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TWO:No computations, drawings, or demonstrations of any kind will be employed to relieve the mind of the reader from the care of remembering and a dependence on his own exertions. Drawings, constants, formul?, tables, rules, with all that pertains to computation in mechanics, are already furnished in many excellent books, which leave nothing to be added, and such books can be studied at the same time with what is presented here.

TWO:We are now in a position to understand the full force of Descartes�� Cogito ergo sum. It expresses the substantiality of self-conscious Form, the equal claim of thought with extension to be recognised as an element of the universe. This recognition of self-consciousness as the surest reality was, indeed, far from being new. The Greek Sceptics had never gone to the length of doubting their own personal existence. On the contrary, they professed a sort of subjective idealism. Refusing to go beyond their own consciousness, they found in its undisturbed self-possession the only absolute satisfaction that life could afford. But knowledge and reality had become so intimately associated with something independent of mind, and mind itself with a mere reflection of reality, that the denial of an external world393 seemed to the vulgar a denial of existence itself. And although Aristotle had found the highest, if not the sole absolute actuality in self-thinking thought, he projected it to such a distance from human personality that its bearing on the sceptical controversy had passed unperceived. Descartes began his demonstration at the point where all the ancient systems had converged, but failed to discover in what direction the conditions of the problem required that they should be prolonged. No mistake can be greater than to regard him as the precursor of German philosophy. The latter originated quite independently of his teaching, though not perhaps of his example, in the combination of a much profounder scepticism with a much wider knowledge of dogmatic metaphysics. His method is the very reverse of true idealism. The Cogito ergo sum is not a taking up of existence into thought, but rather a conversion of thought into one particular type of existence. Now, as we have seen, all other existence was conceived as extension, and however carefully thought might be distinguished from this as absolutely indivisible, it was speedily reduced to the same general pattern of inclusion, limitation, and expansion. Whereas Kant, Fichte, and Hegel afterwards dwelt on the form of thought, Descartes attended only to its content, or to that in which it was contained. In other words, he began by considering not how he thought but what he thought and whence it came��his ideas and their supposed derivation from a higher sphere. Take, for example, his two great methods for proving the existence of God. We have in our minds the idea of a perfect being��at least Descartes professed to have such an idea in his mind,��and we, as imperfect beings, could not have originated it for ourselves. It must, therefore, have been placed there by a perfect being acting on us from without. It is here taken for granted that the mechanical equivalence between material effects and their causes must obtain in a world where spatial relations, and therefore measurement, are presumably394 unknown. And, secondly, existence, as a perfection, is involved in the idea of a perfect being; therefore such a being can only be conceived as existing. Here there seems to be a confused notion that because the properties of a geometrical figure can be deduced from its definition, therefore the existence of something more than a simple idea can be deduced from the definition of that idea itself. But besides the mathematical influence, there was evidently a Platonic influence at work; and one is reminded of Plato��s argument that the soul cannot die because it participates in the idea of life. Such fallacies were impossible so long as Aristotle��s logic continued to be carefully studied, and they gradually disappeared with its revival. Meanwhile the cat was away, and the mice used their opportunity.

TWO:She came at length breathless with running to the end of the garden. A little green gate led to the lane which divided Lytton Avenue from the corner house. It was absolutely quiet there. Leona Lalage could catch just the faintest humming noise, then a glaring white eye flamed out.