Page:Thoughts on art and life.djvu/178

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5.

He who blames me supreme certainty of mathematics feeds on confusion and will never be able to silence the contradictions of sophistical scimdtics ences which lead to an everlasting clamour.

6.

There is no certainty [in science] where one of the mathematical sciences cannot be applied, or in those [sciences] which are not in harmony with mathematics.

7.

Syllogism: to speak doubtfully. Sophism: to speak confusedly; falsehood for truth. Theory: knowledge without practice.

8.

Science is that discourse of the mind which derives its origin from ultimate principles beyond which nothing in nature can be found which forms a part of that science: as in the continued quantity, that is to say, the science of geometry, which, starting from the surfaces of bodies, has its origin in the line, which is the end of the superficies; and we are not satisfied by this, because we know that the line terminates in the point, and the point is that which is the least of things. Therefore the point is the first principle of geometry, and nothing else can exist either

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