"Few contemporaries were as profoundly read in the history of mathematics as was De Morgan. No subject was too insigni…"

"One who extended the theory of equations somewhat further than Vieta was Albert Girard... Like Vieta this ingenious a…"

"A more modern attempt to explain the fruitfulness of mathematical reasoning is that of Poincaré, who finds it all due…"

"The propositions of arithmetic, the... operations, for instance, which play such a fundamental rôle even in the most …"

"It is significant that we owe the first explicit formulation of the principle of recurrence to the genius of Blaise P…"

"Despite the age-long tyranny exercised by the Aristotelian logic... Of all argument forms, there is one which, viewed…"

"This procedure is the demonstration by recurrence. We first establish a theorem for n = 1; then we show that if it is…"

"We can not... escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contr…"

"But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by in…"

"We could call it "proof from n to n + 1" or still simpler "passage to the next integer." Unfortunately, the accepted …"