On the other hand the Porisms, to which Diophantus makes three references ("we have it in the Porisms that.
The "Porisms" quoted are interesting propositions in the theory of numbers, one of which was clearly that the dif f erence between two cubes can be resolved into of two cubes.
The book is valuable also for the propositions in the theory of numbers, other than the "porisms," stated or assumed in it.
Each of these was divided into two books, and, with the Data, the Porisms and Surface-Loci of Euclid and the Conics of Apollonius were, according to Pappus, included in the body of the ancient analysis.
With the mention of the Porisms of Euclid we have an account of the relation of porism to theorem and problem.