Martianus Capella
The Marriage of Philology and Mercury

/314/

Book VIII
Astronomy

→ lat [803] Meanwhile the august company of the gods were amazed at the intricacies of the harmonious and discordant [odd and even] numbers, and acknowledged the lady herself, a majestic, exalted, and awe-inspiring figure, to be in very truth the procreator of the gods. And the host of philosophers, too, who stood nearby – in particular, Pythagoras, with all his disciples, and Plato, expounding the cryptic doctrines of his Timaeus¹ – worshiped the lady with words of mystic praise. Pallas, casting frequent glances at the bride, queried her about her commendation of the handmaid’s learning and joined her in nodding her approval. The Cyllenian [Mercury] took more pride in the brilliance and clarity of Arithmetic than in that of any other bridesmaid, and was elated with her grandiloquence. As Phoebus was delaying the introduction of another bridesmaid for a little while, for fear of detracting from admiration of the previous speaker, a reverential silence came over the audience for a time.

→ lat [804] In the meantime wrinkled Silenus, as an attendant of Bacchus,² had been standing behind, leaning for support. Perhaps the weariness of age was too much for him; then again it may have been the strain of concentrating on the remarkable discourse of the learned lady; or perhaps the occasion of the marriage ceremony had gotten the better of him, swollen from earlier drinking bouts, and he had drenched himself in an overdraught of wine. For some time now he had been relaxed in slumber and quietly snoring, when suddenly he belched like a croaking frog. Several of the gods, shaken by this frightening and raucous sound, turned round, and as those who were standing about noticed the profuse sweating of /315/ the old man “breathing forth his slumber”³ and soaked with intoxication, they burst into laughter, the more explosive as they tried to suppress it. Then, since a marriage ceremony is not supposed to inhibit banter, the attendants of Venus and the maidservants of Bacchus served up such merriment to those who were already convulsed with hiccups that several others who were trying to suppress their laughter broke into violent and wanton ribaldry and unrestrained mirth. Finally, Cupid, unruly as ever and saucy and impudent in his affronts, nimbly and merrily ran up to Silenus and, as the old man had settled his ruddy bald head upon his staff, he gave him a resounding clap with his palm, and the reverberating sound revived the laughter, which was more or less universal.

→ lat [806] While this animated mirth was at its height, Satire, who always considered it her responsibility to edify and reprove my thoughts, said: “You, Felix, or Capella, or whoever you are, with a sense to match the beast’s whose name you bear,⁶ are you going out of your mind with the intrusion of this unseemly jesting? You must realize that you have brought raucous laughter into a heavenly assembly and that it is a reprobate act in the eyes of the gods, and of /316/ Pallas in particular, to represent someone prating nonsense like a madman. → lat [807] And on such an occasion to have Cupid and Satyr prancing about like impudent wantons, at the very time that the maiden of the sky [Astronomy], one of the more beautiful of the handmaids, is about to present herself to the august senate and the view of the gods! Enough of that, and hereafter do not try to defend your nonsense or justify your conduct as license appropriate to a wedding ceremony. At least give ready heed to the Prienian maxim, and if you are not ‘an ass listening to a lyre, know the proper time.”⁷

Soundly cudgeled by such stern and fell reproaches from Satire – a charming lady at other times – and condemned by my own apologies for my impudent conduct, I asked her which of the girls was being prepared for introduction. Satire, the wrath that she had vented upon me not yet subsided, began as follows:

→ lat [808] “The time is now at hand to speak of the path of the starry sphere, the course of the poles and of the region where the hallowed planets trace their diverse and winding courses. I see the canopy of heaven gleam, now struck by a bolt of lightning from the sky. From one direction, Herdsman Boötes, brilliant in the northern light, is wont to watch Septentriones [Ursa Major and Ursa Minor]; in the other direction, where the earth verges out of sight beneath the inclined sky, bright Canopus ranges imperceptible. And now I think I see Phoebus’ team, swiftly coursing, and the blazing horns of the ever-changing moon; and what is more, the middle circle that is bound by the diagonal girdle,⁸ along which a path is traced by glittering planets. You would rather fashion cheap and silly fictions than listen to a girl discoursing on the stars.”

→ lat [809] As Satire was reciting these lines, I succumbed again to the mood to banter, despite her prohibitions and stern rebukes. “A fine performance, my Satire,” I said. “Has your cholcr made a poet out of you? Have you begun to thirst for Permessian waters?⁹ /317/ Are you already anticipating the flashing countenances of the gods?¹⁰ What has suddenly happened to your ever-ironical and subtle contempt for the bombast and conceits of the poets, whereby you content yourself with chaffing and witticisms while consigning their poetry to the realms of absurdity? Is there any reason to rage madly at me and to chide me in a superior and contemptuous way for being amused at the slumbering Silenus? Am I to dispense with all imaginary creatures and introduce no pleasantry or mirth to relieve the boredom of my readers? Come to your senses, Satire; leave off your tragic ranting, and take a hint from the young Pelignian poet: ‘Young lady, take my advice and smile.’”¹¹ → lat [810] Satire and I were soon done with our abusive quarreling, and Apollo stepped out to introduce another of the handmaids.¹²

Before their eyes a vision appeared, a hollow ball of heavenly light, filled with transparent fire, gently rotating, and enclosing a maiden within. Several planetary deities,¹³ especially those which determine men’s destinies, were bathed in its glare, the mystery of their behavior and orbits revealed. Even the fabric of the celestial sphere shone forth in the same flashing light. Lesser deities – ethereal, terrestrial, marine, and subterrestrial – were astounded at the miraculous sight, supposing that Astraea, Themis, or surely Libyan Urania had appeared before them, and they offered the maiden a seat of honor. → lat [811] Decked with gems and decorously arrayed in every detail, she stepped forth nimbly from the sphere. Her brow was starlike and her locks sparkled. The plumage on her wings was crystalline, and as she glided through the sky her whirring wings repeatedly took on a golden hue. In one hand she held a forked sextant, in the other a book containing calculations of the orbits of the planets and their forward and retrograde motions together with the poles of the heavens. These were delineated in metals of various colors. As she came into their midst many of the gods smiled at her; the others admired her radiant beauty. She began her discourse as follows:

/318/ → lat [812] “In the presence of great and venerable learning it would be fit and proper for me not to disclose whatever fruits have come from my diligent study. For I do not consider it modest or becoming to expound their characteristic motions and orbits to the very ones who perform those motions or to presume to instruct the gods in what they are doing. Moreover, matters which over the vast span of ages have been reposited in the sanctums of Egyptian priests, I was keeping secret, not wishing to divulge and profane them. In fact, for almost forty thousand years I kept myself in seclusion there, in reverent observation. And well might I wish that following the disruption caused by the Flood and the restoration of Athens¹⁴ after a long lapse of time, no worldly allurements, no vainglorious speculations of philosophers had known that I was in Greece, destined not to be kept hidden by a philosopher’s cloak, but to be divulged to all. Never, to be sure, would the understanding of your journey and of your return reach mortal intelligence and the taint of mortal cares.¹⁵

→ lat [813] Inasmuch as I have at one time or other in my peregrinations come to be known by the Greeks, whatever has been written by Eratosthenes, Ptolemy, Hipparchus, and other Greeks ought to suffice here and relieve me of the burden of discoursing at greater length. However, because a sense of obligation toward the Cyllenian, the one who reared and educated me, does not permit me to keep silent, and because the sagacious bride also invites me to disclose the secrets of my studies, I shall not keep silent in the presence of you celestial ones, who will be surveying the courses of your own heavenly bodies.

