Claudian. de Nuptiis Honorii et Mariæ.
Claudian’s verses have been thus familiarly Englished:—“The tender boughs live together in love, and the happy trees pass their time entirely in mutual embraces. Palms by consent salute and nod to each other; the poplar, smitten with the poplar, sighs; whilst planes and alders express their affection in the melody of whispers.” This allusion to the “Loves of the Plants” was not a mere imagination of the old poet: their sexual difference was known to the old philosophers. “Naturalists,” says Pliny, “admit the distinction of sex not only in trees, but in herbs, and in all plants.”
Astronomy—Mathematics—Mechanics—Optics, &c.
The Vibration of the Pendulum was employed, for the purpose it is still applied to, by the ancient Arabians, long before the epoch usually assigned to its first discovery. A learned gentleman at Oxford, who carefully examined the Arabian manuscripts in the library of that university, says, “The advantages recommending the study of astronomy to the people of the East were many.” He speaks of “the serenity of their weather; the largeness and correctness of the instruments they made use of much exceeding what the moderns would be willing to believe; the multitude of their observations and writings being six times more than what has been composed by Greeks and Latins; and of the number of powerful princes who, in a manner becoming their own magnificence, aided them with protection.” He affirms, that it is easy “to show in how many respects the Arabian astronomers detected the deficiency of Ptolemy, and the pains they took to correct him; how carefully they measured time by water-clocks, sand-glasses, immense solar dials, and even by the vibrations of the pendulum; and with what assiduity and accuracy they conducted themselves in those nice attempts, which do so much honour to human genius—the taking the distances of the stars, and the measure of the earth.”
Refraction of Light.—According to Roger Bacon, Ptolemy, the great philosopher and geometrician, gave the same explanation of this phenomenon, which Descartes has done since; for he says, that “a ray, passing from a more rare into a more dense medium, becomes more perpendicular.” Ptolemy wrote a treatise on optics whence Alhazen seems to have drawn whatever is estimable in what he advances about the refraction of light, astronomical refraction, and the cause of the extraordinary size of planets when they appear on the horizon. Ptolemy, and after him Alhazen, said, that “when a ray of light passes from a more rare into a more dense medium, it changes its direction when it arrives upon the surface of the latter, describing a line which intersects the angle made by that of its first direction, and a perpendicular falling upon it from the more dense medium.” Bacon adds, after Ptolemy, that “the angle formed by the coincidence of those two lines is not always equally divided by the refracted ray; because in proportion to the greater or less density of the medium, the ray is more or less refracted, or obliged to decline from its first direction.” Sir Isaac Newton subsequently deducing the cause of refraction, from the attraction made upon the ray of light by the bodies surrounding it, says, “that mediums are more or less attractive in proportion to their density.”
Astronomic Refraction.—Ptolemy, acquainted with the principle of the refraction of light, could not fail to conclude that this was the cause of the appearance of planets upon the horizon before they came there. Hence he accounted for those appearances from the difference there was between the medium of air, and that of ether which lay beyond it; so that the rays of light coming from the planet, and entering into the denser medium of our atmosphere, must of course be so attracted as to change their direction, and by that means bring the star to our view, before it really come upon the horizon.
Why Stars appear largest upon the Horizon is attempted to be accounted for by Roger Bacon. He says it may proceed from this, that the rays coming from the star are made to diverge from each other, not only by passing from the rare medium of ether into the denser one of our surrounding air, but also by the interposition of clouds and vapours arising out of the earth, which repeat the refraction and augment the dispersion of the rays, whereby the object must needs be magnified to our eye. He afterwards adds, that there has been assigned by Ptolemy and Alhazen another more reasonable cause. These authors thought that the reason of a star’s appearing larger at its rising or setting than when viewed over head arose from this, that when the star is over head there are no immediate objects perceived between it and us, so that we judge it nearer to us, and are not surprised at its littleness; but when a star is viewed on the horizon, it lies then so low that all we can see upon earth interposes between it and us, which making it appear at a greater distance, we are surprised at observing it so large, or rather imagine it larger than it is. For the same reason the sun and moon, when appearing upon the horizon, seem to be at a greater distance, by reason of the interposition of those objects which are upon the surface of our earth, than when they are over head; and consequently there will arise in our minds an idea of their largeness, augmented by that of their distance, and this of course must make them appear larger to us, when viewed on the horizon, than when seen in the zenith.
Perspective of the Ancients.—Most of the learned deny the ancients the advantage of having known the rules of perspective, or of having put them in practice, although Vitruvius makes mention of the principles of Democritus and Anaxagoras respecting that science, in a manner that plainly shows they were not ignorant of them. “Anaxagoras and Democritus,” says he, “were instructed by Agatarchus, the disciple of Eschylus. They both of them taught the rules of drawing, so as to imitate from any point of view the prospect that lay in sight, by making the lines in their draught, issuing from the point of view there, exactly resemble the radiation of those in nature; insomuch, that however ignorant any one might be of the rules whereby this was performed, yet they could not but know at sight the edifices, and other prospects which offered themselves in the perspective scenes they drew for the decoration of the theatre, where, though all the objects were represented on a plain surface, yet they swelled out, or retired from the sight, just as objects do endowed with all dimensions.” Again he says, that the painter Apatarius drew a scene for the theatre at Tralles, “which was wonderfully pleasing to the eye, on account that the artist had so well managed the lights and shades, that the architecture appeared in reality to have all its projections.” Pliny says, that Pamphilus, who was an excellent painter, applied himself much to the study of geometry, and maintained that “without its aid it was impossible ever to arrive at perfection in that art.” Pliny elsewhere says, that Apelles fell short of Asclepiodorus in “the art of laying down distances in his paintings.” Lucian, in his Dialogue of Zeuxis, speaks of the effects of perspective in pictures, and Philostratus, in his preface to his Drawings, or History of Painting, makes it appear that he knew this science; and in his account of Menoetius’s picture of the siege of Thebes, describes the happy effects of perspective when studied with care.
Optical Problem.—Aristotle was the first who proposed the famous problem respecting the roundness of that image of the sun, which is formed by his rays passing through a small puncture, even though the hole itself be square or triangular. “Why is it,” inquires Aristotle, “that the sun, in passing through a square puncture, forms itself into an orbicular, and not into a rectilinear figure, as when it shines through a grate? Is it not because the efflux of its rays, through the puncture, converges it into a cone, whose base is the luminous circle?”
Squaring the Circle.—If there remain any hope of solving this problem it is founded on that discovery of Hippocrates of Chios, called the squaring of the Lunulæ, which is said to have first put him in heart, they say, to attempt the squaring of the circle. This Hippocrates must not be confounded with the father of medicine, who was of the isle of Cos. He who is spoken of here was a famous geometrician, and lived about five hundred years before Jesus Christ.