Ten Books on Architecture
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4. They are all visible or invisible according to fixed times. While six
of the signs are passing along with the heaven above the earth, the
other six are moving under the earth and hidden by its shadow. But there
are always six of them making their way above the earth; for,
corresponding to that part of the last sign which in the course of its
revolution has to sink, pass under the earth, and become concealed, an
equivalent part of the sign opposite to it is obliged by the law of
their common revolution to pass up and, having completed its circuit, to
emerge out of the darkness into the light of the open space on the other
side. This is because the rising and setting of both are subject to one
and the same power and law.
5. While these signs, twelve in number and occupying each one twelfth
part of the firmament, steadily revolve from east to west, the moon,
Mercury, Venus, the sun, as well as Mars, Jupiter, and Saturn, differing
from one another in the magnitude of their orbits as though their
courses were at different points in a flight of steps, pass through
those signs in just the opposite direction, from west to east in the
firmament. The moon makes her circuit of the heaven in twenty-eight days
plus about an hour, and with her return to the sign from which she set
forth, completes a lunar month.
6. The sun takes a full month to move across the space of one sign, that
is, one twelfth of the firmament. Consequently, in twelve months he
traverses the spaces of the twelve signs, and, on returning to the sign
from which he began, completes the period of a full year. Hence, the
circuit made by the moon thirteen times in twelve months, is measured
by the sun only once in the same number of months. But Mercury and
Venus, their paths wreathing around the sun's rays as their centre,
retrograde and delay their movements, and so, from the nature of that
circuit, sometimes wait at stopping-places within the spaces of the
signs.
7. This fact may best be recognized from Venus. When she is following
the sun, she makes her appearance in the sky after his setting, and is
then called the Evening Star, shining most brilliantly. At other times
she precedes him, rising before day-break, and is named the Morning
Star. Thus Mercury and Venus sometimes delay in one sign for a good many
days, and at others advance pretty rapidly into another sign. They do
not spend the same number of days in every sign, but the longer they
have previously delayed, the more rapidly they accomplish their journeys
after passing into the next sign, and thus they complete their appointed
course. Consequently, in spite of their delay in some of the signs, they
nevertheless soon reach the proper place in their orbits after freeing
themselves from their enforced delay.
8. Mercury, on his journey through the heavens, passes through the
spaces of the signs in three hundred and sixty days, and so arrives at
the sign from which he set out on his course at the beginning of his
revolution. His average rate of movement is such that he has about
thirty days in each sign.
9. Venus, on becoming free from the hindrance of the sun's rays, crosses
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 porro, 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
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.
CHAPTER IV
THE NORTHERN CONSTELLATIONS
1. The Great Bear, called in Greek [Greek: arktos] or [Greek: helike],
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 [Greek: protrygetes]. But Spica in that
constellation is brighter. Opposite there is another star, coloured,
between the knees of the Bear Warden, dedicated there under the name of
Arcturus.
2. Opposite the head of the Bear, at an angle with the feet of the
Twins, is the Charioteer, standing on the tip of the horn of the Bull;
hence, one and the same star is found in the tip of the left horn of the
Bull and in the right foot of the Charioteer. Supported on the hand of
the Charioteer are the Kids, with the She-Goat at his left shoulder.
Above the Bull and the Ram is Perseus, having at his right...[11] with
the Pleiades moving beneath, and at his left the head of the Ram. His
right hand rests on the likeness of Cassiopea, and with his left he
holds the Gorgon's head by its top over the Ram, laying it at the feet
of Andromeda.
[Note 11: From this point to the end of section 3 the text is often
hopelessly corrupt. The translation follows, approximately, the
manuscript reading, but cannot pretend to be exact.]
3. Above Andromeda are the Fishes, one above her belly and the other
above the backbone of the Horse. A very bright star terminates both the
belly of the Horse and the head of Andromeda. Andromeda's right hand
rests above the likeness of Cassiopea, and her left above the Northern
Fish. The Waterman's head is above that of the Horse. The Horse's hoofs
lie close to the Waterman's knees. Cassiopea is set apart in the midst.
High above the He-Goat are the Eagle and the Dolphin, and near them is
the Arrow. Farther on is the Bird, whose right wing grazes the head and
sceptre of Cepheus, with its left resting over Cassiopea. Under the tail
of the Bird lie the feet of the Horse.
4. Above the Archer, Scorpion, and Balance, is the Serpent, reaching to
the Crown with the end of its snout. Next, the Serpent-holder grasps the
Serpent about the middle in his hands, and with his left foot treads
squarely on the foreparts of the Scorpion. A little way from the head of
the Serpent-holder is the head of the so-called Kneeler. Their heads are
the more readily to be distinguished as the stars which compose them are
by no means dim.
5. The foot of the Kneeler rests on the temple of that Serpent which is
entwined between the She-Bears (called Septentriones). The little
Dolphin moves in front of the Horse. Opposite the bill of the Bird is
the Lyre. The Crown is arranged between the shoulders of the Warden and
the Kneeler. In the northern circle are the two She-Bears with their
shoulder-blades confronting and their breasts turned away from one
another. The Greeks call the Lesser Bear [Greek: kynosoura], and the
Greater [Greek: elike]. Their heads face different ways, and their tails
are shaped so that each is in front of the head of the other Bear; for
the tails of both stick up over them.
