Vitruvius

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Hence, just as the sun during his passage through the constellations makes the days and hours longer or shorter, so the boss on a dial, moving from point to point in a direction contrary to that of the revolution of the drum in the middle, is carried day by day sometimes over wider and sometimes over narrower spaces, giving a representation of the hours and days within the limits of each month. ”

“ 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. ”

“ 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 ”

“ 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. ”

“ 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. ”

“ 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 ”

“ 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? ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ Omitting details, therefore,--not for fear of the trouble, but lest I should prove tiresome by writing too much,--I will state by whom the different classes and designs of dials have been invented. For I cannot invent new kinds myself at this late day, nor do I think that I ought to display the inventions of others as my own. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ The men whose names are written above, as well as many others, have invented and left us other kinds: as, for instance, the Conarachne, the Conical Plinthium, and the Antiborean. Many have also left us written directions for making dials of these kinds for travellers, which can be hung up. Whoever wishes to find their baseplates, can easily do so from the books of these writers, provided only he understands the figure of the analemma. ”

“ 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. ”

“ 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 ”

“ 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. ”

“ 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. ”

“ From that point, marked by C, let a line be drawn through the centre at the point A, and this will represent a ray of the sun at the equinox. Then, extending the compasses from the centre to the line in the plane, mark off the equidistant points E on the left and I on the right, on the two sides of the circumference, and let a line be drawn through the centre, dividing the circle into two equal semicircles. ”

“ Then, at the points at which the parallel lines cut the line called the horizon, the letter S is to be on the right and the letter V on the left, and from the extremity of the semicircle, at the point G, draw a line parallel to the axis, extending to the left-hand semicircle at the point H. This parallel line is called the Logotomus. ”

“ Two cones are made, one solid and the other hollow, turned on a lathe so that one will go into the other and fit it perfectly. A rod is used to loosen or to bring them together, thus causing the water to flow rapidly or slowly into the vessels. ”

“ Round these pivots (termed in Greek (Greek characters) Category:Pages with missing Greek characters) 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. ”