; the last is the middle one of those in the forehead of Scorpio, and the one preceding the bright star of the Crown. Cassiopeia rises in 1 hour 20 minutes.

When Andromeda rises, the zodiac rises with it from 15 degrees of Capricorn to 24 degrees of Aquarius; it culminates from 6 degrees of Scorpio to 8 degrees of Sagittarius. The first of her stars to rise is the more southerly of those in her right hand; the last is that at the tip of her left hand. The first to culminate is the one near the bright star of the Crown; the last is the left elbow of Engonasin. Andromeda rises in 2 and 1/8 hours.

When Equus rises, the zodiac rises with it from the beginning of Capricorn to 21 degrees of Aquarius; ^D it culminates from the middle of the Claws to 6 degrees of Sagittarius. The first of its stars to rise is the more southerly of the front feet; the last is the bright one in the hip. The first to culminate is the one in the middle of the southern Claw; the last are the three of Ophiuchus situated in a straight line by the right shoulder, lying outside of him, and the bright one in the left thigh of Engonasin, slightly preceding it. Equus rises in 3 hours.

When Sagitta rises, the zodiac rises with it from 5 degrees of Sagittarius to 10 degrees of Sagittarius; it culminates from 19 degrees of Virgo to 25 degrees of the same. The first to rise are those in the...

notch, the last is that in the tip. The star that culminates first is the one in the left elbow of the Virgin, lagging slightly behind the meridian, and the last to culminate is Spica, slightly preceding the meridian, and the one under the left shoulder of the Centaur. The Arrow rises in 1/3 of an hour.

^B XXII. As the Eagle rises, the zodiac rises with it from 9 degrees of Sagittarius to 14 mid-degrees of Sagittarius; it culminates from 24 degrees of Virgo to 30 mid-degrees of Virgo. The first of the Eagle’s stars to rise is the more northerly of the two small ones in the wings, and the last is the more southerly of the three bright ones in the body. The star that culminates first is Spica, and the last is the more northerly of those in the head of the Centaur. The Eagle rises in 2/5 of an hour.

As the Dolphin rises, the zodiac rises with it from 20 mid-degrees of Sagittarius to 24 mid-degrees of Sagittarius; it culminates from 10 mid-degrees of the Claws to 13 degrees of the Claws. The first stars to rise are those leading the four in the diamond shape, and the last is the more southerly of those in the tail. The star that culminates first is the left foot of Andromeda, and the last is the most northerly of those in the Centaur’s thyrsus, and the one of the Virgin lying to the north of the right meridian knee. The Dolphin rises in 1/4 of an hour.

^C As Perseus rises, the zodiac rises with it from 25 degrees of Capricorn to 14 mid-degrees of Aries; it culminates from 16 mid-degrees of Scorpio to 8 mid-degrees of Capricorn. The first star to rise is the nebulous one in the Sickle, and the last are those lying above the Pleiades in the left foot. The first star to culminate is the bright one in the middle of the Censer, and the one on the Kneeler preceding the right shoulder in the arm, and the last is the more northerly of the Capricorn stars in the knees, and the more northerly of those in the right wing of the Swan, preceding the meridian by about a half-cubit. Perseus rises in 3 hours and a half, and 1/3 of an hour.

As the Charioteer rises, the zodiac rises with it from 11 mid-degrees of Pisces to 16 mid-degrees of Taurus; it culminates from 20 degrees of Sagittarius to 29 degrees of Capricorn. The first stars to rise are those in the head, and the last is the one in the right foot. The first star to culminate ^D is the one leading those in the cloak of Sagittarius, and the middle one of those in the back, and the second star of the Serpent, which Ophiuchus holds, counted from the tip of the tail; the last to culminate is the bright one in the mouth of the Horse, and the one following in the left foot of the Swan, and the more southerly of those preceding the right shoulder of the two bright stars of Cepheus. The Charioteer rises in 3 hours.

XXIII. These, then, are the things that happen regarding the risings of the stars to the north of the zodiacal circle under the aforementioned inclination of the world; regarding the settings, they are as follows.

As Boötes sets, the zodiac sets with it from 6 degrees of Scorpio to 19 mid-degrees of Capricorn; it culminates from 2 degrees of Capricorn to 4 degrees of Aries. The star that sets first is the most southerly of those in the left foot, the last...

is the most northerly of those ^A in the *collops*. Of the other non-wandering stars, the first to culminate is the bright one in the tail of the Swan; also the leader of those in the Goat that lie to the south of those in the tail; the last is the nebulous star of Perseus in the sickle, and the one of the Ram following the three in the head, and the Knot of the cords. Bootes sets in 4 2/3 equinoctial hours.

When the Crown sets, the zodiac sets simultaneously from the 23rd degree of Sagittarius to the middle of Capricorn; it culminates from the beginning of Pisces to the middle of the same. The first to set is the most splendid of the Crown; the last is the dimmer one, and the rearmost of the succeeding circle. Of the other stars, the first to culminate is the bright one at the extremity of the southern Fish, as well as the leaders of the parallelogram situated to the south of it; the last to culminate are the one in the middle of the body of Cassiopeia, and the one in the left hand of Andromeda. The Crown sets in approximately one hour.

When the Kneeler sets, the zodiac sets ^B simultaneously from the 14th degree of Sagittarius to the 16th of Aquarius; it culminates from the 23rd of Aquarius to the middle of Taurus. The first star to set is the one at the extremity of the right hand, the last is the one in the left foot. Of the other stars, the first to culminate is the one in the water of Aquarius adjacent to those in the conglobation; then the more northerly of those in the body of the Horse, and also the left shoulder of Cepheus, which is half a cubit short of the meridian. The last to culminate is the more southerly of the bright stars following the quadrilateral of the Whale, and the nameless bright star situated to the south. The Kneeler sets in approximately 4 3/5 hours.

XXIV. When the Serpent-Bearer sets, the zodiac arc descends from the 11th degree of Scorpio to the 2nd degree of Capricorn; it culminates from the 25th of Capricorn to the middle of Pisces. The first star to set is the one in the left foot, the last is the one ^C in the head. Of the other stars, the first to culminate is the one following those in the tail of the Goat, and the most northerly of those in the right wing of the Swan; the last is the one in the head of Cassiopeia, and the small one in her chair; also the most northerly of those in the chest of Andromeda, and the more southerly of those in the tail of the Whale, which is slightly short of the meridian. The Serpent-Bearer sets in approximately 3 hours.