→ lat [814] The universe is formed in the shape of a globe composed entirely of four elements.¹⁶ The heavens, swirling in a ceaseless and rotary motion, set the earth apart in a stationary position in the middle and at the bottom.¹⁷ I would not disdain, at the very outset of my discourse, to give heed to the physical philosophers who do not believe that the softness of rarefied bodies is drawn and divided /319/ by its very condensations into certain set paths and intervals of circles;¹⁸ but rather that the natures of these bodies, coalescing by their own surgings, are diffused the entire way around in globular layers.¹⁹ The physical philosophers declare that the first envelopment is that of water, the second of air, the third of fire, arranged about a midpoint which they call the center. And coming next is a fifth agglomeration²⁰ of corporeal matter, in which the shining heavenly bodies have their courses, in a region where the inclined paths of the sun, moon, planets, and zodiac are drawn; in the philosophical schools the last is referred to as the ‘circular billow.’ The very calm of that realm keeps its position outermost and its course an encompassing one; it is called ‘starless’ from the fact that it is studded with no constellations.

→ lat [815] If each belt of the encompassing substances is found to be homogeneous, no circle can waver from its ethereal orbit. When we use the word ‘circles’ we do not intend to convey a notion of corporeal demarcations of a fluid substance; we are merely illustrating the risings and settings of planetary bodies as they appear to us. I myself do not consider an axis and poles, which mortals have fastened in a bronze armillary sphere²¹ to assist them in comprehending the heavens, as an authoritative guide to the workings of the universe. For there is nothing more substantial than the earth itself, which is able to sustain the heavens. Another reason is that the poles that protrude from the hollow cavity of the perforated outer sphere, and the apertures, the pivots, and the sockets have to be imagined – something that you may be assured could not happen in a rarefied and supramundanc atmosphere.

→ lat [816] Accordingly, whenever I shall use the terms axis, poles, or celestial circles, for the purpose of gaining comprehension, my terminology is to be understood in a theoretical sense, the distinctions applying not to transitory conditions in the heavens but /320/ to calculations of intervals.²² And so also should my remarks be understood when I shall speak of the world as verging upward or sloping downward, although it is alike in all its regions and is elevated or lies hidden from view according to the position of the horizon or the situation of the lands.

→ lat [817] So much by way of preface. I now point out that whereas a certain Roman author,²³ well known to me, derives the words stella from the verb stare,²⁴ sidera from the verb considere²⁵ and astrum from Astraeus,²⁶ and whereas the Greeks have filled the sky with mythological figures, I prefer to discuss the precepts of the discipline itself. And indeed I shall assert that there are ten so-called circles of the universe. Some of these are parallels, which we can refer to by their Latin designation as ‘equidistant circles,’ having the same poles as the universe itself.²⁷ The poles are defined as equally dividing the segments, if a line is drawn through the center of a circle to the circumference.

→ lat [818] The first of the parallels is the one which is always visible and looms above, never plunging below the horizon, and just grazing the edge of the northern horizon.²⁸ This is called the arctic circle, from the fact that it encompasses, along with the other constellations which will be mentioned later, the constellations of the twin Septentriones → lat [819] . The second of the parallels is the solstitial [or tropic], the limit which the sun reaches in summer and from which it is then turned away.²⁹ → lat [820] The third, or equinoctial, parallel – the middle and greatest of all – marks the measure of the equal length of day and night.³⁰ The sun, in its middle position in the universe, crosses this /321/ parallel twice, when it is rising to its summer heat or descending to its winter quarters. → lat [821] Next after this comes the winter tropic, upon reaching which, at the winter limit, the sun is turned back and begins rising again in its northward course.³¹ → lat [822] The fifth and last parallel is called the australis, or the antarctic circle. This is plunged beneath the surface, and its upper edge barely touches the southern horizon. ³² The powers of reasoning show it to be of the same extent as the arctic circle, which is situated diametrically opposite it.

→ lat [823] It is fitting now to explain the colures, portions of which are overhead, other portions of which are hidden beneath the surface.³³ I am aware that these circles are traced differently’ by different writers. For some assert that one colure is traced from the north pole into the south, and then passing beneath the earth is elevated again in the arctic pole. Others maintain that the circle has its beginning at the south pole, passes through the arctic pole, and returns to its point of origin. These writers, tracing another colure at right angles, cut the girth of the universe into four equal parts. → lat [824] But I propound a view which my dear Hipparchus, a ranking authority, adopts, maintaining that these circles originate in signs of the zodiac and cross each other twice; and, cutting all the parallels at equal angles, they pass through the poles. One colure, originating in the eighth degree of Aries,³⁴ traverses the universe, passing through the poles, and returns to the same point; the other girdles the universe in a similar manner, arising in Cancer. We shall explain this more clearly later.³⁵

→ lat [825] And now we must describe the oblique circles. Of these the zodiac, marked off in twelve segments, is tangent to two of the parallels, the Tropics of Cancer and Capricorn. It intersects the equator twice, but the angles produced are not equal. The zodiac furnishes a path for the sun, the moon, and the five planets. → lat [826] /322/ Among the oblique circles the Milky Way is plainly visible as extending with a much greater girth,³⁶ since it rises in the borders of the arctic circle and sets on the horizon of the antarctic region, and appears to traverse almost the entire heavens. Those who have refused to include this one among the celestial circles seem to me to be foolish.³⁷ There is now one circle left for mention, a circle which I am at a loss to name, since it varies with all times and places. This circle demarcates for us the upper and lower worlds; and, lying upon the surface of the earth in a line that curves completely around, it is called the horizon, or ‘boundary circle.’

