III. The philosophic importance of the Copernican system first perceived by Giordano Bruno, 382—How it led to a revival of Atomism, 383—Common pantheistic tendency of the anti-Aristotelian schools, 384—The analytical method applied to mathematics, 385—Survival of Aristotelian ideas in the physics of Galileo, 385—His affinities with Plato, 386—Influence of Platonic ideas on Kepler, 387. IV. Descartes’ theory of Matter derived from the _Timaeus_, 388—and developed under the influence of Democritus, 389—How the identification of Matter with Extension led to its complete separation from Thought, 390—The denial of final causes a consequence of this separation, 390—Difference between the Cartesian and Baconian views of teleology, 391—Doctrine of animal automatism, 391—Localisation of feeling in the brain, 392—The _Cogito ergo sum_ and its antecedents in Greek philosophy, 392—Descartes interprets Thought after the analogy of Extension, 393—Revival of the Stoic and Epicurean materialism: transition to Hobbes, 394. V. Hobbes not a link between Bacon and Locke, 395—The different meanings which they respectively attached to the notion of experience, 395—Deductive and mathematical method of Hobbes, 396—His opposition to the ethics of Aristotle, 397—His identification of happiness with power, 398—Subordination of the infinite to the finite in Greek philosophy, 398—Contrast offered by the illimitable aspirations of the Renaissance, 399—Elements out of which Spinozism was formed, 400. VI. Platonic method of Spinoza, 401—The limiting principles of Greek idealism, 402—Their tendency to coalesce in a single conception, 403—Similar result obtained by an analysis of extension and thought, 404—Genesis of Spinoza’s Infinite Substance, 405—The uses of unlimited credit in metaphysics, 406—Spinoza’s theory of cognition, 407—The identity of extension and thought, 408. VII. Influence of Aristotle’s logic on Spinoza, 409—Meaning of ‘the infinite intellect of God,’ 410—Contingency as a common property of extension and thought, 411—The double-aspect theory not held by Spinoza, 412—The distinction between necessity and contingency in its application to ethics, 413—The study of illusion in Malebranche and Molière, 414—Intellectual character of Spinoza’s ethics, 415—Parallel between knowledge and virtue, 416—Enumeration of the Greek elements in Spinoza’s philosophy, 417. VIII. The place of Scepticism in Greek thought, 418—Parallel between Locke and the New Academy, 419—Results obtained by a complete application of the analytical method, 420—Close connexion between philosophy and positive science, 420—Increased prominence given to ethical and practical interests by the method of Locke, 421—The idea of Nature and the revival of teleology, 422—New meaning given to hedonism by modern philosophy, 423—The Stoic side of modern utilitarianism, 423—Different combinations of the same ideas in ancient and modern systems, 425.