Introduction
1. The ancestors of the Greeks have appointed such great honours for the
famous athletes who are victorious at the Olympian, Pythian, Isthmian, and
Nemean games, that they are not only greeted with applause as they stand with
palm and crown at the meeting itself, but even on returning to their several
states in the triumph of victory, they ride into their cities and to their
fathers' houses in four-horse chariots, and enjoy fixed revenues for life at the
public expense. When I think of this, I am amazed that the same honours and even
greater are not bestowed upon those authors whose boundless services are
performed for all time and for all nations. This would have been a practice all
the more worth establishing, because in the case of athletes it is merely their
own bodily frame that is strengthened by their training, whereas in the case of
authors it is the mind, and not only their own but also man's in general, by the
doctrines laid down in their books for the acquiring of knowledge and the
sharpening of the intellect.
2. What does it signify to mankind that Milo of Croton and other victors of
his class were invincible? Nothing, save that in their lifetime they were famous
among their countrymen. But the doctrines of Pythagoras, Democritus, Plato, and
Aristotle, and the daily life of other learned men, spent in constant industry,
yield fresh and rich fruit, not only to their own countrymen, but also to all
nations. And they who from their tender years are filled with the plenteous
learning which this fruit affords, attain to the highest capacity of knowledge,
and can introduce into their states civilized ways, impartial justice, and laws,
things without which no state can be sound.
3. Since, therefore, these great benefits to individuals and to communities
are due to the wisdom of authors, I think that not only should palms and crowns be
bestowed upon them, but that they should even be granted triumphs, and judged
worthy of being consecrated in the dwellings of the gods.
Of their many discoveries which have been useful for the development of human
life, I will cite a few examples. On reviewing these, people will admit that
honours ought of necessity to be bestowed upon them.
4. First of all, among the many very useful theorems of Plato, I will cite
one as demonstrated by him. Suppose there is a place or a field in the form of a
square and we are required to double it. This has to be effected by means of
lines correctly drawn, for it will take a kind of calculation not to be made by
means of mere multiplication. The following is the demonstration. A square place
ten feet long and ten feet wide gives an area of one hundred feet. Now if it is
required to double the square, and to make one of two hundred feet, we must ask
how long will be the side of that square so as to get from this the two hundred
feet corresponding to the doubling of the area. Nobody can find this by means of
arithmetic. For if we take fourteen, multiplication will give one hundred and
ninety-six feet; if fifteen, two hundred and twenty-five feet.
5. Therefore, since this is inexplicable by arithmetic, let a diagonal line
be drawn from angle to angle of that square of ten feet in length and width,
dividing it into two triangles of equal size, each fifty feet in area. Taking
this diagonal line as the length, describe another square. Thus we shall have in
the larger square four triangles of the same size and the same number of feet as
the two of fifty feet each which were formed by the diagonal line in the smaller
square. In this way Plato demonstrated the doubling by means of lines, as the
figure appended at the bottom of the page will show.
6. Then again, Pythagoras showed that a right angle can be formed without the
contrivances of the artisan. Thus, the result which carpenters reach very
laboriously, but scarcely to exactness, with their squares, can be demonstrated
to perfection
from the reasoning and methods of his teaching. If we take three rules, one
three feet, the second four feet, and the third five feet in length, and join
these rules together with their tips touching each other so as to make a
triangular figure, they will form a right angle. Now if a square be described on
the length of each one of these rules, the square on the side of three feet in
length will have an area of nine feet; of four feet, sixteen; of five,
twenty-five.
7. Thus the area in number of feet made up of the two squares on the sides
three and four feet in length is equalled by that of the one square described on
the side of five. When Pythagoras discovered this fact, he had no doubt that the
Muses had guided him in the discovery, and it is said that he very gratefully
offered sacrifice to them.
This theorem affords a useful means of measuring many things, and it is
particularly serviceable in the building of staircases in buildings, so that the
steps may be at the proper levels.
8. Suppose the height of the story, from the flooring above to the ground
below, to be divided into three parts. Five of these will give the right length
for the stringers of the stairway. Let four parts, each equal to one of the
three composing the height between the upper story and the ground, be set off
from the perpendicular, and there fix the lower ends of the stringers. In this
manner the steps and the stairway itself will be properly placed. A figure of
this also will be found appended below.
9. In the case of Archimedes, although he made many wonderful discoveries of
diverse kinds, yet of them all, the following, which I shall relate, seems to
have been the result of a boundless ingenuity. Hiero, after gaining the royal
power in Syracuse, resolved, as a consequence of his successful exploits, to
place in a certain temple a golden crown which he had vowed to the immortal
gods. He contracted for its making at a fixed price, and weighed out a precise
amount of gold to the contractor. At the appointed time the latter delivered to
the king's satisfaction an exquisitely finished piece of handiwork, and it
appeared that in weight the crown corresponded precisely to what
the gold had weighed.
10. But afterwards a charge was made that gold had been abstracted and an
equivalent weight of silver had been added in the manufacture of the crown.
Hiero, thinking it an outrage that he had been tricked, and yet not knowing how
to detect the theft, requested Archimedes to consider the matter. The latter,
while the case was still on his mind, happened to go to the bath, and on getting
into a tub observed that the more his body sank into it the more water ran out
over the tub. As this pointed out the way to explain the case in question,
without a moment's delay, and transported with joy, he jumped out of the tub and
rushed home naked, crying with a loud voice that he had found what he was
seeking; for as he ran he shouted repeatedly in Greek, "Ευρηκα, ευρηκα."
11. Taking this as the beginning of his discovery, it is said that he made
two masses of the same weight as the crown, one of gold and the other of silver.
