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 which have once been avowed remain firm, and without being ever contradicted.

But as there are few principles of this kind, and as, apart from geometry, which deals only with very simple figures, there are hardly any truths upon which we always remain agreed, and still fewer objects of pleasure which we do not change every hour, I do not know whether there is a means of giving fixed rules for adapting discourse to the inconstancy of our caprices.

This art, which I call the art of persuading, and which, properly speaking, is simply the process of perfect methodical proofs, consists of three essential parts: of defining the terms of which we should avail ourselves by clear definitions; of proposing principles or evident axioms to prove the thing in question; and of always mentally substituting in the demonstrations the definition in the place of the thing defined.

The reason of this method is evident, since it would be useless to propose what it is sought to prove, and to undertake the demonstration of it, if all the terms which are not intelligible had not first been clearly defined; and since it is necessary in the same manner that the demonstration should be preceded by the demand for the evident principles that are necessary to it, for if we do not secure the foundation we cannot secure the edifice; and since, in fine, it is necessary in demonstrating mentally, to substitute the definitions in the place of the things defined, as otherwise there might be an abuse of the different meanings that are encountered in the terms. It is easy to see that, by observing this method, we are sure of convincing, since the terms all being understood, and perfectly exempt from ambiguity by the definitions, and the principles being granted, if in the demonstration we always mentally substitute the definitions for the things defined, the invincible force of the conclusions cannot fail of having its whole effect.

Thus, never can a demonstration in which these conditions have been observed be subject to the slightest doubt; and never can those have force in which they are wanting.

It is, therefore, of great importance to comprehend and to possess them; and hence, to render the thing easier and more practicable, I shall give them all in a few rules which include