On Architecture

11. The three that complete their circuits above the sun's course do not make progress while they are in the triangle which he has entered, but retrograde and pause until the sun has crossed from that triangle into another sign. Some hold that this takes place because, as they say, when the sun is a great distance off, the paths on which these stars wander are without light on account of that distance, and so the darkness retards and hinders them. But I do not think that this is so. The splendour of the sun is clearly to be seen, and manifest without any kind of obscurity, throughout the whole firmament, so that those very retrograde movements and pauses of the stars are visible even to us.

12. If then, at this great distance, our human vision can discern that sight, why, pray, are we to think that the divine splendour of the stars can be cast into darkness? Rather will the following way of accounting for it prove to be correct. Heat summons and attracts everything towards itself; for instance, we see the fruits of the earth growing up high under the influence of heat, and that spring water is vapourised and drawn up to the clouds at sunrise. On the same principle, the mighty influence of the sun, with his rays diverging in the form of a triangle, attracts the stars which follow him, and, as it were, curbs and restrains those that precede, not allowing them to make progress, but obliging them

13. Perhaps the question will be raised, why the sun by his great heat causes these detentions in the fifth sign from himself rather than in the second or third, which are nearer. I will therefore set forth what seems to be the reason. His rays diverge through the firmament in straight lines as though forming an equilateral triangle, that is, to the fifth sign from the sun, no more, no less. If his rays were diffused in circuits spreading all over the firmament, instead of in straight lines diverging so as to form a triangle, they would burn up all the nearer objects. This is a fact which the Greek poet Euripides seems to have remarked; for he says that places at a greater distance from the sun are in a violent heat, and that those which are nearer he keeps temperate. Thus in the play of Phaethon, the poet writes: kai/ei ta\ po/rrw ta)/gguqen d' eu)/krat' e)/xei.

14. If then, fact and reason and the evidence of an ancient poet point to this explanation, I do not see why we should decide otherwise than as I have written above on this subject.

Jupiter, whose orbit is between those of Mars and Saturn, traverses a longer course than Mars, and a shorter than Saturn. Likewise with the rest of these stars: the farther they are from the outermost limits of the heaven, and the nearer their orbits to the earth, the sooner they are seen to finish their courses; for those of them that have a smaller orbit often pass those that are higher, going under them.

15. For example, place seven ants on a wheel such as potters use, having made seven channels on the wheel about the centre, increasing successively in circumference; and suppose those ants obliged to make a circuit in these channels while the wheel is turned in the opposite direction. In spite of having to move in a direction contrary to that of the wheel, the ants must necessarily complete their journeys in the opposite direction, and that ant which is nearest the centre must finish its circuit sooner, while the ant that is going round at the outer edge of the disc of

16. The reason why some of these stars are temperate, others hot, and others cold, appears to be this: that the flame of every kind of fire rises to higher places. Consequently, the burning rays of the sun make the ether above him white hot, in the regions of the course of Mars, and so the heat of the sun makes him hot. Saturn, on the contrary, being nearest to the outermost limit of the firmament and bordering on the quarters of the heaven which are frozen, is excessively cold. Hence,Jupiter,whose course is between the orbits of these two, appears to have a moderate and very temperate influence, intermediate between their cold and heat.

I have now described, as I have received them from my teacher, the belt of the twelve signs and the seven stars that work and move in the opposite direction, with the laws and numerical relations under which they pass from sign to sign, and how they complete their orbits. I shall next speak of the waxing and waning of the moon, according to the accounts of my predecessors.

