Sentence examples for Without proofs from inspiring English sources

Patiganita consists of versified mathematical rules, without proofs, and examples arranged under the two headings parikarman ("basic operations") and vyavahara (applied or "procedural mathematics").

The scheme of Brunelleschi and Alberti, as given without proofs in Alberti's De pictura (1435; On Painting), exploits the pyramid of rays that, according to what they had learned from the Westernized versions of the optics of Ibn Al-Haytham (c. 965 1040), proceeds from the object to the painter's eye.

First, we introduce two lemmas without proofs.

Therefore, we state them without proofs.

So we state the theorems without proofs.

Now, we formulate another two lemmas without proofs.

They cried fraud, though without proof.

They are accusations without proof.

That suffices without proof or evidence.

Consumers may received $150 without proof of loss.

It's incredible what people will pay for without proof".