In the succeeding chapter we shall review the philosophy of the rationalist, Descartes, who was a contemporary of Hobbes. We shall find that Descartes and Hobbes are alike in this: that both employed Galileo’s mathematical theory as authoritative. They differed, however, in the way in which they used Galileo’s theory. Descartes reduced mathematics to the rational, and conceived it to be the instrument of the reason; Hobbes reduced the rational to the mathematical, and conceived the reason as a form of mechanics. The starting-point of Descartes was the subjective, and he was held at a standstill until the relation of thought and mechanics was solved by him. The point of view of Hobbes was objective, and since all was mechanical, he discussed only incidentally the relation between thought and mechanical existence. Hobbes conceived the world in the terms of only one series, the mechanical. Descartes’ main motive was to preserve the rational; and, consequently, the world to him consisted of a double or dualistic series of terms. We therefore place Descartes, with Spinoza and Leibnitz, in a group called Rationalists. Hobbes was a materialist, and his greatness consisted in going the full length of materialism: he went beyond all the scientists of his time by extending the mechanical theory to the mental life. =The Life and Writings of Hobbes= (1588–1679). The life of Hobbes falls into five natural periods. In his first and last periods he was the classical scholar. During his middle period of about thirteen years he was the philosopher. Furthermore, at one time he was absorbed in mathematics and at another in controversy. His period as mathematician was begun not until he was forty years old, and was preparatory to his creative philosophical period, which was begun when he was about fifty. 1. _As a Classical Scholar_ (including his early years) (1588–1628)――the first forty years of his life. At Oxford (1603–1608); first journey abroad (1608–1612); beginning of his relations with the Devonshire family and also of his acquaintance with the “new science”; time of leisurely study (1612–1628) and acquaintance with Bacon, Herbert of Cherbury, and Ben Jonson; translation of _Thucydides_ (1628). 2. _As Mathematician_ (1628–1638). Second journey abroad (1629–1631) for eighteen months as tutor to the son of Sir Gervase Clifton; reads _Euclid_ while abroad; third journey abroad (1634–1637), when he meets Galileo; begins to develop the conception of motion and sensation; by 1638 he is counted among the notable philosophers and he meets the Parisian scientists, Mersenne and Gassendi.