Editing Diophantus (section)

==Other works==
Another work by Diophantus, ''On Polygonal Numbers'' is transmitted in an incomplete form in four Byzantine manuscripts along with the ''Arithmetica''.{{sfn|Christianidis|Oaks|2023|p=11}} Two other lost works by Diophantus are known: ''Porisms'' and ''On Parts''.{{sfn|Christianidis|Oaks|2023|p=15}} 

Recently, [[Wilbur Knorr]] has suggested that another book, ''Preliminaries to the Geometric Elements'', traditionally attributed to [[Hero of Alexandria]], may actually be by Diophantus.<ref>Knorr, Wilbur: Arithmêtike stoicheiôsis: On Diophantus and Hero of Alexandria, in: Historia Matematica, New York, 1993, Vol.20, No.2, 180-192</ref>

===On polygonal numbers===
This work on [[polygonal number]]s, a topic that was of great interest to the [[Pythagoreans]] consists of a preface and five propositions in its extant form.{{sfn|Christianidis|Oaks|2023|p=10-11}} The treatise breaks off in the middle of a proposition about how many ways a number can be a polygonal number.{{sfn|Christianidis|Oaks|2023|p=11}}

===The ''Porisms''===
The ''Porisms'' was a collection of [[Lemma (mathematics)|lemmas]] along with accompanying proofs. Although ''The Porisms'' is lost, we know three lemmas contained there, since Diophantus quotes them in the ''Arithmetica'' and refers the reader to the ''Porisms'' for the proof.{{sfn|Christianidis|Oaks|2023|p=15}} 

One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i.e. given any {{math|''a''}} and {{math|''b''}}, with {{math|''a'' > ''b''}}, there exist {{math|''c'' and ''d''}}, all positive and rational, such that

:{{math|''a''{{sup|3}} − ''b''{{sup|3}} {{=}} ''c''{{sup|3}} + ''d''{{sup|3}}}}.

===''On Parts''===
This work, on [[fractions]], is known by a single reference, a [[Neoplatonic]] [[scholia|scholium]] to [[Iamblichus]]' treatise on [[Nicomachus]]' ''[[Introduction to Arithmetic]]''.{{sfn|Christianidis|Oaks|2023|p=15}} Next to a line where Iamblichus writes "Some of the Pythagoreans said that the [[Unit (number)|unit]] is the borderline between number and parts" the scholiast writes "So Diophantus writes in ''On Parts'', for parts involve progress in diminution carried to infinity."{{sfn|Christianidis|Oaks|2023|p=15}}