→ lat [827] Now that I have briefly and clearly described the celestial circles, I shall discuss their intervals, starting at my original point. I shall again begin with the sublime arctic circle. Here, following a geometrical procedure, I have set two points for drawing a circle: the one to mark the center, and the other the circumference. At the very pole of the universe I³⁸ have set a brilliant star, and from it to the head of Draco, which I had previously noted stretches to the circle of the horizon, I have drawn a line.³⁹ About this line, with the center fixed, I have drawn, in my mind, a circle encompassing an equal space on every side. The circumference extends through the following constellations: beginning at the head of Draco, to the right foot of Engonasis [Hercules], through the middle of the breast of Cepheus, through the front feet of Ursa Major,⁴⁰ and back to the head of Draco.

→ lat [828] Closest to this circle is the summer tropic. By extending another line from the celestial pole to the eighth degree of Cancer, a point which the sun reaches at the solstice, we produce the same sort of circle, but with larger girth, passing through the following signs: beginning with the eighth degree of Cancer, whose entire body it cuts through lengthwise, the circle next comes to the chest /323/ and belly of Leo; then to the shoulders of Ophiuchus [Serpentarius], the head of Cygnus, the hoofs of Equus, and the right arm of Andromeda, then to the left shin and the left shoulder of Perseus, then to the knees of Heniochus [Auriga, the Charioteer] and, close by, the heads of Gemini, and back again to the eighth degree of Cancer.⁴¹

→ lat [829] The celestial equator, measured twice, from either pole, traces its circle in both Aries and Libra, with a line passing through the following constellations: from the eighth degree of Aries, through its entire body, to the retracted hoof of Taurus, thence to Orion’s Belt, next through the elevated coil of Hydra, through Crater and Corvus to the eighth degree of Libra, between the two brilliant stars of that constellation; then to the knees of Ophiuchus, then through Aquila to the head of Pegasus, and back again to the eighth degree of Aries.⁴²

→ lat [830] The winter tropic, with its location marked in a corresponding manner in the eighth degree of Capricornus, passes through the following constellations: beginning at the eighth degree of Capricornus, through its entire body, to the feet of Aquarius, thence to the end of the tail of Cetus, then to Lepus and the front paws of Canis; then through Argo and the back of Centaurus to the sting of Scorpio; next through the last part of Sagitta, and back again to the eighth degree of Capricornus.⁴³

→ lat [831] The last of the celestial parallels, called the antarctic, encompasses as much space as the arctic circle. I could reveal which constellations are marked by its circular course, for no part of the celestial sphere is unknown to me. But since the circle stretches through regions not known or visible to men of the upper hemisphere, I shall omit mention of them, lest my unverified statement appear to smack of falsehood.⁴⁴

/324/ → lat [832] Let us indicate the colures more clearly. They too conceal part of their circles and do not reveal themselves entirely to our view; yet our assumptions about them are reliable, and it is possible to trace their courses. The first of these⁴⁵ takes its beginning at the equinoctial point (that is, the eighth degree of Aries); it touches the far angle of Dcltoton [Triangulum]; next it touches the top of the head of Perseus and his right arm; next, cutting his hand, it crosses the arctic circle and reaches the celestial north pole; from here it goes through the tail of Draco to the left side of Bootes, and then to the star of Bootes;⁴⁶ next to the right, and then the left, foot of Virgo; to the eighth degree of Libra; and from here it goes to the right hand of Centaurus, in which he holds Panthera; not far distant from the place where it touched the left hoof of Centaurus, it disappears from sight, in a region below the horizon; emerging again below Cetus, it passes through his body and shoulder to the head, and returns to the eighth degree of Aries.⁴⁷

→ lat [833] A second colure, which is called the tropical colure, originates at the eighth degree of Cancer, passes to the left front paw of Ursa Major, through his chest and neck; then it reaches the celestial north pole; from here it goes through the hind quarters of Ursa Minor, on through Draco and the left wing and neck of Cygnus, touches the tip of Sagitta and the beak of Aquila, from which point it descends to the eighth degree of Capricornus; not far from here it plunges from view and rises again below Argo; it cuts through its rudder and upright stern and returns to the eighth degree of Cancer.⁴⁸

→ lat [834] It is evident that two circles remain to be discussed, those which, as I mentioned above, are called the oblique circles. One of these, the zodiac, is not like the others, which I have drawn as lines; it obviously is the broadest of all the circles. When I was dividing this belt into 12 segments, I was aware of the reason for my assigning 30 degrees to each part. Moreover, I stretched the breadth of this belt across twelve portions, so that it covered in /325/ latitude as much space as twelve of the degrees of the belt’s longitude.⁴⁹ It will be easy to point out the reason for this when I come to speak about the sun. The sun (sol) is the only (solus)⁵⁰ body to be borne in its course along the middle line of this belt. → lat [835] It is also quite clear that this belt stretches across twelve very conspicuous constellations. For the existence of the Milky Way is confirmed as much by eyesight as by reasoning powers. Its breadth frequently diminishes below the regular extent⁵¹ but is compensated by its great expanse in the stretch between constellations of Cassiopeia and the sting of Scorpio.

→ lat [836] One circle remains to be mentioned – the horizon, which, by reason of the fact that it always varies with the rising and descending of the celestial sphere, cannot be traced through a definite sequence of stars.⁵² → lat [837] Now it is appropriate to explain what interval of distance or space has been admitted between the celestial circles by nature’s intervention. Between the arctic circle, which I have cut into eight spaces,⁵³ and the summer tropic, there is as much difference in space as between 8 and 6. Similar interjacent areas are contained in similar spaces; thus it follows that one belt is larger than the other by one and a third times. Another intervening distance, between the summer tropic and the equator, is smaller than the belt above it as is the ratio of four to six. From the equator to the winter tropic there is a corresponding distance; from the winter tropic to the antarctic circle there is the same amount of space as between the arctic circle and the summer tropic; and the antarctic circle has the same distance to its pole as the arctic circle has to its pole.⁵⁴

→ lat [838] Now that we have briefly discussed the circles and the spaces lying between them, let us deal cursorily with the bodies which are called fixed stars. It is an accepted fact that there are 35 /326/ resplendent constellations spread across the entire heavens, unless one wishes to include their burdens, which are known by the names of animals: these are Capra [the Goat], which rests upon Heniochus; and Haedi [the Kids], which he holds on his shoulders; or Serpens, which Ophiuchus grasps; or Panthcra, which Centaurus carries. These constellations ought rather to be considered as parts of their more prominent constellations.