6. The Serpent is said to lie stretched out between their tails, and in
it there is a star, called Polus, shining near the head of the Greater
Bear. At the nearest point, the Serpent winds its head round, but is
also flung in a fold round the head of the Lesser Bear, and stretches
out close to her feet. Here it twists back, making another fold, and,
lifting itself up, bends its snout and right temple from the head of the
Lesser Bear round towards the Greater. Above the tail of the Lesser Bear
are the feet of Cepheus, and at this point, at the very top, are stars
forming an equilateral triangle. There are a good many stars common to
the Lesser Bear and to Cepheus.
I have now mentioned the constellations which are arranged in the heaven
to the right of the east, between the belt of the signs and the north. I
shall next describe those that Nature has distributed to the left of the
east and in the southern regions.
CHAPTER V
THE SOUTHERN CONSTELLATIONS
1. First, under the He-Goat lies the Southern Fish, facing towards the
tail of the Whale. The Censer is under the Scorpion's sting. The fore
parts of the Centaur are next to the Balance and the Scorpion, and he
holds in his hands the figure which astronomers call the Beast. Beneath
the Virgin, Lion, and Crab is the twisted girdle formed by the Snake,
extending over a whole line of stars, his snout raised near the Crab,
supporting the Bowl with the middle of his body near the Lion, and
bringing his tail, on which is the Raven, under and near the hand of the
Virgin. The region above his shoulders is equally bright.
2. Beneath the Snake's belly, at the tail, lies the Centaur. Near the
Bowl and the Lion is the ship named Argo. Her bow is invisible, but her
mast and the parts about the helm are in plain sight, the stern of the
vessel joining the Dog at the tip of his tail. The Little Dog follows
the Twins, and is opposite the Snake's head. The Greater Dog follows the
Lesser. Orion lies aslant, under the Bull's hoof; in his left hand
grasping his club, and raising the other toward the Twins.
3. At his feet is the Dog, following a little behind the Hare. The Whale
lies under the Ram and the Fishes, and from his mane there is a slight
sprinkling of stars, called in Greek [Greek: harpedonai], regularly
disposed towards each of the Fishes. This ligature by which they hang is
carried a great way inwards, but reaches out to the top of the mane of
the Whale. The River, formed of stars, flows from a source at the left
foot of Orion. But the Water, said to pour from the Waterman, flows
between the head of the Southern Fish and the tail of the Whale.
4. These constellations, whose outlines and shapes in the heavens were
designed by Nature and the divine intelligence, I have described
according to the view of the natural philosopher Democritus, but only
those whose risings and settings we can observe and see with our own
eyes. Just as the Bears turn round the pivot of the axis without ever
setting or sinking under the earth, there are likewise stars that keep
turning round the southern pivot, which on account of the inclination of
the firmament lies always under the earth, and, being hidden there, they
never rise and emerge above the earth. Consequently, the figures which
they form are unknown to us on account of the interposition of the
earth. The star Canopus proves this. It is unknown to our vicinity; but
we have reports of it from merchants who have been to the most distant
part of Egypt, and to regions bordering on the uttermost boundaries of
the earth.
CHAPTER VI
ASTROLOGY AND WEATHER PROGNOSTICS
1. I have shown how the firmament, and the twelve signs with the
constellations arranged to the north and south of them, fly round the
earth, so that the matter may be clearly understood. For it is from this
revolution of the firmament, from the course of the sun through the
signs in the opposite direction, and from the shadows cast by
equinoctial gnomons, that we find the figure of the analemma.
2. As for the branch of astronomy which concerns the influences of the
twelve signs, the five stars, the sun, and the moon upon human life, we
must leave all this to the calculations of the Chaldeans, to whom
belongs the art of casting nativities, which enables them to declare the
past and the future by means of calculations based on the stars. These
discoveries have been transmitted by the men of genius and great
acuteness who sprang directly from the nation of the Chaldeans; first of
all, by Berosus, who settled in the island state of Cos, and there
opened a school. Afterwards Antipater pursued the subject; then there
was Archinapolus, who also left rules for casting nativities, based not
on the moment of birth but on that of conception.
3. When we come to natural philosophy, however, Thales of Miletus,
Anaxagoras of Clazomenae, Pythagoras of Samos, Xenophanes of Colophon,
and Democritus of Abdera have in various ways investigated and left us
the laws and the working of the laws by which nature governs it. In the
track of their discoveries, Eudoxus, Euctemon, Callippus, Meto,
Philippus, Hipparchus, Aratus, and others discovered the risings and
settings of the constellations, as well as weather prognostications from
astronomy through the study of the calendars, and this study they set
forth and left to posterity. Their learning deserves the admiration of
mankind; for they were so solicitous as even to be able to predict, long
beforehand, with divining mind, the signs of the weather which was to
follow in the future. On this subject, therefore, reference must be made
to their labours and investigations.
CHAPTER VII
THE ANALEMMA AND ITS APPLICATIONS
1. In distinction from the subjects first mentioned, we must ourselves
explain the principles which govern the shortening and lengthening of
the day. When the sun is at the equinoxes, that is, passing through
Aries or Libra, he makes the gnomon cast a shadow equal to eight ninths
of its own length, in the latitude of Rome. In Athens, the shadow is
equal to three fourths of the length of the gnomon; at Rhodes to five
sevenths; at Tarentum, to nine elevenths; at Alexandria, to three
fifths; and so at other places it is found that the shadows of
equinoctial gnomons are naturally different from one another.
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