When the Serpent, which the Serpent-Bearer holds, sets, the arc of the zodiac sets simultaneously with it from the 26.5 degree of Scorpio to the 9th degree of Capricorn; it culminates from the 8th degree of Aquarius ^D to the middle of Pisces. The first stars to set are those in the body, which are common to the left hand of the Serpent-Bearer, and the last is the one at the tip of the tail. Of the other stars, the first to culminate is the one in the right foot of Cepheus, and the last of them, the more southerly one, which is in the middle of the urn of Aquarius...

middle one of those in the tail of Aries; the last is the one among those lying between the extreme tip of the Pleiades and the Hyades, which are on the right forehead—the more northerly and brighter of them, distant by about two-thirds of a cubit from the meridian. Likewise, in the larger circuit of the River of Orion, the second from the north, which is bright, distant from the meridian by half a cubit; likewise, the one between the truncation of Taurus and that which is in the shoulder blade, preceding the meridian by about two-thirds of a cubit. Lyra sets in two-thirds of an hour.

When the Swan descends, the zodiac from the 5th degree of Aquarius to the 14th degree of Pisces descends with it; it culminates from the 24th degree of Aries to the 12th degree of Gemini. The first star to set is the one which is in the mouth of the Horse; the last is the more northerly of those in the tip of the right wing. Of the other stars, the first to culminate are the bright star in the right thigh of Perseus, and the one following those in the tail of Aries; the last are the third from the west of those in the feet of the Twins, and the leading one of those in the knees, preceding the meridian by about half a cubit. The Swan sets in 3 hours and 6 parts.

XXV. Of Cepheus, only the parts around the head set. The zodiac from the 8th to the 14th degree of Aries descends with it; it culminates from the 9th to the 16th degree of Cancer. The first star sets; and of the other stars, the first to culminate are the more southerly of those in Cancer, lying near the nebulosity from the east, a little short of the meridian, and the bright star in the prow of the Argo; the last is the bright one in the front knees of the Bear, a little short of the meridian; and the middle of the three stars of Cancer that are around the southern Claw; and the bright star in the middle of the neck of the Hydra, a little short of the meridian.

When Cassiopeia sets, the zodiac from the 21st degree of Aries to the 24th degree of Taurus descends with it; it culminates from the 24th degree of Cancer to the 5th degree of Virgo. The first star to set is the one in the head; the last is the one in the feet. Of the other stars, the first to culminate are the front foot of Leo, the brightest of those in the head, and the brightest of the Hydra; the last are the second of the bright stars from the tail of Draco, the one in the beak of the Crow, and the one on the base of the neck; and the one of the Argo at the meridian.

^A Cassiopeia sets in 2 hours and two thirds of an hour.

When Andromeda descends, the arc of the zodiac descends with it from 22 1/2 degrees of Pisces to 28 1/2 of Aries; and at the meridian are the stars from 21 1/2 degrees of Gemini to 2 of Leo. The first star to set is the one in the head, and the last is the one further north in the right foot. Among the other stars, the ones that culminate at the start are the one in the beak of the Great Bear, and the one in the head of the preceding Twin; then the one most to the north of those in the head of the Dog. Finally, there culminate the one at the tip of the tail of Draco, and the middle star of the three on its neck which are in a straight line; also the third of the four stars in Taurus that are to the east after the bright star. Andromeda sets in about 3 hours.

^B When the Horse descends, the zodiac descends with it from 15 1/2 degrees of Aquarius to 13 of Pisces; and at the meridian are the stars from 4 1/2 of Taurus to 11 1/2 of Gemini. The first star to set is the bright one in its mouth, and the last is the bright one on its loin. Of the other stars, the one that holds the meridian first is the one further north of those between the point of the Pleiades and the Hyades that are on the left forehead; also the one in the shoulder of Taurus, a little before the meridian. Finally, there culminate the third foot of Gemini from the west, and the preceding of the three on the knees. The Horse sets in 2 1/2 hours.

When the Arrow descends, the zodiac descends with it from 27 1/2 degrees of Capricorn to 2 1/2 of Aquarius; and at the meridian are the stars from 14 to 21 degrees of Aries. The first stars to set are those in the notch, and the last is the one on the point. Of the other stars, the first to culminate is the one on the right shoulder of Perseus, and the star further north of the three unnamed ones which are situated in a straight line above the tail of Aries, and the one on its back, preceding the meridian by about half a cubit; also the leading star of the three bright ones in the southern jaw of Cetus. Finally, there culminate the bright star in the middle of the body of Perseus, a little preceding the meridian, and the following star of those in the southern jaw of Cetus, a little before the meridian. The Arrow sets in a third of an hour.

^C XXVI. When the Eagle descends, the zodiac descends with it from 17 1/2 degrees of Capricorn to 23 of Capricorn; and at the meridian are the stars from 2 to 8 degrees of Aries. The first stars to set are the two small ones in the wings, and the last is the one further north of the two bright stars in the body. Of the other stars, the one to culminate first is the one in the left foot of Andromeda, and the middle one of those in the head of Aries. Also, the one further south of the following stars of the quadrilateral of Cetus; and the last to culminate is the following star of those on the base of the triangle, preceding those in the northern jaw. The Eagle sets in a third of an hour.

When the Dolphin descends, the zodiac descends with it from 2 to 8 1/2 degrees of Aquarius; and at the meridian are the stars from 20 1/2 of Aries to 29 of Aries. The first to set is the preceding...

of those which are in the tail; the last is more northerly of those ^A in the following side of the Rhombus. Of the other stars, the bright one in the middle of Perseus’ body culminates first, a little before the meridian, and the one following those in the southern jaw of Cetus, situated a little before the meridian. Lastly, those in the left foot of Perseus culminate; and the more northerly part of the preceding side of the Pleiades. Delphinus sets in half an hour.

With Perseus, the zodiac descends from the 29th degree of Taurus; from the middle of Leo to the 10th degree of Virgo culminates. The more northerly of the preceding ones in the Gorgon ^B sets first; the last are those in the right knee. Of the other stars, the one in the belly of Leo culminates first, being situated almost a semicubit before the meridian. Also the fourth of those after the bright star of Hydra, situated almost a semicubit before the meridian. Also the last of those in the hull of the Ship. The ones in the tail of Corvus and those in its feet culminate last. Perseus sets in 2 hours and 20 minutes.

With Auriga, the zodiac descends from the 23rd degree of Taurus to the middle of the 2nd degree of Cancer; from the 2nd degree of Virgo to the 22nd degree of the Claws culminates. Those in the left foot set first; the last are those in the head. Of the other stars, the one at the ^C extremity of the tail of Draco and the most northerly of the Crown culminate first; the last is that in the middle of the southern Claw. Auriga sets in a little more than 3 hours.

