The ... is deficient, sometimes pardonably, sometimes without excuse, in generalization. The book of , to which Diophantus sometimes refers, seems on the other hand to have been entirely devoted to the discussion of general properties of numbers. It is three times expressly quoted in the ... Of all these propositions he says... 'we find it in the Porisms'; but he cites also a great many similar propositions without expressly referring to the . These latter citations fall into two classes, the first of which contains mere , such as the algebraical equivalents of the theorems in Euclid II. ...The other class contains general propositions concerning the resolution of numbers into the sum of two, three or four squares. ...It will be seen that all these propositions are of the general form which ought to have been but is not adopted in the . We are therefore led to the conclusion that the Porismata, like the pamphlet on Polygonal Numbers, was a synthetic and not an analytic treatise. It is open, however, to anyone to maintain the contrary, since no proof of any is now extant.
James Gow (scholar)