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with it than with one of more simplicity. weight of Aristotle's name, which, in the sixteenth century, not only biassed the judgment, but engaged the passions, connected as it was with general orthodoxy and the preservation of established systems, was thrown into the scale against Copernicus. It was asked what demonstration could be given of his hypothesis; whether the movements of the heavenly bodies could not be reconciled to the Ptolemaic; whether the greater quantity of motion, and the complicated arrangement which the latter required, could be deemed sufficient objections to a scheme proceeding from the Author of nature, to whose power and wisdom our notions of simplicity and facility are inapplicable; whether the moral dignity of man, and his peculiar relations to the Deity, unfolded in Scripture, did not give the world he inhabits a better claim to the place of honour in the universe, than could be pretended, on the score of mere magnitude, for the sun. It must be confessed, that the strongest presumptions in favour of the system of Copernicus were not discovered by himself.
11. It is easy, says Montucla, to reckon the number of adherents to the Copernican theory during the sixteenth century. After Rhæticus, they may be nearly reduced to Reinhold, author of the Prussian tables; Rothman, whom Tycho drew over afterwards to his own system; Christian Wursticius (Ursticius), who made some proselytes in Italy; finally, Mæstlin, the illustrious master of Kepler. He might have added Wright and Gilbert, for the credit of England. Among the Italian proselytes made by Wursticius, we may perhaps name Jordano Bruno, who strenuously asserts the Copernican hypothesis; and two much greater authorities in physical science, Benedetti and Galileo himself. It is evident that the preponderance of valuable suffrages was already on the side of truth."
12. The predominant disinclination to contravene the apparent testimonies of sense and Scripture had, perhaps, more effect than the desire of originality in suggesting the middle course taken by Tycho Brahe. He was a Dane of noble birth, and early drawn, by the impulse of natural genius, to the study of astronomy.
Frederic III., his sovereign, after Tycho had already obtained some reputation, erected for him the observatory of Uraniburg in a small isle of the Baltic. In this solitude he passed above twenty years, accumulating the most extensive and accurate observations which were known in Europe before the discovery of the telescope and the improvement of astronomical instruments. These, however, were not published till 1606, though Kepler had previously used them in his Tabula Rodolphina. Tycho himself did far more in this essential department of the astronomer than any of his predecessors; his resources were much beyond those of Copernicus, and the latter years of this century may be said to make an epoch in physical astronomy. Frederic, Landgrave of Hesse, was more than a patron of the science. The observations of that prince have been deemed worthy of praise long after his rank had ceased to avail them. The emperor Rodolph, when Tycho had been driven by envy from Denmark, gave him an asylum and the means of carrying on his observations at Prague, where he died in 1601. He was the first in modern times who made a catalogue of stars, registering their positions as well as his instruments permitted him. This catalogue, published in his Progymnasmata in 1602, contained 777, to which, from Tycho's own manuscripts, Kepler added 223 stars.
13. In the new mundane system of Tycho Brahe, which, though first regularly promulgated to the His system. world in his Progymnasmata, had been communicated in his epistles to the Landgrave of Hesse, he supposes the five planets to move round the sun, but carries the sun itself with these five satellites, as well as the moon, round the earth. Though this, at least at the time, might explain the known phænomena as well as the two other theories, its want of simplicity always prevented its reception. Except Longomontanus, the countryman and disciple of Tycho, scarce any conspicuous astronomer adopted an hypothesis which, if it had been devised some time sooner, would perhaps have met with better success. But in the seventeenth century, the wise all fell into the
Montucla, p. 653-659.
Copernican theory, and the many were content without any theory at all.
14. A great discovery in physical astronomy may be assigned to Tycho. Aristotle had pronounced comets to be meteors generated below the orbit of the moon. But a remarkable comet in 1577 having led Tycho to observe its path accurately, he came to the conclusion that these bodies are far beyond the lunar orbit, and that they pass through what had always been taken for a solid firmament, environing the starry orbs, and which plays no small part in the system of Ptolemy. He was even near the discovery of their elliptic revolution, the idea of a curve round the sun having struck him, though he could not follow it by observation."
15. The acknowledged necessity of reforming the Julian calendar gave in this age a great importance to Gregorian astronomy. It is unnecessary to go into the details Calendar. of this change, effected by the authority of Gregory XIII., and the skill of Lilius and Clavius, the mathematicians employed under him. The new calendar was immediately received in all countries acknowledging the pope's supremacy; not so much on that account, though a discrepancy in the ecclesiastical reckoning would have been very inconvenient, as of its real superiority over the Julian. The Protestant countries came much more slowly into the alteration; truth being no longer truth when promulgated by the pope. It is now admitted that the Gregorian calendar is very nearly perfect, at least as to the computation of the solar year, though it is not quite accurate for the purpose of finding Easter. In that age it had to encounter the opposition of Mæstlin, an astronomer of deserved reputation, and of Scaliger, whose knowledge of chronology ought to have made him conversant with the subject, but who, by a method of squaring the circle which he announces with great confidence as a demonstration, showed the world that his genius did not guide him to the exact sciences.
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 aperture 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." 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. 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.a
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."
y Montucla, p. 695.
* Id. p. 698.
a Id. p. 708.
b Id. p. 690.
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.
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 Meccanica was written in 1592, though not published for more than forty years afterwards. 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 period. 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.
19. But on the same principle that we exclude the work of Galileo on mechanics from the sixteenth century, Statics of it seems reasonable to mention that of Simon Ste- Stevinus. vinus of Bruges; since the first edition of his Statics and