Optics. 16. The science of optics, as well as all other branches of the mixed mathematics, fell very short of astronomy in the number and success of its promoters. It was carried not much farther than the point where Alhazen, Vitello, and Roger Bacon left it. Maurolycus of Messina, in a treatise published in 1575, though written, according to Montucla, fifty years before, entitled Theoremata de Lumine et Umbra, has mingled a few novel truths with error. He explains rightly the fact that a ray of light, received through a small aperature of any shape, produces a circular illumination on a body intercepting it at some distance; and points out why different defects of vision are remedied by convex or concave lenses. He had however mistaken notions as to the visual power of the eye, which he ascribed not to the retina but to the crystalline humour; and on the whole, Maurolycus, though a very distinguished philosopher in that age, seems to have made few considerable discoveries in physical science.[1365] Baptista Porta, who invented, or at least made known, the camera obscura, though he dwells on many optical phenomena in his Magia Naturalis, sometimes making just observations, had little insight into the principles that explain them.[1366] The science of perspective has been more frequently treated, especially in this period, by painters and architects than by mathematicians. Albert Durer, Serlio, Vignola, and especially Peruzzi, distinguished themselves by practical treatises; but the geometrical principles were never well laid down before the work of Guido Ubaldi in 1600.[1367]
[1365] Id. p. 695.
[1366] Montucla, p. 698.
[1367] Id. p. 708.
Mechanics. 17. This author, of a noble family in the Apennines, ranks high also among the improvers of theoretical mechanics. This great science, checked, like so many others, by the erroneous principles of Aristotle, made scarce any progress till near the end of the century. Cardan and Tartaglia wrote upon the subject; but their acuteness in abstract mathematics did not compensate for a want of accurate observation and a strange looseness of reasoning. Thus Cardan infers that the power required to sustain a weight on an inclined plane varies in the exact ratio of the angle, because it vanishes when the plane is horizontal, and becomes equal to the weight when the plane is perpendicular. But this must be the case if the power follows any other law of direct variation, as that of the sine of inclination, that is, the height, which it really does.[1368] Tartaglia, on his part, conceived that a cannon-ball did not indeed describe two sides of a parallelogram, as was commonly imagined even by scientific writers, but, what is hardly less absurd, that its point-blank direction and line of perpendicular descent are united by a circular arch, to which they are tangents. It was generally agreed, till the time of Guido Ubaldi, that the arms of a lever charged with equal weights, if displaced from the horizontal position, would recover it when set at liberty. Benedetti of Turin had juster notions than his Italian contemporaries; he ascribed the centrifugal force of bodies to their tendency to move in a straight line; he determined the law of equilibrium for the oblique lever, and even understood the composition of motions.[1369]
[1368] Id. p. 690.
[1369] Montucla, p. 693.
18. If, indeed, we should give credit to the sixteenth century for all that was actually discovered, and even reduced to writing, we might now proceed to the great name of Galileo. For it has been said that his treatise Della Scienza Mechanica was written in 1592, though not published for more than forty years afterwards.[1370] But as it has been our rule, with not many exceptions, to date books from their publication, we must defer any mention of this remarkable work to the next volume. The experiments, however, made by Galileo, when lecturer in mathematics at Pisa, on falling bodies, come strictly within our limits. He was appointed to this office in 1589, and left it in 1592. Among the many unfounded assertions of Aristotle in physics, it was one that the velocity of falling bodies was proportionate to their weights; Galileo took advantage of the leaning tower of Pisa to prove the contrary. But this important, though obvious experiment, which laid open much of the theory of motion, displeased the adherents of Aristotle so highly, that they compelled him to leave Pisa. He soon obtained a chair in the university of Padua.
[1370] Playfair has fallen into the mistake of supposing that this treatise was published in 1592; and those who, on second thoughts, would have known better, have copied him.
Statics of Stevinus. 19. But on the same principle that we exclude the work of Galileo on mechanics from the sixteenth century, it seems reasonable to mention that of Simon Stevinus of Bruges; since the first edition of his Statics and Hydrostatics was printed in Dutch as early as 1585, though we can hardly date its reception among the scientific public before the Latin edition in 1608. Stevinus has been chiefly known by his discovery of the law of equilibrium on the inclined plane, which had baffled the ancients, and, as we have seen, was mistaken by Cardan. Stevinus supposed a flexible chain of uniform weight to descend down the sides of two connected planes, and to hang in a sort of festoon below. The chain would be in equilibrio, because, if it began to move, there would be no reason why it should not move for ever, the circumstances being unaltered by any motion it could have; and thus there would be a perpetual motion, which is impossible. But the part below, being equally balanced, must, separately taken, be in equilibrio. Consequently the part above, lying along the planes, must also be in equilibrio; and hence the weight of the two parts of the chain must be equal, or if that lying along the shorter plane be called the power, it will be to the other as the lengths; or if there be but one plane, and the power hang perpendicularly, as the height to the length.