The thirty-five constellations⁵⁵ then are divided by a circle that cuts across them; some are northern constellations, others southern.⁵⁶ The northern constellations are found in the region of the zodiac toward the Septentrioncs; the southern constellations are further in. The northern sector is occupied by the two Septentriones; by Draco, which winds about and glides between them; by Arcturus, also known as Bootes; by Corona Ariadnes and Nixus [Hercules], which some call Engonasis [the Kneeler]; by Lyra, Cygnus, Cepheus, Cassiopeia, Perseus, Deltoton, Heniochus, Andromeda, Pegasus, Ophiuchus, Delphinus, Aquila, and Sagitta.

The southern constellations are as follows: Hydrus, Crater, Corvus, Procyon, Orion, Canicula, Lepus, Eridanus (which flows from the foot of Orion), Cetus, Centaurus, Argo, Piscis Australis, Caelulum, and Ara.

We consider Aqua, which flows from the cup of Aquarius, as more appropriately a part of that sign; and the star which some call Canopus and others Ptolemaeus (which is not visible to inhabitants of the northern hemisphere and begins to appear in the vicinity of Alexandria), I shall consider as part of the river Eridanus.⁵⁷

→ lat [839] These constellations are kept separate by the zodiac, which maintains twelve equal divisions of signs but has only eleven constellations. For Scorpio occupies its own space with its body and the space of Libra with its claws; the feet of Virgo also occupy the upper /327/ part of Libra’s space,⁵⁸ but the greater part is occupied by Scorpio. What we call Libra, the Greeks refer to as Chelae [the Claws]. I pass over the names of the twelve signs, since these are common knowledge.

→ lat [840] I realize that the topic coming next in order is the discussion of the circles or zones to which the constellations are assigned. But this calls for considerable elaboration, contrary to my plan of brevity; moreover, because the limbs of several signs are cleft in pieces – into halves or thirds – by various fixed circles, I leave this subject in darkness. Merely to cite a few examples, so that we may pass on to other matters: the left hand of Bootes is located within the arctic circle, the rest of his bodv is assigned to another zone; the body of Cepheus is divided in the middle, at the chest, and assigned to different celestial belts. Nixus, trampling with his left foot upon the head of the arctic Draco, rises with his own head to the summer tropic, giving one arm to Lyra and the other to Corona; and there are other unpleasant and melancholy details such as these.

→ lat [841] A more fitting subject for discussion is the question of which constellations are rising or setting when other constellations are rising. When Cancer is rising, Corona Ariadnes and a half part of Piscis Australis are setting; also Ophiuchus, feet first, as far as the upper arms, and Serpens, which he is holding (that is, except for the jaws and the entire head); also half of Bootes. But all of Orion is rising, as well as the beginning of Eridanus, and the bright star⁵⁹ in the tongue of Canicula. When Leo is rising, the remainder of Corona becomes hidden, and Piscis Australis, and portions of Ophiuchus, Serpens, and Bootes; likewise Aquila and the right part of Nixus; but the head of Hydra, Lepus, and Procyon, and the first part of Canicula are rising. While Virgo is rising, Lyra, Delphinus, and Sagitta are setting, as well as the greater portion of Cygnus, the last part of Eridanus, and the head and neck of Pegasus; at the same time the first part of Hydrus as far as Crater, and all of Canicula, and the [842] → lat stern of the ship Argo are rising. When Libra is rising, the remaining portions of Pegasus and Cygnus, the head of Andromeda, the shoulders of Cepheus, Cetus, and the meanders in the river Eridanus are setting; at the same time, half of Corona, the /328/ right foot of Nixus, Bootes, all of Hydrus except the end of the tail, and the equine part of Centaurus are rising. When Scorpio is rising, the remainder of Andromeda, and the part of Cepheus which lies outside the arctic circle, and portions of Cassiopeia and Orion are setting; and, at the same time, all of Corona Ariadnes, the head of Ophiuchus, the entire body of Nixus except the left hand, the end of the tail of Hydrus, and all of Centaurus except the front feet are rising. When Sagittarius is rising, Orion, Canicula, and the feet of Hcniochus are disappearing. But all of Ophiuchus, and the left hand of Nixus, and Lyra, and the head and shoulders of Cepheus, and the front feet of Centaurus are rising.

→ lat [843] When Capricornus is rising, all of Heniochus with Capra and Haedi is setting, together with the left part of Perseus, and the stern of Argo, and Procyon; at the same time, Cygnus, Aquila, Sagitta, and Altarium are rising. When Aquarius is rising, the equine portion of Centaurus and the head of Hydrus are setting; and the horse Pegasus is rising. When Pisces is rising, all of Hydrus, and the rest of the equine portion of Centaurus, and Crater are setting; moreover, the right part of Andromeda and Piscis Australis are rising. When the sign of Aries is rising, the feet of Centaurus and Altarium are setting; but the left part of Andromeda and the upper part of Perseus, as far as the belly, and Dcltoton are rising. And when the sign of Taurus is rising, the feet of Bootes, and the lower part of Ophiuchus, as far as the knees, are setting; but the remaining part of Cetus and the left foot of Orion are rising. When Gemini is rising, Ophiuchus, as far as his knees, is setting; and Eridanus, Cetus, and Orion are rising.⁶⁰

→ lat [844] The differences in times required for risings and settings must be explained. Those constellations that rise transversely and set vertically have swifter risings than settings; conversely, those that rise vertically and set transversely have slower risings than settings.⁶¹ Cancer rises vertically and sets at an inclination, even though it has only a slight curvature in Capricornus. Cancer rises in 2¹/₂ hours and sets in 1¹¹/₁₂ hours. The difference here is minimal. /329/ Leo rises in 2¹/₂ hours and sets in 1²/₃ hours. Virgo rises in 2²/₃ hours and sets in 1¹/₃ hours. The same holds for Libra. But Scorpio’s rising time is less [than Virgo’s], and the duration of its setting is greater: it rises in 2¹/₃ hours and sets in 1²/₃ hours. Sagittarius rises in 2¹/₁₂ hours and sets in 1¹¹/₁₂ hours.

→ lat [845] Conversely, those constellations that rise transversely and set vertically have shorter risings than settings. Among these, the sign of Capricornus, which rises in 1¹¹/₁₂ hours, sets in 2¹/₁₂ hours. The next sign, of Aquarius, rises in 1²/₃ hours and sets in 2¹/₃ hours. Pisces rises in 1¹/₃ hours and sets in 2²/₃ hours. Aries consumes the same amount of time for risings and settings as Pisces. Taurus rises in 1²/₃ hours and sets in 2¹/₃ hours. And Gemini rises in 1¹¹/₁₂ hours and sets in 2¹/₁₂ hours.

