69 
number Prop. 17 and 20, Book III ; Prop. 20 and 44, Book 
IV ; and lastly Prop. 12, Book YI . 
In this resume of the “ Porismes cites par Diophante ” he 
again refers to the lost treatise from which Diophantus is 
supposed to have quoted ; and he here claims to have been 
the first who had fully understood the nature of these pro- 
perties of numbers. 
He there says : — “ Diophante ne parle pas expressement 
des Porismes, comme Proclus, et n’a pas a les definir. Mais 
il cite dan ses Questions Arithmetiques sous le titre de 
Porismes, des propositions extraites dun ouvrage, apparem- 
ment d’un Recueil de Porismes, qui ne nous est pas parvenu . 
Ces propositions, auxquelles je crois que Ton n’avait jamais 
fait attention, du moins a titre de Porismes dans le sens 
d’Euclide, avant que nous les eussions signalees dans YApergu 
Historique, se rapportent aux proprietes des nombres ; et ce 
qui a de l’interet ici, c’est que, sons le nom de Porismes , 
elles ont dans leurs ^nonces la forme des Donnees, la meme 
que nous attribuons aux Porismes” 
This point is of some importance in the history of the 
restoration of the Porisms ; and hence M. Chasles’s claim to 
this discovery cannot be allowed. I possess a copy of a 
letter (the original is in the Chetham Library), from the 
Rev. Charles Wildbore, sometime editor of the Gentlemans 
Mathematical Diary, to the Rev. J ohn Lawson, then 
Rector of Swanscombe, Kent, and brother of the Rev. 
Charles Lawson, Head Master of the Grammar School, 
Manchester, which announces the same discovery. The 
essential portions of this letter, and of the one which 
gave rise to it, will render this sufficiently clean 
Mr. Wildbore was a geometer of a very high order,* and he 
had been engaged on Porisms before it became known that 
Dr. Simson had restored them. Mr. Lawson in a letter to 
him, dated “August 10th, 1775,” says “I have very important 
*See his investigation of “ Lawson’s Theorems,” in the Manchester Memoirs 
Vol. II. N.S. pp. 414 — 452. 