Thus far regarding all the figures north of the zodiac. We shall render the rest in the following book, observing this, that this book may not exceed a just measure.

The end of the second book of Hipparchus’ Commentaries on the Phenomena of Aratus and Eudoxus.

HIPPARCHUS' COMMENTARIES ON THE PHENOMENA OF ARATUS AND EUDOXUS, BOOK THREE.

^D 1. Having spoken, O Aischrion, in the previous book regarding the figures north of the zodiacal circle, with which of the twelve signs each of them rises and sets, and which sign culminates as each of them rises or sets, and which of the

^A fixed stars arrive at the meridian when that one begins to rise or set, and again when it sets; and furthermore, in how many equinoctial hours each rises or sets. We shall now write the same for each of the stars south of the zodiac, and for the twelve signs themselves.

Now, concerning those south of the zodiacal circle: when Hydra rises, the zodiac rises concurrently with it from 19 degrees of Cancer to 16 degrees of Libra; and it culminates from 3 degrees of Aries to 18 degrees of Cancer. The first star to rise is the more northerly of those in the throat, and the last is the one at the tip of the tail. The first star to culminate is that in the sickle of Perseus, which appears cloud-like, and the knot of the Fishes, which is about half a cubit distant from the three bright stars in the head of Cancer, and is positioned about half a cubit from the meridian. The last (star) to culminate is the more southerly of the leading stars in the head of Leo, and the more southerly of those in the middle of the mast of the Argo. Hydra rises in 7 hours and 15 minutes.

When Crater rises, the zodiac rises concurrently with it from 7 degrees and 20 minutes of Leo up to 11 degrees of Virgo; and it culminates from 21 degrees of Taurus to the middle of Gemini. The first star to rise is the more northerly of the four in the base, and the last is the most southerly of the 6 stars in Cetus. The first stars to culminate are those in the head of Auriga, near the middle of it, and the last (to culminate) are the fourth star from the west of the four in the feet of the Twins, and the bright, unnamed star below the Hare. Crater rises in 1 hour and 15 minutes. ^B

II. When Corvus rises, the zodiac rises concurrently with it from 16 degrees of Virgo up to 23 degrees of Virgo. It culminates from 14 degrees of Gemini to 22 degrees of Gemini. The first star to rise is the one on the loin, and the last is the one in the feet. The first to culminate is the one in the leading hand of the leading Twin, and the right foot of the following Twin; the last are the third from the west of those in the shoulders of the Twins, and the one at the base of the forelegs of Canis, positioned a little short of the meridian. Corvus rises in 36 minutes.

When Centaurus rises, the zodiac rises concurrently with it from 10 degrees of Libra up to 4 degrees of Sagittarius; and it culminates from 12 degrees of Cancer to 17 degrees and 30 minutes of Virgo. The first star to rise is the one on the left shoulder, and the last is the following one of the forelegs. The first star to culminate is the one from the west of the bright stars in the deck of the Argo, and the following one of the southern jaw of Hydra; the last is Vindemiator, ^D leading the meridian by about half a cubit. Centaurus rises in 4 hours and 20 minutes.

When the Fera (Wild Beast), which Centaurus holds, rises, the zodiac rises concurrently with it from 23 degrees of Scorpio to 21 degrees of Sagittarius; and it culminates from 5 degrees of Virgo to 10 degrees of Libra. The first to rise is that

which is in the preceding part of the hind feet; it is the most northerly of those under the right shoulder of the Centaur; and the last is the most southerly of all, and lies at the tip of that which is on the loin. The first star to culminate is the one in the head of Leo, the more northerly of the following ones, and the one on his forefeet; the last is the bright one on the loin of the Great Bear, and the one situated on the right angle of the right-angled triangle which is under the Crater. The Beast rises in 2 hours and 1/4 of an hour. ^A

When the Altar rises, the zodiac rises concurrently with it from 15 degrees of Sagittarius to 23 degrees of Sagittarius; and it culminates from 2 degrees of the Claws to 10 degrees of the Claws. The first star to rise is that in the focus, and the last is the more southerly of those in the base. The first star to culminate is the more southerly of those in the left foot of Boötes, and the bright one in the hind feet of the Centaur; the last is the one from the Great Bear of the right knee of the meridian. The Altar rises in the space of half an hour. ^B

III. As the Southern Fish is rising, the zodiac rises concurrently with it from the 17th degree of Aquarius to the 21st degree of Virgo; it culminates from the 4th degree of Sagittarius to the 25th degree of Sagittarius. The first of all to rise is the more northerly star of those in the tail; the last is the bright one at the tip of the snout. The first to culminate is that in the middle of the Bow, and the more southerly of those in the right shoulder of the Serpent-Bearer, situated about half a cubit before the meridian; the last is the bright one in the hind feet, and the one in the tail of the Serpent which the Serpent-Bearer holds; and the leading one of the two bright stars in the yoke of the Lyre, about half a cubit preceding the meridian. The Fish rises in 4/5 of an hour. ^C

When the Whale rises, the zodiac rises concurrently with it from the 20th degree of Pisces to the 7th degree of Taurus; it culminates from the middle of Sagittarius to the middle of Capricorn. The first of all to rise is the more northerly of those in the tail; the last is the more southerly of the following bright ones in the Quadrilateral. The first to culminate is the leader of those in the yoke of the Lyre, and the last is the bright one in the tail of the Bird. The Whale rises in 2 hours. ^D

When Orion rises, the zodiac rises concurrently with it from the 28th degree of Taurus to the 3rd degree of Cancer; it culminates from the 9th degree of Aquarius to the 13th degree of Pisces. The first star to rise is the one in the left hand; the last is the one in the right foot. The first of the others to culminate is the right foot of Cepheus, and the middle one of those in the water-urn of Aquarius; the last is the small one in the seat of Cassiopeia, and the most northerly of those in the chest of Andromeda. Orion rises in the space of 2 hours and 1/6 of an hour.

When the River which is from Orion rises, the zodiac rises concurrently with it from the 13th degree of Taurus to the 10th degree of Cancer; it culminates from the 27th degree of Capricorn to the 22nd degree of Pisces. The one that rises first is the preceding

^A of the northerly ones in the parallelogram which is situated in the great flexure near Cetus; the last is the brightest, and the leading one, and the most southerly of all. Of the others, the first to culminate is 13 degrees, along with the one following those situated towards the north among those in the tail, and the more southerly of those in the left foot of Cygnus; the last to culminate is the one in the knees of Cassiopeia, and the one at the very end of the tail of the more southerly of the Fishes. The River rises in 3 hours and 3/5 of an hour.

