Part 23 (1/2)

11. Taking this as the beginning of his discovery, it is said that he made two ma.s.ses 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 ma.s.s 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 ma.s.s, he poured back the lost quant.i.ty 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 quant.i.ty of water.

12. After this experiment, he likewise dropped the ma.s.s 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 quant.i.ty: namely, as much less as a ma.s.s of gold lacks in bulk compared to a ma.s.s of silver of the same weight. Finally, filling the vessel again and dropping the crown itself into the same quant.i.ty of water, he found that more water ran over for the crown than for the ma.s.s 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 ma.s.s, 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 ent.i.tled [Greek: Cheirokmeta], 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 G.o.ds. 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 a.n.a.lemma, in accordance with which the hours are marked to conform to the situation and the shadow of the gnomon. The a.n.a.lemma 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 compa.s.ses, we find out the operation of the sun in the universe.

2. The word ”universe” means the general a.s.semblage 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 pa.s.ses 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 pa.s.sing 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, pa.s.s 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 pa.s.s up and, having completed its circuit, to emerge out of the darkness into the light of the open s.p.a.ce 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, pa.s.s 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 s.p.a.ce of one sign, that is, one twelfth of the firmament. Consequently, in twelve months he traverses the s.p.a.ces 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 s.p.a.ces 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, s.h.i.+ning 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 pa.s.sing 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, pa.s.ses through the s.p.a.ces 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 s.p.a.ce 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 s.p.a.ces 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 pa.s.ses 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 s.p.a.ce 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 pa.s.s.