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224 Meyer, "Lucian disposed of the whole in a jest by making a radical doubter be sold as a slave, and still doubt under the lash of slavery."

"But what does Descartes mean," asked Oldenburg, "by his unprofitable dicing with quadrangles, triangles, and the devil knows what angles?"

"Mathematical proof," answered Meyer, "is alone admissible. The definitions are the exact representations of an object described with its name and attributes; the postulates and axioms by which the proposition is proved are such truisms that whoever knows the alphabet must see them."

"You must come yet nearer, and be yet more definite," interposed Spinoza. "Definitions merely affirm the essence of a thing; attributes cannot be learned by definitions, they must be learned by experience. By mathematical laws alone can we understand and follow up all things, all processes of both the external and internal world. Everything is the necessary and inevitable result of its primal cause. Mathematical truths alone have the same inherent necessity and external evidence as our consciousness of ourselves. By the same means that I know certainly that I am, I also know that the three angles of a triangle are equal to two right angles. The intricacies of higher mathematical problems make no difference, for they all rest on the same simple and incontrovertible principles, and every link of their necessary progress is as