→ lat [846] This underlies the inequalities in the duration of days and nights. When the sun begins to enter those signs which rise slowly, and as the signs following after are rising, a lengthening of days occurs; when it enters those signs which rise quickly and set slowly, it causes nights to become longer and days shorter. Again a puzzling question is raised,⁶² and the accompanying answer will serve to explain. If all the signs comprise equal amounts of space, and if, at all times, night and day, six signs must be above the earth’s horizon, then all days and nights ought to be of equal duration. There is no doubt that six signs are above the earth and that six are hidden, and also that days and nights do differ in their duration. For a day at the summer solstice has 14¹/₆ hours, and a day at the winter solstice has 9⁵/₆ hours;⁶³ conversely, winter nights are prolonged, to the length of days at the summer solstice, and summer nights correspond in length to winter days. With such discrepancy in the length of the periods, the natural assumption is that the signs are not to → lat [847] be considered equal. But such a conclusion is refuted by /330/ obvious facts and by our measurements, for the setting out of multiple clepsydras⁶⁴ proves that all the signs do occupy equal amounts of space. Although the signs do consume varying amounts of time in their risings and settings, nevertheless, if you balance the risings and settings of all of them, pairing them up, you will see that they correspond to the full measure.

→ lat [848] Now that this difficulty has been resolved, there is another, more elusive problem with regard to the inequality of spaces. Our dissenters will say: ‘If the spaces occupied by the signs are equal, either the sun traverses some signs at a retarded speed or your accounting of the discrepancies of daylight is proved to be faulty. It is a recognized fact that thirty-two days elapse during the sun’s course in Gemini, and twenty-eight days in Sagittarius, with the number of days varying between those amounts in the other signs. This would surely not be the case if the sun were borne at a uniform speed and the signs occupied equal amounts of space. But if the sun’s velocity is always uniform, it must follow that the signs do not occupy equal spaces.’

→ lat [849] But a long-standing misconception is responsible for this confusion, a notion which all men have believed until now,⁶⁵ that, inasmuch as the earth is the center of the universe and the outermost sphere, it is also the center of the sun’s orbit; but this is manifestly not true. For just as the spaces encompassed by the celestial circle and the middle orbit are different, so the points about which they revolve are different. Consequently, the earth is not the center of the sun’s orbit, but is eccentric to it.⁶⁶ In alternate periods the sun depresses its course to a closer position to the earth and again elevates it, depending upon its juxtaposition with the signs of the zodiac; and although the equipoised sun moves along the middle line of the zodiac belt, the obliquity of its course causes it to be depressed or elevated. Would anyone doubt that Cancer and /331/ Gemini are elevated in the so-called steeper⁶⁷ regions of the universe and that Sagittarius and Capricornus are depressed where they curve away? Whereas the zodiac and the signs that are fixed in the sky are equidistant from the earth in all directions, the solar orbit, which has a lower course, is either elevated or depressed. Hence it comes about that the signs seem to be traversed by the sun in varying numbers of days.

→ lat [850] So much for the discussion of the celestial signs and circles. Now I shall take up the orbits of the planets. Not because of their errant motions – for their courses are defined in the same way as the sun’s, and they do not admit of anv error⁶⁸ – rather, because their peculiar behavior confounds mortals’ minds, I shall call them not ‘errant bodies’ (planetae) but ‘confusing bodies’ (planontes), as Aratus declares.⁶⁹ They have their proper names, and they are also called by other names.

→ lat [851] Saturn is called ‘the Shiner’ (Phaenon), and Jupiter ‘the Blazer’ (Phaëthon), and Mars ‘the Fiery’ (Pyrois), Menus ‘the Light-bringer’ (Phosphoros), and Mercury ‘the Twinkier’ (Stilbon).⁷⁰ But the races of mankind have given countless names to the sun and the moon. A distinction must be noted between these seven bodies and the fixed stars; the latter move only with the rotation of the celestial sphere, being set in their own fixed positions, whereas the planets are borne along in their own proper motions, in addition to their being swept along with the celestial rotation.

→ lat [852] For in varying amounts of time the planets strive to make up the distance that they are carried backward by a single diurnal rotation: the moon in a month, the sun in a year, Saturn in thirty years, and the others in periods of time proportional to the amount of space that they traverse.

→ lat [853] Although all these bodies are seen to move toward the eastern horizon, they do not move counter to the universe in a straight /332/ and direct line; rather they plod along with sideways motions across the fixed stars of the zodiac. It is well that they do, for the universe could not endure a contrary motion of its parts.

Again the doctrines of the Peripatetics maintain that the planets do not move counter to the motion of the celestial sphere but are outdistanced by the speed of the latter and cannot keep up with it.⁷¹ Even if this were true, it could not disturb my calculations. For whether Saturn, with its excessive speed, vies with the celestial sphere and is scarcely outdistanced by it, the difference in their courses being slight, whereas the moon, which moves more slowly, is overtaken in the same sector of the sky in less than thirty days; or whether the moon is swifter than those other bodies that strive in contrary motion to the celestial sphere, because its orbit is over a shorter distance, and Saturn is slower because of the great extent of its farflung orbit – take your choice; it is not contrary to my models, since, indeed, the motion of those bodies is regulated by relationships between themselves.

→ lat [854] There is one motion that is common to all seven planets – an easterly one. Another point to be noted is that they all differ in the times and circumstances of their periods. For five of the planets undergo stations and retrogradations, but the sun and the moon are propelled in a steady course. Moreover, these two luminous bodies eclipse each other in turn; but the other five are never eclipsed.⁷² Three of these, together with the sun and the moon, have their orbits about the earth, but Venus and Mercury do not go about the earth.

→ lat [855] This general observation must be made, that the earth is eccentric to the orbits of all the planets (that is, it is not located at the center of their circles); and a second observation must be made about all seven, that although the celestial sphere rotates with the same uniform motion, the planets make daily changes in their positions and orbits; for no planet rises from the same position from which it arose on the previous day.

→ lat [856] This being the case, it follows that the sun has 183 circles⁷³ which it describes as it goes back and forth from the summer tropic /333/ to the winter tropic; it alternates its course over the same circles. While the sun is traversing this number of circles, Mars describes twice as many, Jupiter twelve times as many, and Saturn twenty-eight times as many. These circles are also referred to as parallels. All of the planets have forward motions, together with the celestial sphere, and they go about the earth with their risings and settings.