IV. On the rising of Lepus

When Canis rises, the zodiac rises with it from the 15th degree of Cancer to the middle of the 5th degree of Leo; it culminates from the 28th degree of Pisces to the middle of the 24th degree of Aries. The first star to rise is the one at the tip of the forward and more northerly foot, and the last is the one at the tip of the tail. Of the others, the first to culminate is the one in the feet of Cassiopeia, and the more northerly of those in the right foot of Andromeda, slightly preceding the meridian; the last is the bright one on the right thigh of Perseus, and the following one of those in the tail ^C of Cancer. Canis rises in 1 hour and 2/3 of an hour.

When Procyon rises, the zodiac rises with it from the middle of the 4th degree of Cancer to the 9th degree of Cancer; it culminates from the 15th degree of Pisces to the middle of the 20th degree of Pisces. The first star to rise is the leading and double one, and the last is the following and bright one. Of the other stars to culminate, the first is the one in the middle of the body of Cassiopeia, and the four following ones which are in the tail of Cetus. The last to culminate are the closest to these, which are in the zone of Andromeda, and the more northerly of those in the quadrilateral of Cetus. Procyon rises in 1/3 of an hour.

When Argo rises, the zodiac rises with it from the 6th degree of Leo to the middle of the 9th degree of Chelae ^D; it culminates from the middle of the 26th degree of Aries to the middle of the 4th degree of Cancer. The first star to rise is the one which is as if triple among those in the tip of the tail of Canis, and the last is the most southerly of those in the section of the Ship and is bright. Of the other stars to culminate, the first is the one on the left thigh of Perseus, and the most southerly of those in the section of Taurus; the last is the leading, distinct one of the head of Hydra, which is in the southern feet of Canis.

V. Concerning the setting of the constellations south of the zodiac circle

^A it culminates from the middle of the 19th degree of the Claws to the middle of the 10th degree of Sagittarius. The first star to set is the more southerly of those in the jowl, and the last is the one at the tip of the tail. Culminating among the other stars at the beginning is the 3rd bright star from the tail of the Dragon, preceding the meridian by about a half-cubit, and the bright star in the belt of Boötes, and the one preceding the bright star at the tip of the northern Claw, and the one at the tip of the tail of the Hydra, preceding the meridian by a half-cubit; and last to culminate is the more southerly temple of the Dragon, and of the Serpent, which Ophiuchus holds, the one at the tip of the tail, and the leading one of those in the cloak of Sagittarius. The Hydra sets in 4 hours.

When the Crater sets, the zodiac sets with it from the 21st degree of Cancer to the middle of the 13th of Leo; it culminates from the middle of the 12th degree of Scorpio to the beginning of Sagittarius. The first star to set is the more northerly of those in the base, and the last is the more southerly and more northerly of those in the basin. Culminating among the other stars at the beginning are the 3rd and 5th vertebrae of the Scorpio after the chest, and the 3rd star from the right shoulder of the Ingeniculi [Hercules], situated in the arm, preceding the meridian by a half-cubit; and last to culminate is the one at the joint of the left thigh of the Ingeniculi, and the tip of the Bow. The Crater sets in 1 hour and 20 minutes.

When the Raven sets, the zodiac sets with it from the middle of the 29th degree of Leo to the 11th of the Claws; it culminates from the 10th degree of Sagittarius to the middle of the 6th of Capricorn. The prior star to set is the one in the rear thighs, being the last, and the one following those in the head. Culminating among the other stars at the beginning is the one in the jowl of the Dragon ^B, preceding the meridian by about a half-cubit, and the left elbow of the Ingeniculi, preceding the meridian by a half-cubit; and last to culminate is the leading one of the three bright stars in the first coil of the Dragon, and the one in the right wing of the Swan, situated a little before the meridian, and the one on the tip of the Arrow, and the more southerly of those in the face of Capricorn. The Beast sets in 2 hours.

VI. When the Altar sets, the zodiac is hidden from the middle of the 19th degree of Leo ^C to the 9th degree of the Claws; it culminates from the 5th degree of Sagittarius to the middle of the 9th of Capricorn. The first to set is the more southerly of those on the rim, which is also a double star; the last is the more northerly of those in the base. Culminating among the other stars at the beginning is the bright star in the left thigh of the Ingeniculi, and the middle star of those in the bow of Sagittarius; and last to culminate is the more southerly of the bright stars in the knees of Capricorn. The Altar sets in 2 hours and 10 minutes.

When the Southern Fish sets, the zodiac descends with it from the 24th degree of Sagittarius ^D to the middle of the 18th of Capricorn; it culminates from the 3rd degree of Pisces to the 2nd degree of Aries. The first star to set is the more

southerly of those in the tail, and the last is the one that is very bright on the snout. Culminating from the other stars, at the beginning is the one that is in the extreme tail of the southern Fish; at the end, the left foot of Andromeda; and in the middle of them, those that are in the head of Andromeda and the small side, which is in the Whale, the more southerly of the following ones. The Fish sets in 1 hour and 4/5 parts. ^A

When the Whale is setting, the zodiac descends with it from the 28th degree of Aquarius to the 14th of Aries; it culminates from the 22nd degree of Taurus to the 15th degree of Cancer. The first star to begin to set is the more southerly of those in the tail, and the last is the following one in the northern hump. Of the other stars, culminating at the beginning is the more southerly of those in the head and right foot of the Charioteer; at the end, the bright star in the front legs of the Bear and the bright star in the middle of the sides of the Ship, which precedes the meridian by about a half-cubit. The Whale sets in 4 hours less an eighth part. ^B

When Orion is setting, the zodiac descends with it from the 7th degree of Taurus to the 30th of Taurus; it culminates from the 12th degree of Leo to the 13th of Virgo. The first star to set is the one in the left foot, and the last are the most northerly of those in the club. Culminating from the other stars, at the beginning is the one in the hind knees of the Great Bear and the one to the south of the bright star in the loin; at the end, the more northerly shoulder of Virgo. The Orion sets in approximately 2 hours. ^C

When the River from Orion sets, the zodiac descends with it from the 7th degree of Pisces to the 5th degree of Taurus; it culminates from the 4th degree of Gemini to the 10th of Leo. The first star to set is the leading one, which is the brightest of all, and the last is the first—that is, the one placed to the south of Orion’s foot. Culminating from the other stars, at the beginning of the setting are those of Gemini, the "Propus" (Forward Foot), which is placed a little on this side of the meridian, and the two in the middle of the body of the Hare; at the end, the following of those in the back of Leo and the one in the hind knees of the Bear, which is lagging behind the meridian by about a half-cubit. The River sets in 4 hours and 1/2 and 1/5 part of an hour. ^D

VII. When the Hare sets, the zodiac descends with it from the 27th degree of Aries to the 14th of Taurus; it culminates from the 30th degree of Cancer to the 21st degree of Leo. The first star to set is the one in the front legs, and the last is the one on the tip of the tail. Culminating from the other stars, at the beginning is the star in the small square of the Bear that is on its shoulders, the one in the tip of the tail of the Dragon, the one in the heart of Leo, and the more northerly of those in the cut-off part of the Ship, which precedes the meridian by a little; at the end, there culminate the hind foot of Leo and those in the hind legs, as well as the most southerly of those in the base of the Cup. The Hare sets in 1 hour and 1/3 part.

