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 all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading.

I. Not to undertake to define any of the things so well known of themselves that clearer terms cannot be had to explain them.

II. Not to leave any terms that are at all obscure or ambiguous without definition.

III. Not to employ in the definition of terms any words but such as are perfectly known or already explained.

I. Not to omit any necessary principle without asking whether it is admitted, however clear and evident it may be.

II. Not to demand, in axioms, any but things that are perfectly evident of themselves.

I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it.

II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated.

III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.

These eight rules contain all the precepts for solid and immutable proofs, three of which are not absolutely necessary and may be neglected without error; while it is difficult and almost impossible to observe them always exactly, although it is more accurate to do so as far as possible; these are the three first of each of the divisions.