→ lat [857] Now Venus and Mercury, although they have daily risings and settings, do not travel about the earth at all; rather they encircle the sun in wider revolutions. The center of their orbits is set in the sun. As a result they are sometimes above the sun; more often they are beneath it, in a closer approximation to the earth. Mercury’s and Venus’ greatest elongation from the sun is one and one half signs. When both planets have a position above the sun, Mercury is closer to the earth; when they are below the sun, Venus is closer, inasmuch as it has a broader and more sweeping orbit.⁷⁴

→ lat [858] As to the moon, which is closest to the earth, I shall speak later about its coursings. Immediately above the moon’s orbit some authorities place the orbits of Mercury and Venus; others argue that the sun’s orbit comes next.⁷⁵ Then come the orbits of Mars, Jupiter, and Saturn. To ascertain the dimensions of all these orbits – an undertaking which astronomers consider a difficult one – a basic assumption must be drawn from geometry, one which the bridesmaid Geometry herself offers in the present work and which has been approved by Eratosthenes and Archimedes; namely, that there are 406,010 stadia⁷⁶ in the earth’s circumference. By irrefutable reckonings it is found that the moon’s orbit is one hundred times greater than the earth’s /334/ circumference. This orbit is also found to be six hundred times as great as the moon itself. → lat [859] During repeated eclipses of the sun, by comparing the extent of the shadow which the moon, lying directly beneath, casts upon the earth, with the size of the moon itself, we obtain these two accurate dimensions. If this subject is not tedious, I shall explain how I obtained these measurements.

It often happens that an eclipse of the sun occurring at the latitude of Meroe darkens the entire orb, but at a nearby climate – that is, one passing through Rhodes – the obscuration is partial, and at the latitude of the mouth of the Borysthenes [Dnieper] there is no obstruction and the full orb shines forth.⁷⁷ Since the correct distance in stadia at which the latitude of Rhodes is located is known, I have found that the breadth of the shadow which the moon casts is one eighteenth part of the earth. Now since the body which casts the conical shadow is larger than the shadow itself, it has been ascertained from the latitudes on either side at which the sun was partially obscured, that the moon itself is three times as large as its shadow.⁷⁸

Thus it has been determined by the foregoing calculations that the moon is one sixth as large as the earth. → lat [860] That the moon’s diameter is one six-hundredth of its orbit is determined by the use of clepsydras. [Place two copper vessels in position, an empty one below, one full of water above. Mark the rising of the moon and that of a fixed star rising simultaneously with it. At the moment when the upper edge of the moon begins to appear above the horizon, quickly release the stopper from the upper vessel, the one containing the water, and let the water flow until the moon’s entire orb appears. At this point remove the first vessel into which the water has flowed and put another in its place, into which the water may flow until, on the following night, the very same star rises which rose together with the moon on the previous night. Remove the upper vessel, from which the water flowed out in the space of twenty-four hours. Compare it with the amount which flowed out into the first vessel while the orb of the moon was rising, and you will find that the entire amount increased six hundredfold. Hence it is clear that the orbit of /335/ the moon surpasses the diameter of the moon by six hundred times.]⁷⁹ We conclude, then, that the lunar orbit is one hundred times as great as the earth.

→ lat [861] After this demonstration, let us turn our attention to the other orbits. Will anyone doubt that the sun’s orbit is 12 times as great as the moon’s, if the latter completes its orbit in a month and the former in a year? The orbit of Mars is then found to be twenty-four times as great, Jupiter’s one hundred and forty-four times as great, and Saturn’s three hundred and thirty-six times as great. If the calculations are carried farther, we find both the number of stadia in the orbit of Saturn and how many times greater it is than the entire earth. For if the moon’s orbit is 100 times as great as the earth and Saturn’s orbit is three hundred and thirty-six times as great as the moon’s orbit, then the orbit of Saturn is thirty-three thousand six hundred times greater than the earth’s size.

→ lat [862] Now let us consider the moon’s course, which is closest to the earth. Natural philosophers are agreed that its light lasts for a month. I his may be so, but there is no doubt that the full moon is always illuminated. For if, on that side which lies directly facing the sun, it is illuminated over the entire hemisphere,⁸⁰ even when, on the thirtieth day, it reveals none of its light to us, yet on the upper side, which is facing the sun, it beams in full light. Then, as it leaves its conjunction with the sun and begins to be observed from the side, it becomes partially illuminated on the underside, until, reaching a position opposite the sun, it is illuminated on the side which is visible to us. → lat [863] The brightness of the sun encircles the lunar orb and bathes with light the entire part which faces it. These brilliant rays also reach the earth, like an image of light reflected in a mirror. When the moon receives the light in the phase of its first rising, it is obscured from us; and as it draws away from the sun in the west, it begins to grow light. → lat [864] Its appearance at first /336/ illumination, encircled by horns, as it were, is called menoeides [crescent-shaped]; at an eastward elongation of 90 degrees, when the sun’s rays have illuminated its orb half way, it is called dichotomos [halved]; when it has progressed another 45 degrees, it is called amphikurtos [gibbous], that is, larger than half, smaller than full; and when the moon is 180 degrees removed from the sun, in a position of opposition, and is illuminated over the entire portion which faces the earth, it is called panselenos [full moon]. Gradually diminishing from this point, it repeats the names that are applied to the aforementioned phases.⁸¹

In one day and night the moon courses through 13 degrees of its orbit, while the other planets, in keeping with the great extent of their orbits, during the same interval course through the following portions of their orbits: Mars, one half of a degree; Jupiter, one twelfth of a degree; and Saturn, one twenty-eighth of a degree.

→ lat [865] The moon completes its circuit of the zodiac in 27²/₃ days, but it requires 29¹/₂ days to overtake the sun. The reason for the larger period is that while the moon is completing its orbit, the sun has gone on from the position where it previously gave its light to the moon, and is found in the next sign or even the one following that. For if the moon receives its light in the last degree of Libra, Scorpio, or Sagittarius, it does not catch up with the sun in the sign immediately following but in the one after that. Thus the sun sometimes passes through these three signs unaccompanied, and, in the signs diametrically opposite, the moon will often be in conjunction with the sun twice. Inasmuch as the sun tarries in these signs for 30 days, in Gemini for 32 days, the moon, which overtakes the sun in 29¹/₂ days, will surely be able to find it in the same sign.

→ lat [866] The moon attains the full phase sometimes on the 14th, sometimes on the 15th, and more frequently on the 16th day; but a compensation occurs on the waning side.⁸² For if it attains the full phase on the fourteenth day, it loses its light on the 15th day, so that the full number of days elapses. The moon completes its year in 354 days, for 12 conjunctions of the sun and the moon occur in this period. As a result, a solar year exceeds a lunar year by 11 days, but the difference is made up by intercalations.

/337/ → lat [867] Let us discuss the degrees of latitude through which the moon courses. I pointed out above that there are 12 degrees of latitude in the belt of the zodiac, through which the planets have their various deviations. Some planets deviate through three degrees of latitude, some through four, others through eight, and some through all 12. The sun’s course does not depart from the ecliptic except in the sign of Libra, where it is deflected to the north or the south by half a degree.⁸³ But the moon, ranging through all 12 degrees, is at times borne upward toward the north and at times verges downward toward the south, deflecting its course on either side to the extent of 6 degrees, as Hipparchus also acknowledges.