^A As the Dog sets, the zodiac descends with it from the 11th degree of Taurus to the 29th degree of Taurus; and there culminate from the 17th degree of Leo to the 11th of Virgo. The first star to set is the bright one in the hind feet, and the last is the most southerly of the visible ones in the head. Of the other stars, there culminate at the beginning the leading one of those in the hind feet of the Bear, and the one on the loin of Leo; at the end there culminate the one in the feet of the Crow, and the more southerly of the Virgin, lagging behind the meridian by about 2 parts of a cubit. The Dog sets in 1 1/2 hours.

As the Procyon sets, the zodiac descends with it from the 15th degree of Gemini to the 18th degree of Gemini; and there culminate from the beginning of the Claws to the 4th degree of the Claws. The first star to set is the leading and double one, and the last is the following and bright one. ^B Of the other stars, there culminate at the beginning the middle one of those in the left foot of Bootes, being slightly behind the meridian, and the more northerly of those in the head of the Centaur, leading the meridian by about half a cubit. At the end there culminate the one at the tip of the tail of the Bear, being slightly behind the meridian, and the more northerly of those in the left foot of Bootes, and the one at the tip of the tail of the Hydra, and the right shoulder of the Centaur. Procyon sets in 1/5 of an hour.

As the Argo sets, the zodiac descends with it from the 16th degree of Aries to the 18th degree of Gemini; and there culminate from the 17th degree of Cancer to the 5th degree of the Claws. The first star to set is the brightest and most southerly of those in the Rudder, which some call Canopus; and the last is the more northerly of those in the mast. Of the other stars, there culminate at the beginning the more southerly of the leading ones in the head of Leo, lagging behind the meridian by about half a cubit, and the small one in the root of the neck of the Hydra; at the end there culminate the ones at the tip of the tail of the Great Bear, and the more northerly of those in the left foot of Bootes, leading the meridian by about half a cubit, and the one at the tip of the tail of the Hydra; and the right shoulder of the Centaur, leading the meridian slightly. The Argo sets in approximately 5 hours.

On the rising and setting of the zodiacal signs

^D VIII. Having thus far set forth what concerns the rising and setting of each of the stars positioned outside the zodiacal circle, we shall next explain the joint-risings and joint-settings of the twelve signs of the zodiac.

When Cancer is rising, the zodiac rises with it from the 23rd degree of Gemini to the 18th degree of Cancer; and there culminate from the 5th degree of Pisces to the half of the 1st degree of Aries. The first star to rise is the one at the tip of the northern Claw, and the last is the one at the tip of the southern Claw. Of the other stars, there culminate first the bright one in the head of Andromeda, and last the [leader] of the three bright ones in the head of Aries, and the one adjacent to the southern part of the Whale, toward its middle body, void of

name and bright; and the southern of the following stars in the quadrilateral of the Whale; and the left foot of Andromeda, situated a little within the meridian. Cancer rises at 1 hour and [a fraction] ^A part.

When Leo rises, the zodiac rises with it from the middle of the 8th degree of Cancer to the middle of the 19th of Leo; it culminates from the 20th of Pisces to the middle of the 12th of Taurus. The first star to rise is the more northerly of the leading ones in the head, and the last is that in the hind feet. Of the other stars, the first to culminate is the following one of those in the zone of Andromeda, and the more northerly of the following ones in the quadrilateral of the Whale; the last is the brightest of the Hyades, and the one at the bend of the left elbow of the Charioteer, situated as if a half-cubit within the meridian. Leo rises in 3 hours and 15 minutes. ^B

As Virgo rises, the zodiac rises with it from the 22nd degree of Leo to the 8th of the Scorpion [Libra]; it culminates from the middle of the 15th degree of Taurus to the 9th of Cancer. The first of the stars in the head to rise is the one more northerly than the leader, and the last is that in the right foot. Of the other stars, the first to culminate is the bright one on the left shoulder of the Charioteer; the last is the bright one at the extremity of the Ship; and the more northerly of those in the mouth of the Hydra, situated as if a half-cubit within the meridian. Virgo rises in 3 hours and 48 minutes. ^C

IX. When the Claws rise, the zodiac rises with them from the 16th degree of the Claws to the 16th of the Scorpion; it culminates from the 18th of Cancer to the 11th of Leo. The first to emerge is the more southerly and bright one of those at the ends of the Claws, and the last is the southernmost of those in the forehead of the Scorpion. Of the other stars, the first to culminate is the more southerly of the leading ones in the head of Leo, and the more northerly of those in the middle of the mast of the Ship; the last is the following one of the two stars in the back of Leo. The Claws rise in 1 hour and 36 minutes. ^D

When the Scorpion rises, the zodiac rises with it from the 3rd degree of the Scorpion to the 9th of Sagittarius; it culminates from the middle of the 8th degree of Leo to the middle of the 23rd of Virgo. The first star to rise is the most northerly of those in the forehead, and the last is the 3rd vertebra counted from the one in the Centaur, and the 6th from those that are in the chest. Of the other stars, the first to culminate is the bright one in the chest of the Greater Bear, and of the Hydra [the one among the four] after the brightest before the Crater, the third from the west; last are the Spica and the left shoulder of the Centaur, preceding the meridian by as if a half-cubit space. The Scorpion rises in 3 hours, less 10 minutes.

When Sagittarius rises, the zodiac rises with it from the middle of the 6th degree of Sagittarius to

the 7th degree and 20 minutes of Capricorn; and it culminates from the 19th degree of the Claws to the 18th degree of the Scorpion. ^A And the first star to rise is the more northerly of the bright ones in the knees, and the last is the succeeding one of the bright stars in the tail. Of the other stars, the first to hold the mid-heaven is the brightest of those in the belt of Boötes, and in the Claws, the one preceding the extremity of the northern Claw; and of the Serpent that moves through the Bears, the third bright star numbered from the tip of the tail, preceding the meridian by a half-cubit space; and finally, the right shoulder of the Ingeniculi [Hercules] culminates, and the one that lies to the north of those in his right leg. Capricorn rises in 1 hour and 50 minutes.

