The Ten Books on Architecture
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, "[Greek: Eurêka, eurêka]."
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 [Greek:
Cheirokmêta], 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 I
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 [Greek: poloi]) 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