History of the Intellectual Development of Europe, Volume II (of 2) / Revised Edition

by John William Draper

His remonstrance with the Church.Humboldt, referring to the movement of Jupiter's satellites, remarks: "It was this which led Kepler, in his 'Harmonices Mundi,' to state, with the firm confidence and security of a German spirit of philosophical independence, to those whose opinions bore sway beyond the Alps, 'Eighty years have elapsed during which the doctrines of Copernicus regarding the movement of the earth and the immobility of the sun have been promulgated without hindrance, because it was deemed allowable to dispute concerning natural things and to elucidate the works of God, and, now that new testimony is discovered in proof of the truth of those doctrines—testimony which was not known to the spiritual judges, ye would prohibit the promulgation of the true system of the structure of the universe.'"

Rectification of the Copernican theory.Thus we see that the heliocentric theory, as proposed [268] by Copernicus, was undergoing rectification. The circular movements admitted into it, and which had burdened it with infinite perplexity, though they had hitherto been recommended by an illusive simplicity, were demonstrated to be incorrect. They were replaced by the real ones, the elliptical. Kepler, as was his custom, ingenuously related his trials and disappointments. Alluding on one occasion to this, he says: "My first error was that the path of a planet is a perfect circle—an opinion which was a more mischievous thief of my time, in proportion as it was supported by the authority of all philosophers, and apparently agreeable to metaphysics."

The philosophical import of these laws.The philosophical significance of Kepler's discoveries was not recognized by the ecclesiastical party at first. It is chiefly this, that they constitute a most important step to the establishment of the doctrine of the government of the world by law. But it was impossible to receive these laws without seeking for their cause. The result to which that search eventually conducted not only explained their origin, but also showed that, as laws, they must, in the necessity of nature, exist. It may be truly said that the mathematical exposition of their origin constitutes the most splendid monument of the intellectual power of man.

Necessity for mechanical science.Before the heliocentric theory could be developed and made to furnish a clear exposition of the solar system, which is obviously the first step to just views of the universe, it was necessary that the science of mechanics should be greatly improved—indeed, it might be said, created; for during those dreary ages following the establishment of Byzantine power, nothing had been done toward the acquisition of correct views either in statics or dynamics. It was impossible that Europe, in her lower states of life, could produce men capable of commencing where Archimedes had left off. She had to wait for the approach of her Age of Reason for that.

Leonardo da Vinci.The man of capacity at last came. Leonardo da Vinci was born A.D. 1452. The historian Hallam, enumerating some of his works, observes, "His knowledge was almost preternatural." Many of his [269] writings still remain unpublished. Long before Bacon, he laid down the maxim that experience and observation must be the foundation of all reasoning in science; that experiment is the only interpreter of nature, and is essential to the ascertainment of laws. Unlike Bacon, who was ignorant of mathematics, and even disparaged them, he points out their supreme advantage. Seven years after the voyage of Columbus, this great man—great at once as an artist, mathematician, and engineer—gave a clear exposition of the theory of forces obliquely applied on a lever; a few years later he was well acquainted with the earth's annual motion. He knew the laws of friction, subsequently demonstrated by Amontons, and the principle of virtual velocities; he described the camera obscura before Baptista Porta, understood aerial perspective, the nature of coloured shadows, the use of the iris, and the effects of the duration of visible impressions on the eye. He wrote well on fortification, anticipated Castelli on hydraulics, occupied himself with the fall of bodies on the hypothesis of the earth's rotation, treated of the times of descent along inclined planes and circular arcs, and of the nature of machines. He considered, with singular clearness, respiration and combustion, and foreshadowed one of the great hypotheses of geology, the elevation of continents.

Stevinus continues the movement in Natural Philosophy.This was the commencement of the movement in Natural Philosophy; it was followed up by the publication of a work on the principles of equilibrium by Stevinus, 1586. In this the author established the fundamental property of the inclined plane, and solved, in a general manner, the cases of forces acting obliquely. Six years later Galileo's treatise on mechanics appeared, a fitting commencement of that career which, even had it not been adorned with such brilliant astronomical discoveries, would alone have conferred the most illustrious distinction upon him.

Discovery of the laws of motion.The dynamical branch of Mechanics is that which is under most obligation to Galileo. To him is due the establishment of the three laws of motion. They are to the following effect, as given by Newton:

(1.) Every body perseveres in its state of rest or [270] of uniform motion in a right line unless it is compelled to change that state by forces impressed thereon.

(2.) The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which that force is impressed.

(3.) To every action there is always opposed an equal reaction, or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.