When Aquarius emerges, the zodiac rises with it from the 6th degree of Capricorn to the 21st degree and 20 minutes of Aquarius; it culminates from the 27th degree of the Claws to the 7th degree of Sagittarius. ^B The first of the stars to rise is the one preceding that which is in the left hand; the last, however, is the bright one on the right foot. Of the remainder, the first to culminate is that which is in the head of Boötes. The last is the more northerly of those that are in the bow of Sagittarius; and three placed in a straight line, and lacking a name, which are along the right shoulder of Ophiuchus: and likewise the bright one which is in the left thigh of the Ingeniculi, preceding the meridian by almost a half-cubit. Aquarius rises in 2 hours and two parts of an hour.

When the Fishes are rising, the zodiac ascends with them from the 7th degree of Aquarius to the 16th degree of Aries; it culminates from the 26th degree of the Scorpion to the 9th degree of Capricorn. ^C The first star to emerge is the one at the tip of the snout of the southern Fish; the last is that which is in the Knot of the cords. Of the others, the first to culminate is that which is in the process of the right thigh of the Ingeniculi; and that which lies to the north of those which are in the sting of the Scorpion; but the one that is in the head of the Ingeniculi is about two parts of a cubit short of the meridian; lastly, the more southerly of those that are in the knees of Capricorn culminates: and the one which is in the throat of the Bird, and in the flexure of the right wing. The Fishes rise in 3 hours and 10 parts. ^D

XI. When Aries rises, the zodiac rises with it from the middle of the 19th degree of the Fishes to the 24th degree and 20 minutes of Aries; it culminates from the 4th degree and 20 minutes of Sagittarius to the 14th degree of Capricorn. The first star to rise is that which is on the fore-foot; the last is the succeeding one of those that are in the tail. Of the others, the star that culminates is the one preceding those that are in the yoke of the Lyre: likewise the succeeding one

^A of those that are in the back of Sagittarius, two cubits preceding the meridian; the last to culminate is the one succeeding those in the left hand of Aquarius, and the one in the chest of Capricorn, and the one leading among those in the tail of the Dolphin. Aries rises in 1 hour and 24 minutes.

When Taurus is rising, the zodiac rises with it from the 7th degree of Taurus to the 29th degree of Taurus; and it culminates from the 2nd degree of Capricorn to the 9th degree of Aquarius. The first star to rise is the southernmost of the four that are in the abscission, and the last is the one at the tip of the right horn. Of the other stars, the one that culminates first is the bright one in the middle of the tail of the Swan; the last [to culminate] is the one preceding the three that are in the head of Cepheus; and his right foot, preceding the meridian by about half a cubit; and the middle one of those in the urn of Aquarius, preceding the meridian by about half a cubit. Taurus rises in 1 hour and 8 minutes.

When Gemini is rising, the zodiac rises with it from the 2nd degree of Gemini to the 30th of Gemini; and it culminates from the 11th degree of Aquarius to the 9th degree of Pisces. The first star to rise is the one in the left hand of the leading Twin, and the last is the one in the right hand of the succeeding Twin. Of the other stars, the one that culminates first is ^B the bright one in the body of Cepheus, and the bright one in the right foot of Aquarius, and the bright one in the mouth of the Southern Fish; the last to culminate is the middle one of the three that are on the right shoulder of Andromeda. Gemini rises in 1 hour, 50 minutes, and 20 seconds.

Concerning the setting of the twelve zodiacal signs.

XII. Again, when Cancer is setting, the zodiac descends with it from the 27th degree of Gemini to the 20th degree of Cancer; and it culminates from the 17th degree of the Claws to the 12th degree of Scorpio. The first star to set is the bright one that is in the feet of Cancer, situated in a straight line, looking toward the sunset, more southerly than those around the nebula in Cancer; the last is that at the tip of the northern claw of Cancer. Of the other stars, the right foot of Bootes and the bright star of the Claws which is at the tip of the southern claw culminate; and finally culminate the one on the right arm of the Kneeler, which is the third from the right shoulder, and the 3rd, 4th, and 5th vertebrae of the Scorpio of those behind the chest. Cancer sets in 1 hour and 56 minutes. ^{C D}

When Leo is setting, the zodiac descends with it from the 21st degree of Cancer to the 14th degree of Virgo; and it culminates from the 13th degree of Scorpio to the 21st degree of Sagittarius. The first star of Leo to set is the one in the front feet, and the last is that at the tip of the tail. Of the other stars, at the beginning of the setting, the right foot of Gemini and the left knee of Serpentarius culminate, situated as if a half-cubit behind the meridian, and the 1st vertebra of Scorpio; and finally culminate...

the northernmost of the Draconis [Dragon] head and the one in the middle of the back of Sagittarius, as if a half-cubit preceding the meridian. Leo sets in 2 hours and two parts of an hour.

^A When Virgo is setting, the zodiac descends with it from the 27th degree of Leo to the 7th of Libra; it culminates from the 11th of Sagittarius to the 4th of Capricorn. The first to set is the one that is in the left wing; the last is the one in the northern foot. Of the other stars, at the beginning there culminate the second from the end of the tail of Ophiuchus, and the one in the flank of Sagittarius which leads the dimmer of the opposite angles; finally there culminate the bright one which is in the middle of the body of Cygnus, and the more southern of those following in the rhombus of Delphinus. Virgo sets in 2 hours and 12 minutes.

XIII. When the Chelæ set, the zodiac descends from the middle of the Chelæ to the 15th degree of Scorpio; ^B it culminates from the 10th degree to the 28th middle of Capricorn. The first star to set is the bright one which is in the extremity of the southern Chela; the last one is that in the northern Chela. Of the other stars, there culminate at the beginning the most northern of those which are in the right wing, and finally the bright one in the mouth of Equus. The Chelæ set in 1 hour and 15 minutes.

When Scorpio is setting, the zodiac descends from the middle part of the Chelæ to the 6th degree of Scorpio; it culminates from the 7th middle to the 22nd degree of Capricorn. ^C The first star to set is the one that is in the spondylus [vertebra]; the last is the more northern of those which are in the forehead. Of the remaining stars, there culminate at the beginning [the middle one] of those which are in the right wing of Cygnus, situated as if a half-cubit on this side of the meridian, and the more northern of those which are in the knees of Capricorn; finally there culminate the bright one in the middle of the tail of Cygnus, and the leading one of the bright stars in the tail of Capricorn, falling short of the meridian by almost two-thirds of a cubit. ^D Scorpio sets in 1 hour.

