72 GREEK GEOMETRY. 



This great geometrician continued at all the intervals of his 

 other labours intently to investigate the subject on which he 

 thus first threw a steady light. 



His first care upon having made this discovery was to 

 extend the particular propositions until he had obtained the 

 general one. A note among his memoranda appears to have 

 been made, according to his custom, of marking the date at 

 which he succeeded in any of his investigations.* " Hodie hfec 

 de porismatis inveni, E. S., 23 April, 1722." Another note, 

 27th April, 1722, shows that he had then obtained the general 

 proposition; he afterwards communicated this to Maclaurin 

 when he passed through Glasgow on his way to France ; and 

 he, on his return, communicated to Dr. Simson without demon- 

 stration a proposition concerning conies derived from what he 

 had shown him a proposition which led his friend to insert 

 some important investigations in his Conic Sections. In 1723 

 the publication of his paper took place in the ' Philosophical 

 Transactions ;' it is extremely short, and does not appear to 

 contain all that the author had communicated ; for we find this 

 sentence inserted before the last portion of the paper : " His 

 adjecit clarrissimus professor propositiones duas sequentes 

 libri primi Porismatum Euclidis, a se quoque restitutas." 

 The paper contains the first general proposition and its ten 

 cases, and then the second with its cases. No general descrip- 

 tion or definition is given of Porisms ; and it is plain that 

 his mind was not then finally made up on this obscure subject, 

 although he had obtained a clear view of it generally. 



At what time his knowledge of the whole became matured 

 we are not informed ; but we know that his own nature was 



* In one there is this note upon the solution of a problem of tactions, 

 " Feb 9, 1734 : Post horam primam ante meridiem ;" and much later 

 in life we find the same particularity in marking the time of discovery. 

 His birthday was October 14, and having solved a problem on that day 

 1764, he says 14 Qctobr. 1764. 



14 Octobr. 1687. 

 Deo Opt. Max. bemgmssimo Servaton 



Laus et gloria. 77 (scil. Anno ^Etatis.) 



