The Ten Books on Architecture
the space of a sign in thirty days. Though she thus stays less than
forty days in particular signs, she makes good the required amount by
delaying in one sign when she comes to a pause. Therefore she completes
her total revolution in heaven in four hundred and eighty-five days, and
once more enters the sign from which she previously began to move.
10. Mars, after traversing the spaces of the constellations for about
six hundred and eighty-three days, arrives at the point from which he
had before set out at the beginning of his course, and while he passes
through some of the signs more rapidly than others, he makes up the
required number of days whenever he comes to a pause. Jupiter, climbing
with gentler pace against the revolution of the firmament, travels
through each sign in about three hundred and sixty days, and finishes in
eleven years and three hundred and thirteen days, returning to the sign
in which he had been twelve years before. Saturn, traversing the space
of one sign in twenty-nine months plus a few days, is restored after
twenty-nine years and about one hundred and sixty days to that in which
he had been thirty years before. He is, as it appears, slower, because
the nearer he is to the outermost part of the firmament, the greater is
the orbit through which he has to pass.
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 to retrograde towards himself until he passes out into
the sign that belongs to a different triangle.
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: [Greek: kaiei
ta porrô, tangythen d eukrat echei].
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 the wheel must, on account of the size of its circuit,
be much slower in completing its course, even though it is moving just
as quickly as the other. In the same way, these stars, which struggle on
against the course of the firmament, are accomplishing an orbit on paths
of their own; but, owing to the revolution of the heaven, they are swept
back as it goes round every day.
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.
CHAPTER II
THE PHASES OF THE MOON
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 by the sun's disc and facing upward, her
lower half, as it is not luminous, is invisible on account of its
likeness to the air. When she is perpendicular to the sun's rays, all
her light is confined to her upper surface, and she is then called the
new moon.
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 firmament,
one half of her is luminous: that is, the half which faces toward the
sun is lighted up by him.
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.
CHAPTER III
THE COURSE OF THE SUN THROUGH THE TWELVE SIGNS
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 course that he had in
Gemini. Next, crossing from Leo into Virgo, and advancing as far as the
bosom of her garment, he still further shortens his circuit, making his
course equal to what it was in Taurus. Advancing from Virgo by way of
the bosom of her garment, which forms the first part of Libra, he
determines the autumn equinox at the end of one eighth of Libra. Here
his course is equal to what his circuit was in the sign Aries.
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