When Sagittarius is setting, the zodiac descends from the 3rd degree of Scorpio to the 27th middle of Sagittarius; it culminates from the 20th degree of Capricorn to the 5th middle of Pisces. The first to set is the bright one of the hind foot; the last is the more northern of those which are in the sagum [cloak]. Of the other stars, at the beginning there culminate the one which is in the right hand of Cepheus and that which is in the flexure of the left wing of Cygnus; and furthermore the one following those which are in the back of Capricorn, preceding the meridian slightly; finally there culminate the left foot of Cepheus and that which is in the umbilicus of Equus. Sagittarius sets in 3 hours.

XIV. When Capricorn descends, the zodiac descends from the 2nd degree of Capricorn to the 24th middle of Capricorn; it culminates from the 11th middle of Pisces to the 9th of Aries. The first to set is the more southern of those which are in the knees; the last is the one following those which are in the tail. Of the remaining stars there culmi-

culminate, at the beginning, the more obscure of those that are in the throne of Cassiopeia, and the one more northerly of those in the chest of Andromeda; last to culminate is the left shoulder of Perseus, situated about two parts of a cubit to the near side of the meridian. Capricorn sets in 1 hour and two parts of an hour.

With Aquarius, the zodiac sets from the 18th degree of Capricorn, at the middle, to the 15th of Aquarius; it culminates from the 3rd degree of Aries to the middle of the 7th of Taurus. The first to set is the star preceding those which are in the left hand; the last to set is the one following those in the urn. Of there remaining, there culminate: at the beginning, the nebulous star that is in the harpe of Perseus, and the left foot of Andromeda, a little preceding the meridian; likewise, the middle one of those in the head of Aries; then last, the one in the middle of the shoulder blade of Taurus, preceding the meridian by about half a cubit, and the one of the Hyades that is in the snout, placed about half a cubit to the near side of the meridian. Aquarius sets in 2 hours and 1/8 of an hour.

As the Fishes are setting, the zodiac descends with them from the 23rd degree of Aquarius to the 5th of Aries; it culminates from the 17th of Taurus to the 6th of Cancer. The first star to set is the one in the snout of the more northerly Fish; there culminate, of the other stars, at the beginning, the one that is at the root of the right horn of Taurus, and the left shoulder of the Charioteer, preceding the meridian by about half a cubit; ^B and finally there culminate the more northerly of those in the anterior legs of the Bear, and ^C the two westernmost of the four situated around the nebula in Cancer, as well as the more southern of the anterior feet of the Dog. The Fishes set in 3 hours and a half.

XV. With Aries, the zodiac sets from the 29th degree of the Fishes to the 26th of Aries; it culminates from the 29th of Gemini to the 29th of Cancer. The first star to set is the one in the anterior feet; the last is the one following those in the tail. Of the others, there culminates at the beginning the one placed at the tip of the tail of the Dog, about half a cubit to the near side of the meridian, and the one in the middle of the southern side of the Beam; finally, the one preceding those that are in the posterior feet of the Bear, preceding the meridian by about half a cubit, and the third of the bright stars in the neck and chest of Leo, from the north, situated about two parts of a cubit to the near side of the meridian. Aries sets in 2 hours.

As Taurus is setting, the zodiac sets with it from the 20th degree of Aries to the 26th of Taurus; it culminates from the 22nd degree of Cancer to the 7th of Virgo. The first star to set is the more southern of the four situated in the incision; the last is the one at the tip of the left horn. Of the remaining stars there culminate, at the beginning, the most southern of the three in the neck, and ^D those which are nearest to the bright stars lying toward the north, situated about half a cubit to the near side of the meridian; finally there culminate those in the middle of the left wing of the Virgin, a little to the near side of the meridian.

Taurus sets in 4 hours.

As the Gemini are setting, the zodiac descends in tandem with them, from the 4th degree of Gemini to the middle of the 2nd degree of Cancer; there culminate stars from the 17th degree of Virgo to the middle of the 20th degree of the Claws [Libra]. The first star to set is that which is called Propus, and the last is that which is in the right hand of the following Gemini. At the beginning, the Protrygeter and the right shoulder of the Virgin culminate, preceding the meridian by about half a cubit; and finally, there culminates the bright star in the extremity of the northern Claw, remaining about two parts of a cubit from the meridian. The Gemini set in 2 hours and 40 minutes.

On the distance between stars according to time intervals

XVI. Besides the theory of the risings and settings of the zodiacal signs, I think it is also very useful for us to trace which of the fixed stars are distant from one another by successive equinoctial hourly intervals. For this is useful to us both for determining the hour of the night exactly, and for calculating the times of lunar eclipses, and for observing many other matters pertaining to the study of the stars.

Wherefore, on that circle which is described through the poles and the tropics, there lies the star at the extremity of the tail of the Dog, positioned in the semi-circle which contains the summer tropic. The star which is positioned at the base of the neck of the Hydra is distant from this star by one hourly interval. Very close, too, is the bright star in the front knees of the Bear.

The second hourly interval is bounded by the small starlet that precedes the heart of the Lion by a little more than a cubit's space. This same little star precedes the meridian circle defined by the poles by the distance of the second hour.

The third hourly interval, around the middle of the Lion, is bounded by the more southerly of the two stars lying on either side of the bright one in the Lion’s loins.

The fourth hourly interval, around the beginning of the Virgin, is bounded by the star situated at the right angle of the right-angled triangle which lies beneath the Crater, and which is [also] in the loins of the Greater Bear, the bright star being less than the twentieth part of an hour from the circle marking the fourth hour.

The terminus of the fifth hour is in the middle of the Virgin; if we wish to speak exactly, there is no star [there], but the Protrygeter and the bright star lying on the right shoulder of the Virgin are more than a tenth part of an hour away from that terminus.

