Under the leadership of Bacon in England, Calvin in France, Luther in Germany, and Knox in Scotland, European thought was being stirred up while the great discoveries just related were being made. Just as Boyle's chemical discoveries caused the divorcing of chemistry from alchemy, and the naturalistic philosophy of the times led to the specialization of scientists and the breaking off of philosophy from science, so the intellectual awakening aroused by Bacon and his contemporaries led to the suppression of belief in witchcraft and to revolutionary ideas in religion and ethics.
Locke endeavored to base a "rational Christianity" on the ground of experience. Until his times, theology was tangled up with a maze of physical problems which dismayed even such intellects as those of Newton, Hume, and Locke.
Newton's researches were chiefly based upon mathematical and astronomical problems. While a student at Cambridge in 1660, he studied the works of Descartes, Kepler, Van Schooten, Barrow, and particularly those of the Greek and British mathematicians. The works of J. Wallis were very valuable to him. The "Arithmetic of Affinities" of Wallis drew his attention to astronomical problems and thus led to his great triumphs later on.
Newton's "Principia" has already been referred to as being one of the greatest works of the intellect ever produced.
The result of Newton's meditation upon the nature of the central force that keeps the planets in their courses was that he furnished a mathematical basis for Kepler's laws by proving that if the planets describe elliptical orbits about the sun, the force acting toward the sun, keeping them in revolution, must vary inversely as the square of the distance. On the revolution of the moon around the earth he found a practical confirmation of this law of gravitational attraction. He then took up the study of motion in general and showed that every particle of matter attracts every other particle in accordance with the same principle of inverse squares.
Botanical gardens were established in Padua in 1545, and not long after in Pisa, Leyden, Paris, and London. Much attention was devoted to medicinal plants, and numerous herbal books were published. Malpighi, Grew, and Camerarius (1665-1721) published works on botany and plant morphology. Ray and Linnæus (1707-1778) studied the classification of plants and compiled textbooks of descriptive botany.
Buffon (1707-1788) published his famous "Natural History of Animals" which did for zoölogy what the works of Linnæus did for botany.
Looking backward, we can now see that all scientific knowledge has been gained by the trial and error method and cumulative analyses of a multitude of observations. Progress is not made uniformly but in a recurrent, cyclic manner. Reactions follow advances, but in the end all goes forward.