The Greeks were taught by Leucippus, Empedocles and Anaxagoras that matter is formed of atoms. Space is infinite; atoms are indivisible. Atoms are in a continuous state of activity. Atoms constitute worlds and planets. Falling through space they give rise to eddying motions by mutual impact. Many philosophers rejected these views. Throughout the ages, however, they were learned by students and when Leibnitz advanced his new atomic theory, the world was ready to consider it. The Leibnitzian monads were like Plato's ideas--eternal purposes. Aristotle held that monads are absolute, indivisible beings. Leibnitz suggested that each monad is in process of evolution and realizes its nature through inner necessity. It is not determined from without. Each form of matter existed in germ in an embryo. Nothing in a monad can be lost, and future stages are predetermined in the earlier stages. Each monad is charged with the past and big with the future. The biologists at this period generally accepted this incasement theory. Caspar F. Wolff suggested, in 1759, that there is an epigenesis or a progressive evolution and differentiation of organs from a homogeneous primitive germ. This view did not meet with approval until Darwin published his great discoveries in the middle of the last century. The history of the atomic theories furnishes a clear illustration of the long period of preparation that great scientific ideas must pass through before they are united by a generalizing genius of exceptional capacity and launched in the form of a new theory. Modern mathematical science grew out of the analytical geometry of Descartes. He showed that the true method for the discovery of scientific facts was to accept nothing as true which was clearly not recognizable as true. All assumptions should be proved. Each difficulty should be separately studied. No intermediate steps should be skipped, and details should be methodically enumerated. Thoughts must be guided in an orderly manner, beginning with the simplest characteristics of an object and proceeding in a logical sequence to the most complicated aspects of each subject. Descartes carried out his own rules in his work. His improvements in the differential calculus, and those in the integral calculus made by Cavalieri, and in the calculus of probabilities by Pascal and Fermat, furnished scientists with instruments capable of solving almost every physical problem met with in their investigations. One of the first results of the new analytical methods was the establishment of the science of optics.