James Gow (scholar)

"It was Pythagoras who discovered that the 5th and the octave of a note could be produced on the same string by stopping at 2⁄3 and ½ of its length respectively. Harmony therefore depends on a numerica…"

"Though the defects in Diophantus' proofs are in general due to the limitation of his symbolism, it is not so always. Very frequently indeed Diophantus introduces into a solution arbitrary conditions a…"

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

"Sometimes... Diophantus solves a problem wholly or in part by synthesis. ...Although ...Diophantus does not treat his problems generally and is usually content with finding any particular numbers whic…"

"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 t…"

"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…"

"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 mathema…"

"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."