My aim is... to place before a young student a nucleus of…

A student of history, who cares little for Greek or mathematics in particular, but who likes to watch how things grow, will be able to extract from these pages a notion of the whole history of mathematical science down to Newton's time...

The solution of the higher indeterminates depends almost entirely on very favourable numerical conditions and his methods are defective. But the extraordinary ability of Diophantus appears rather in the other department of his art, namely …

The history of Greek mathematics is, for the most part, only the history of such mathematics as are learnt daily in all our public schools. ...If it was not wanted, as it ought to have been, by our classical professors and our …

The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries.

Probably Greek logistic, or calculation, extended to more difficult operations... and... probably Greek arithmetic, or theory of numbers, owed much more to induction than is permitted to appear by its first and chief professors.

With Diophantus the history of Greek arithmetic comes to an end. No original work, that we know of, was done afterwards.