→ lat [868] A name has been given to the moon’s oblique motion; it is spoken of as belicoides [spiral-shaped]. As it ascends or descends it cuts across the line of the ecliptic – which, as I indicated above, is a middle line with 6 degrees on either side – in sharp or broadened angles. The moon is not able to return to its former position in the same month with respect to the sun (that is, in the same degree and in the same position in latitude) until the two hundred and thirtyfifth month, which is in the nineteenth year.⁸⁴ Fifty-five years are required for it to return to the same place on the same day, in conjunction with the same fixed stars; and a lapse of a ‘great year’ is required for the fixed stars and the planets to return to their identical respective positions.⁸⁵

→ lat [869] When the moon cuts across the ecliptic in its northward ascension, it is said to be in ascending elevation; when it is returning to the ecliptic from the north, it is in descending elevation; when it is moving from the ecliptic in a southerly direction, it is in descending declination; and when it is returning from there to the ecliptic, it is in ascending declination. These ascents and descents cause the eclipses of the two bodies. When the moon, in its ascents or descents, touches the ecliptic, if it happens on the thirtieth day – that is, when it lies directly beneath the sun with its entire body – it causes an eclipse of the sun upon earth; for by interposing its body, it darkens regions lying beneath it, while other parts of the earth, which are not /338/ covered up, are illuminated by the sun.⁸⁶ The moon does not cause these eclipses every month, because it is not always found on the ecliptic on the thirtieth day; it is then passing above it or below it, so that it is not in an obstructing position.

→ lat [870] Similarly, an eclipse of the moon occurs ‘when it is located along the line of the ecliptic in a position of opposition; that is, on the fifteenth day.⁸⁷ It is darkened by the conical shadow of the earth. For the sun sends the shadow of the earth along its ecliptic line; when the moon’s orb reaches this line, since it will not be able to receive the light of the sun with the earth standing in the way, it will become darkened, the customary light being taken away. At other times, when it is in a position of latitude above or below the ecliptic, it will shine forth with an appearance of full light.

→ lat [871] Eclipses cannot recur within six months,⁸⁸ since the moon courses through 12 degrees of latitude and cannot be found on the ecliptic on the fifteenth or the first day. If, in returning to the ecliptic from the north, it comes into close lateral proximity with the sun but does not move into an obstructing position, it is said to produce an approximation in transit; but, if, in coming from the north, it does move into conjunction and obstructs the sun, it is said to produce an eclipse in northern transit. If it comes from the south and does not move into conjunction, it produces an approximation in southern transit; and if, in returning to the ecliptic from the south, it crosses the path of the sun, it produces an ascending eclipse node. These phenomena and vagaries of the moon confound mortals with their variety.⁸⁹

→ lat [872] Now the sun, as we remarked above, moves with a twofold motion; namely, it is either swept along from the east with the celestial rotation or it moves obliquely in its own motion along its own course in a direction contrary to that of the universe. It daily changes the line of its rising from that point where it revolves with the universe; /339/ we refer to the lines along which it moves as circles; therefore there is no doubt that there are 183 of them. For, whether the sun is descending in its course from Cancer to the winter tropic or coming to the summer tropic from the winter solstice, it is revolving along the same circles each time. These circles cut across the zodiac twice, and are always drawn through signs that are opposite each other; the first circle of Aries is also the first of Libra, and the thirtieth of Aries is the thirtieth of Libra; similarly, the first of Taurus is the first of Scorpio, and so on. Thus 183 circles are produced from 366 points. The circles are referred to as parallels and, as I have indicated, they intersect the zodiac at corresponding degrees of opposite signs. The sun traverses these circles annually in 365¹/₄ days, whether it is moving in the direction of the summer tropic or returning to the winter tropic.

→ lat [873] We must not overlook the fact that although the two hemispheres are of equal dimensions – one from the equator to the north pole, the other from the equator to the south pole – and although, as I have mentioned, the signs on cither side are equal, the sun nevertheless courses through them in unequal periods. It completes its ascending course to the summer tropic in 185¹/₄ days, and its descending course to the winter tropic in 180 days.⁹⁰ The obvious cause of the discrepancy is that, as I have said, the earth is eccentric to the sun’s orbit, which is more elevated in the upper hemisphere and draws closer to the earth in the lower. There is no doubt that the sun courses over its shorter curve more swiftly and over its more extended curve more slowly.

→ lat [874] The sun, when it climbs upward to Cancer from the equator, brings summer to mortals who are known to be living between the summer tropic and the arctic circle; while it is descending from Cancer to the equinoctial sign of Libra, it brings autumn; and when it retires to the winter tropic, winter holds forth, because chill invades when the warmth of the sun is remote; again, as it rises from wintry Capricornus to the equinoctial sign of Aries, the season of spring smiles upon us; and as it moves from there once again, the scorching heat of summer is renewed in Cancer. Dwellers in the antipodes undoubtedly experience these seasons at opposite times: /340/ Capricornus brings their summer; Cancer, winter; and the sun at the equator brings temperate conditions to either zone.

→ lat [875] There still remains for discussion the matter of the increase and decrease of the duration of night, since winter nights correspond in length to summer days, and summer nights tb winter days; and twice a year the equinoctial day is equal to its night. For, while the sun is going from the vernal equinox to Cancer, all the days are longer than the nights; likewise, from the autumnal equinox to the winter solstice the days are shortened and the nights lengthened.

→ lat [876] The shortest day of the year, at the winter solstice, has 8 hours; and the longest day, at the summer solstice, has 16 hours,⁹¹ although it is true that the number of hours varies with the latitude. There are 8 latitudes or climates. The closest to the summer tropic is the one through Meroe;⁹² then comes the one through Syene; the third through Alexandria, extending on through Cyrene to that portion of Africa to the south of Carthage;⁹³ the fourth and middle climate is the one through Rhodes,⁹⁴ which is drawn through the middle of the Peloponnesus and Sicily and extends to the mouth of the Baetis River; the fifth climate goes through Rome and Macedonia and, in the other direction, through Gaul and Lusitania, touching down at the Tagus River; the sixth goes through the Hellespont and Thrace and Gaul bordering upon Germany; the seventh, through the mouth of the Borysthenes and the Black Sea and, in the opposite direction, through Germany and Britain; the last climate is above the Maeotis [Sea of Azov] and below the Rhipaean Mountains.⁹⁵

/341/ → lat [877] The length of days is determined by the climates: the longest day at Meroe has 13 equinoctial hours, the shortest day 11; the longest day at Syene has 14 hours, the shortest 10; at Alexandria the longest has 14, the shortest 10; the longest day at Rhodes has 14 hours,⁹⁶ the shortest 9; the longest day at Rome has 15 hours, the shortest 9; the longest day at the Hellespont has 15 hours, the shortest 8; the longest day at the mouth of the Borysthenes has 16 hours, the shortest 8; in the Rhipaean Mountains the longest has 16; the shortest 8. Then, as you draw nearer to the pole, the day becomes ever longer, and the night shorter; consequently, it is to be assumed that there is perpetual daylight directly under the pole.