After making them, he filled a large vessel with water to the very brim, and
dropped the mass of silver into it. As much water ran out as was equal in bulk
to that of the silver sunk in the vessel. Then, taking out the mass, he poured
back the lost quantity of water, using a pint measure, until it was level with
the brim as it had been before. Thus he found the weight of silver corresponding
to a definite quantity of water.
12. After this experiment, he likewise dropped the mass of gold into the full
vessel and, on taking it out and measuring as before, found that not so much
water was lost, but a smaller quantity: namely, as much less as a mass of gold
lacks in bulk compared to a mass of silver of the same weight. Finally, filling
the vessel again and dropping the crown itself into the same quantity of water,
he found that more water ran over for the crown than for the mass of gold of the
same weight. Hence, reasoning from the fact that more water was lost in the case
of the crown than in that of the mass, he detected the mixing of silver with the
gold, and made the theft of the contractor perfectly clear.
13. Now let us turn our thoughts to the researches of Archytas of Tarentum
and Eratosthenes of Cyrene. They made many discoveries from mathematics which
are welcome to men, and so, though they deserve our thanks for other
discoveries, they are particularly worthy of admiration for their ideas in that
field. For example, each in a different way solved the problem enjoined upon
Delos by Apollo in an oracle, the doubling of the number of cubic feet in his
altars; this done, he said, the inhabitants of the island would be delivered
from an offence against religion.
14. Archytas solved it by his figure of the semi-cylinders; Eratosthenes, by
means of the instrument called the mesolabe.
Noting all these things with the great delight which learning gives, we
cannot but be stirred by these discoveries when we reflect upon the influence of
them one by one. I find also much for admiration in the books of Democritus on
nature, and in his commentary entitled Χειρὁκμητα, in which he made use of his
ring to seal with soft wax the principles which he had himself put to the
test.
15. These, then, were men whose researches are an everlasting possession, not
only for the improvement of character but also for general utility. The fame of
athletes, however, soon declines with their bodily powers. Neither when they are
in the flower of their strength, nor afterwards with posterity, can they do for
human life what is done by the researches of the learned.
16. But although honours are not bestowed upon authors for excellence of
character and teaching, yet as their minds, naturally looking up to the higher
regions of the air, are raised to the sky on the steps of history, it must needs
be, that not merely their doctrines, but even their appearance, should be known
to posterity through time eternal. Hence, men whose souls are aroused by the
delights of literature cannot but carry enshrined in their hearts the likeness
of the poet Ennius, as they do those of the gods. Those who are devotedly
attached to the poems of Accius seem to have before them not merely his vigorous
language but even his very figure.
17. So, too, numbers born after our time will feel as if they were discussing
nature face to face with Lucretius, or the art of rhetoric with Cicero; many of
our posterity will confer with Varro on the Latin language; likewise, there will
be numerous scholars who, as they weigh many points with the wise among the
Greeks, will feel as if they were carrying on private conversations with them.
In a word, the opinions of learned authors, though their bodily forms are
absent, gain strength as time goes on, and, when taking part in councils and
discussions, have greater weight than those of any living men.
18. Such, Caesar, are the authorities on whom I have depended, and applying
their views and opinions I have written the present books, in the first seven
treating of buildings and in the eighth of water. In this I shall set forth the
rules for dialling, showing how they are found through the shadows cast by the
gnomon from the sun's rays in the firmament, and on what principles these
shadows lengthen and shorten.
Chapter One
The Zodiac and the Planets
1. It is due to the divine intelligence and is a very great wonder to all who
reflect upon it, that the shadow of a gnomon at the equinox is of one length in
Athens, of another in Alexandria, of another in Rome, and not the same at
Piacenza, or at other places in the world. Hence drawings for dials are very
different from one another, corresponding to differences of situation. This is
because the length of the shadow at the equinox is used in constructing the
figure of the analemma, in accordance with which the hours are marked to conform
to the situation and the shadow of the gnomon. The analemma is a basis for
calculation deduced from the course of the sun, and found by observation of the
shadow as it increases until the winter solstice. By means of this, through
architectural principles and the employment of the compasses, we find out the
operation of the sun in the universe.
2. The word "universe" means the general assemblage of all nature, and it
also means the heaven that is made up of the constellations and the courses of
the stars. The heaven revolves steadily round earth and sea on the pivots at the
ends of its axis. The architect at these points was the power of Nature, and she
put the pivots there, to be, as it were, centres, one of them above the earth
and sea at the very top of the firmament and even beyond the stars composing the
Great Bear, the other on the opposite side under the earth in the regions of the
south. Round these pivots (termed in Greek πὁλοι) as centres, like those of a
turning lathe, she formed the circles in which the heaven passes on its
everlasting way. In the midst thereof, the earth and sea naturally occupy the
central point.
3. It follows from this natural arrangement that the central point in the
north is high above the earth, while on the south, the
region below, it is beneath the earth
and consequently hidden by it. Furthermore, across the middle, and obliquely
inclined to the south, there is a broad circular belt composed of the twelve
signs, whose stars, arranged in twelve equivalent divisions, represent each a
shape which nature has depicted. And so with the firmament and the other
constellations, they move round the earth and sea in glittering array,
completing their orbits according to the spherical shape of the heaven.
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: καἱει τἁ πὁρρω, τἁγγυθεν δ εὑκρατ ἑχει.
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 Two
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 Three
The Course of the Sun though 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 Four
The Northern Constellations
1. The Great Bear, called in Greek ἁρκτος or ἑλἱκη, 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 προτρυγητἡς. But Spica in
that constellation is brighter. Opposite there is another star, coloured,
between[266] 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...
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.
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.[267]
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 κυνὁσουρα,
and the Greater ἑλικη. 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 Five
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 ἁρπεδὁναι, 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.
Chpater Six
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.