Sentence examples for direct proofs from inspiring English sources

In his Ḥall shukūk fī Kitāb Uqlīdis ("Solution of the Difficulties of Euclid's Elements") Ibn al-Haytham investigated particular cases of Euclid's theorems, offered alternative constructions, and replaced some indirect proofs with direct proofs.

New (direct) proofs for some criteria are provided.

In the class direct proofs, one "freezes the coefficients" with constant coefficients.

Some new results or new simple (direct) proofs of previous criteria are provided.

Bolzano thinks that indirect proofs can be transformed into direct proofs through the simplification of the false propositions contained in them.

The direct proofs of the existence of this kind of active oxygen species were given by our H2-TPR and O2-TPD experiments.

But he offered no direct proof.

Though no direct proof was established, within 10 years Roosevelt's population was nearly all black.

But direct proof against him that rises to American legal standards has been hard to obtain.

Besides, most times even direct proof isn't enough for some men.

He has said this many times – and he mentions me as direct proof.