For definitions. Not to define any terms that are perfectly known.
For axioms. Not to omit to require any axioms perfectly evident and simple.
For demonstrations. Not to demonstrate any things well-known of themselves.
For it is unquestionable that it is no great error to define and clearly explain things, although very clear of themselves, nor to omit to require in advance axioms which cannot be refused in the place where they are necessary; nor lastly to prove propositions that would be admitted without proof.
But the five other rules are of absolute necessity, and cannot be dispensed with without essential defect and often without error; and for this reason I shall recapitulate them here in detail.
Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition;
Not to employ in definitions any but terms perfectly known or already explained.
Rule necessary for axioms. Not to demand in axioms any but things perfectly evident.
Rules necessary for demonstrations. To prove all propositions, and to employ nothing for their proof but axioms fully evident of themselves, or propositions already demonstrated or admitted;
Never to take advantage of the ambiguity of terms by failing mentally to substitute definitions that restrict and explain them.
These five rules form all that is necessary to render proofs convincing, immutable, and to say all, geometrical; and the eight rules together render them still more perfect.
I pass now to that of the order in which the propositions should be arranged, to be in a complete geometrical series.
| After having established[1] | |
This is in what consists the art of persuading, which is comprised in these two principles: to define all the terms of
- ↑ The rest of the phrase is wanting; and all this second part of the composition, either because it was not redacted by Pascal, or because it has been lost, is found neither in our MS. nor in Father Desmolets.—Faugère