The limit of the sixth hour is on the equinoctial circle, very close indeed to the Centaur, [defined by] the succeeding one of the bright stars in the most southerly part of the thyrsus, which are distant by about half a cubit and occupy about the middle of the Centaur's breast. Likewise the middle one of those which are

in the left foot of Boötes, distant by about the twentieth part of an hourly interval from the circle defining the four hours. ^A

XVII. Between the point of the autumnal equinox and the winter tropic, of the six hourly intervals, the first defines the hour very closely upon the circle passing through the middle of the Claws, namely the left shoulder of Boötes, and the bright star at the extremity of the southern Claw; the shoulder being, without any great difference, further behind, while the Claw is about the thirtieth part of an hour in advance of the aforementioned circle passing through the poles. ^B The second hourly interval defines, about the beginning of Scorpio, the more northerly of the two bright stars which are in the right hand of Ophiuchus, which lie in the body of the Serpent behind the right knee of Ophiuchus; and the one preceding the bright star of the Crown is left behind the circle passing through the poles by about the thirtieth part of an hour; and similarly also the middle one of the three bright stars in the forehead of Scorpio. ^C The third hour is defined about the middle of Scorpio by the star which is on the right shoulder of the Kneeler [Ingeniculus], and the one in the middle of his right shin, deviating toward the east by about the thirtieth part of an hour. The fourth defines the beginning of Sagittarius, and the bright star in the left thigh of the Kneeler, and the most bright and leading of the four in the quadrilateral of the Little Bear, and the more northerly of those on the right shoulder of Ophiuchus. ^D The fifth hour defines the middle of Sagittarius, and the one following the three in the head of Sagittarius, deviating toward the east by about the thirtieth part of an hour. The sixth hour is defined as closely as possible upon the circle passing through the tropical points by the more northerly of the bright stars in the [Sagittarius head], being left behind the circle by about the twentieth part of one hour.

XVIII. Between the winter tropic point and the vernal equinox, of the six hourly intervals, the first hourly interval is defined by the more northerly of the leading stars in the rhombus of the Dolphin, and by the leader of those on the back of Capricorn. The second hourly interval defines, about the beginning of Aquarius, the bright star in the mouth of the Horse, and the more southerly of those preceding the right shoulder of Cepheus. The third hourly interval is defined about the middle of Aquarius by the middle of the three stars in the head of Cepheus, which are placed in a straight line, and the more northerly of the two stars in the neck of the Horse, being in advance of the circle passing through the poles by about the thirtieth part of an hour. The fourth hourly interval defines, about the beginning of the Fishes, the most southerly of those stars in the right hand of Andromeda, left behind the circle passing through the poles by about the twentieth part of an hour. The fifth hourly interval defines, about the middle of the Fishes, the star in the middle of the body of Cassiopeia, which is counted as the third from the head.

^A The sixth hourly interval terminates closest to that circle which is described through the equinoctial points and the poles, which hangs over the summit of the one situated above Aries, and the one preceding the three bright stars that are in the head of Aries, which is located about the twentieth part of an hour on this side of the circle.

In that quadrant which extends from the vernal equinox point to the summer tropical point, the first hourly interval is terminated by the brightest of those that are in the Gorgoneion, which Perseus carries in his left hand. The second hourly interval terminates about the beginning of Taurus, [marking] the one following the three positioned in a straight series out of the five stars that are around the right knee of Perseus. The limit of the third interval is about the middle of Taurus, [marking] the fourth and seventh of those that are in the skin which Orion holds in his left hand. Also, the splendid one in the middle of the horns of Taurus, which forms an almost equilateral triangle with the bright ones at the extremities of the horns. The fourth hour is defined about the beginning of the Twins by the one following the two small and bright ones, which are positioned in a straight line toward the east from the right horn; these are also in the belt of Orion, toward the more northerly limit. The one more to the south of the two bright stars that are in the middle of the body of the Hare defines the fourth [hour] very closely. The fifth hourly space terminates about the middle of the Twins, [marked by] the middle of the three bright stars that are in the knees of the Twins, which precedes the circle passing through the poles by about the thirtieth part of an hour, as well as the bright one of the hind feet of the Dog. ^{B C}

OF ERATOSTHENES, OTHERWISE OF HIPPARCHUS, ON ARATUS' PHENOMENA

(74) ^D I. It is necessary to begin the exposition of the phenomena in such a way that the sphere is turned toward the south, the Bears are kept opposite, the rising is on the right, and the setting on the left. Furthermore, the natural position of the sphere of the universe is of such a kind that Cancer culminates at the summer solstice; the Claws hold the horoscope at the equinoctial [line];

in the west are the Claws, and the head of the Dragon looks upward toward the horizon, where ^A sunsets and sunrises mingle with one another.

It has also two poles: the arctic, which is entirely lofty and is also called the northern; and the antarctic, which is in the invisible region and is also called the southern. It has four great circles besides the horizon, since we have already mentioned that it possesses the meridian, the equinoctial, the zodiac, and the galaxy; and four minor ones: the arctic, which is entirely visible and upon which four signs are fixed—the two Bears, Cepheus from the chest up, and the Dragon; the summer tropical [circle], which has a greater part above the earth and a lesser part below the earth, upon which are fixed eight signs—Bootes, the Crown, the Kneeler, the Lyre, Cassiopeia, the Charioteer, the Bird, and Perseus. The winter solstice ^B circle has more below the earth and less above the earth; upon it six signs are catasterized—Eridanus, the Argo, the Centaur, upon which is the Beast, the Altar, and the great southern Fish, which is invisible.

The equinoctial circle has equal parts above and below the earth; upon it are catasterized twelve signs: the Horse, Ophiuchus (upon which is the Serpent), the Water-Snake (upon which are catasterized the Mixing Bowl, the Crow, Procyon, the Eagle, the Dolphin, Orion, the Arrow, the Triangle, Andromeda, the Hare, ^C the Whale, and the Dog), so that the total of signs is twenty-three, apart from the notable stars catasterized within them, such as Arcturus in Bootes; the Goat and the Kids in the Charioteer; the Pleiades and Hyades in Taurus; the Ear of Corn and the Grape-gatherer in the Virgin; Sirius in the Dog; and any others similar to these.

The zodiacal circle has twelve signs: Cancer, Leo, Virgo, the Claws (which is the Balance), Scorpius, Sagittarius, Capricornus, Aquarius, Pisces, Aries, Taurus, and Gemini; so that the total of signs is thirty-three. There are also five wandering stars besides the sun and moon: ^D Saturn, Jupiter, Mars, Venus, and Mercury.

Aratus has provided the explanation of the phenomena, beginning from the Bears and covering all the northern parts around until the zodiac; then he shifts and begins from Orion, since it is a bright star, and weaves through the rest. Furthermore, all those from the zodiac to the south are called southern as far as the antarctic. From there, Aratus passes on to what follows.

With these matters thus held, it remains to move on to the circles that cross [others] and the signs cut by them. Similarly, we shall also speak of their rising together and setting together, so that we may omit nothing, as far as the constellations