1. ACCORDING to the teaching of Berosus, who came from the state, or rather nation, of the Chaldees, and was the pioneer of Chaldean learning in Asia, the moon is a ball, one half luminous and the rest of a blue colour. When, in the course of her orbit, she has passed below the disc of the sun, she is attracted by his rays and great heat, and turns thither her luminous side, on account of the sympathy between light and light. Being thus summoned

2. As she moves on, passing by to the east, the effect of the sun upon her relaxes, and the outer edge of the luminous side sheds its light upon the earth in an exceedingly thin line. This is called the second day of the moon. Day by day she is further relieved and turns, and thus are numbered the third, fourth, and following days. On the seventh day, the sun being in the west and the moon in the middle of the firmament between the east and west, she is half the extent of the firmament distant from the sun, and therefore half of the luminous side is turned toward the earth. But when the sun and moon are separated by the entire extent of the firmament, and the moon is in the east with the sun over against her in the west, she is completely relieved by her still greater distance from his rays, and so, on the fourteenth day, she is at the full, and her entire disc emits its light. On the succeeding days, up to the end of the month, she wanes daily as she turns in her course, being recalled by the sun until she comes under his disc and rays, thus completing the count of the days of the month.

3. But Aristarchus of Samos, a mathematician of great powers, has left a different explanation in his teaching on this subject, as I shall now set forth. It is no secret that the moon has no light of her own, but is, as it were, a mirror, receiving brightness from the influence of the sun. Of all the seven stars, the moon traverses the shortest orbit, and her course is nearest to the earth. Hence in every month, on the day before she gets past the sun, she is under his disc and rays, and is consequently hidden and invisible. When she is thus in conjunction with the sun, she is called the new moon. On the next day, reckoned as her second, she gets past the sun and shows the thin edge of her sphere. Three days away from the sun, she waxes and grows brighter. Removing further every day till she reaches the seventh, when her distance from the sun at his setting is about one half the extent of the

4. On the fourteenth day, being diametrically across the whole extent of the firmament from the sun, she is at her full and rises when the sun is setting. For, as she takes her place over against him and distant the whole extent of the firmament, she thus receives the light from the sun throughout her entire orb. On the seventeenth day, at sunrise, she is inclining to the west. On the twenty-second day, after sunrise, the moon is about mid-heaven; hence, the side exposed to the sun is bright and the rest dark. Continuing thus her daily course, she passes under the rays of the sun on about the twenty-eighth day, and so completes the account of the month.

I will next explain how the sun, passing through a different sign each month, causes the days and hours to increase and diminish in length.

1. THE sun, after entering the sign Aries and passing through one eighth of it, determines the vernal equinox. On reaching the tail of Taurus and the constellation of the Pleiades, from which the front half of Taurus projects, he advances into a space greater than half the firmament, moving toward the north. From Taurus he enters Gemini at the time of the rising of the Pleiades, and, getting higher above the earth, he increases the length of the days. Next, coming from Gemini into Cancer, which occupies the shortest space in heaven, and after traversing one eighth of it, he determines the summer solstice. Continuing on, he reaches the head and breast of Leo, portions which are reckoned as belonging to Cancer.

2.After leaving the breast of Leo and the boundaries of, Cancer, the sun, traversing the rest of Leo, makes the days shorter, diminishing the size of his circuit, and returning to the same

3. When the sun has entered Scorpio, at the time of the setting of the Pleiades, he begins to make the days shorter as he advances toward the south. From Scorpio he enters Sagittarius and, on reaching the thighs, his daily course is still further diminished. From the thighs of Sagittarius, which are reckoned as part of Capricornus, he reaches the end of the first eighth of the latter, where his course in heaven is shortest. Consequently, this season, from the shortness of the day, is called bruma or dies brumales. Crossing from Capricornus into Aquarius, he causes the days to increase to the length which they had when he was in Sagittarius. From Aquarius he enters Pisces at the time when Favonius begins to blow, and here his course is the same as in Scorpio. In this way the sun passes round through the signs, lengthening or shortening the days and hours at definite seasons.

I shall next speak of the other constellations formed by arrangements of stars, and lying to the right and left of the belt of the signs, in the southern and northern portions of the firmament.

1. THE Great Bear, called in Greek a)/rktos or e(likh, has her Warden behind her. Near him is the Virgin, on whose right shoulder rests a very bright star which we call Harbinger of the Vintage, and the Greeks protrughth/s. But Spica in that constellation is brighter. Opposite there is another star, coloured, between