→ lat [878] However, at each climate the days lengthen and again shorten each year; and you must understand that from winter solstice the days increase in length in such a manner that in the first month a twelfth part of the increase to midsummer is added, in the second month a sixth part, in the third month a fourth part, in the fourth month another fourth part, in the fifth month a sixth part, and in the sixth month a twelfth part. The reason for the difference is that the zodiac winds around Cancer and Capricornus but cuts across the equator almost directly.

→ lat [879] So much for the sun’s course. Now it is appropriate to consider the courses of the planets, and especially of those that orbit around the sun as it makes its celestial revolution. Stilbon (Mercury], completing an orbit in nearly a year, has a motion in latitude of 8 degrees, and is impelled in alternating directions. The circles of this planet and Venus, as I have said above, are epicycles; that is, they do not encompass the globe of the earth within their orbits, but describe an orbit to one side, in some way. The fact that they are seen to have risings and settings is caused by their being swept along by the motion of the celestial sphere.

→ lat [880] This same Stilbon, though it accompanies the sun in its varied epicycles, will never be able to depart from the sun by more than 22 degrees⁹⁷ of elongation; never will it be able to be two signs away, as at times it passes by the sun, then comes to a halt, and then retrogresses. This varied motion assumes different figures. Although its risings are inconspicuous and of short duration, it nevertheless has /342/ risings and settings. Indeed, when the elongation permits and the planet is not obliterated by the sun’s rays, it puts in a glimmering appearance, risen above the horizon, just ahead of the brilliance of the rising sun.

This planet can never have acronical risings, something that can happen only to planets that are situated diametrically opposite the sun (opposition is counted in the seventh sign). Consequently, a planet that cannot get farther than a sign and a portion of the following sign away from the sun cannot have acronical risings.

→ lat [881] Again, it does not experience settings in opposition to the sun; but it assumes its phase as an evening star when it grows bright upon being released from the brilliance of the sun, after the latter’s setting.⁹⁸ Likewise it has two last visibilities: one phase when, as is its habit, it appears ahead of the sun and is then obliterated by the brillant rays that overtake it; another when, as a result of its retrogradation, it moves into the vicinity of the sun and fades from sight in the west. It cannot be removed from the sun’s light within 20 degrees, although it may have greater elongations; it cannot be found beyond the second sign. These last visibilities and clear risings will occur in the fourth month, and not always then.

→ lat [882] Now Venus, which is sometimes called Phosphoros, was manifestly thoroughly investigated by Pythagoras of Samos and his pupils. It has been shown to complete its orbit in a period of about a year. For in 300 and some days it ranges, like the moon, through all 12 degrees of latitude in the zodiac, getting 50 degrees distant from the orb of the sun, although it cannot have an elongation of more than 46 degrees.⁹⁹ Located on its own epicycle, it goes about the sun, varying its course; sometimes it passes ahead of the sun, sometimes it follows after it, and does not catch it; again at times it is borne above the sun and at times beneath it; and it does not always complete an orbit within a year. → lat [883] For at a time when it is in retrograde motion, it takes longer than a year to traverse its orbit; but when it is going in direct motion, it completes its course even in /343/ eleven months. When it makes its risings in the early morning, ahead of the sun, it is called Lucifer; when it blazes forth after the setting of the sun, it is called Vesper or Vesperugo. Venus is the only one of the five planets, like the moon, to cast a shadow, and it is the only planet to be clearly discernible and not yielding for a long period of time to the splendor of the rising sun. Venus frequently lingers for four months in early morning rising, but in the west, as an evening star, never for more than 20 days. Its risings and settings are renewed in 10 or 9 months.¹⁰⁰

→ lat [884] Pyrois, or Mars, has its own course, beyond the sun, and revolves about the earth, which is eccentric to its orbit, in almost two years. Mars has five degrees of deviation in latitude. Although it appears to have risings, settings, stations, and retrogradations in common with the two planets lying above it, it has its own apogee, first station, and exaltation apart from the others. Its apogee (that is, the point where its orbit reaches its highest elevation above the earth) is in the sign of Leo;¹⁰¹ its first station is a unique one. Inasmuch as Mars is in close proximity with the sun, it feels the effect of the rays even from a position of quadrature and undergoes a station ninety degrees away from the sun on either side.¹⁰² Mars has its exaltation or apsis in the twenty-ninth degree of Capricornus.¹⁰³

→ lat [885] The propitious planet Jupiter, being higher than the others, completes its orbit in 12 years and has a deviation in latitude of five degrees. Its apogee occurs in Virgo, and its exaltation in the fifteenth degree of Cancer.¹⁰⁴ Its ascents and descents prove that its orbit is eccentric with respect to the earth.

→ lat [886] Phacnon – that is, Saturn – being situated above all the other planets, completes a revolution in slightly less than 30 years and has a deviation in latitude of 3 degrees or even only 2 degrees. Its apogee is in the sign of Scorpio, and its exaltation in the twentieth degree of Libra.¹⁰⁵ The risings of Saturn are like those of the two planets beneath it, in that the rays of the rising sun do not obscure it beyond 12 degrees. The terms ‘morning rising’ or ‘setting’ are applied to /344/ these planets when they are able to appear in the sky at that distance from the submerged sun.

→ lat [887] There is another rising, called acronical, which occurs when the clear orb of a planet rises in the cast as the sun is plunging beneath the western horizon. Last visibilities of the superior planets occur when their shimmering light disappears as the rays of the sun overtake it. These planets make their morning stations 120 degrees away from the sun, and then, at opposition, 180 degrees away, they make their evening risings;¹⁰⁶ likewise, on the other side, they make their evening stations 120 degrees away. The latter are also called ‘second’ stations, and the former ‘first’ stations. At a distance of less than 12 degrees the rays of the sun overtake and obliterate these planets. The powerful effect of the sun’s rays is responsible for the anomalies in the orbits of all the aforementioned planets and for their stations, retrogradations, and progressions. The rays strike the planets, causing them to rise aloft or to be depressed, or to deviate in latitude or to retrograde.¹⁰⁷