Rules for Demonstrations. 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.
Blaise Pascal
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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 or explain them.
Blaise Pascal
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 of 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.
Blaise Pascal
Rules for Definitions. I. Not to undertake to define any of the things so well known of themselves that the 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.
Blaise Pascal
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.
Blaise Pascal
...when we wish to demonstrate a general theorem, we must give the rule as applied to a particular case; but if we wish to demonstrate a particular case, we must begin with the general rule. For we always find the thing obscure which we wish to prove, and that clear which we use for the proof; for, when a thing is put forward to be proved, we first fill ourselves with the imagination that it is therefore obscure, and on the contrary that what is to prove it, is clear, and so we understand it easily. 40
Blaise Pascal
Pascal, Blaise
Passeroni, Giancarlo
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