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. CHAPTER IX PRELUDE TO MODERN SCIENCE--THE EIGHTEENTH CENTURY When the eighteenth century opened science had begun to make men think, and the works of the great scientists had changed the trend of thought on all sides. Liberty of conscience, of worship, and of opportunity were demanded, as well as representative government, economic freedom, and individual equality before the law. Men wanted to be free agents. The philosophical writings of Berkeley, Locke, Hume, Spinoza, Voltaire, Rousseau, and others supplemented the books of the scientists and promoted rational thinking. Syllogistic reasoning displaced the practice of accepting beliefs upon authority. This change in public thought reacted most favorably upon science. Gottfried Wilhelm Leibnitz (1646-1716) conceived matter as a plurality of simple forces. Many kinds of matter, he said, exist. There is no single natural force, but an infinite number. Each force is represented by some individual substance. Force is indivisible, immaterial, and unextended. Simple forces he called essential forms, units, atoms, or monads. The monads are not mathematical points, nor physical points. Real points are metaphysical. In other words, Leibnitz created a philosophy of eternal force atoms.