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.

P. 330) on Euclid's **Porisms** (q.v.).