But in any case proofs were needed; he had waited a whole month for them and grew more impatient the longer he waited.
This museum is full of proofs of the utter falsity of their views.
Of course mathematical proofs do not have personal characters.
The best proofs contain specific information and are in official documents.
His proofs are generally long and clumsy; this is accounted for in some measure by the absence of symbols and technical terms. Apollonius was ignorant of the directrix of a conic, and although he incidentally discovered the focus of an ellipse and hyperbola, he does not mention the focus of a parabola.
