174 On the ORIGIN and 



quire to be pointed out , and I have only to obferve, that it 

 was not long after the publication of Simson's pofthumous 

 works, when, being both of us occupied in fpeculations con- 

 cerning Porifms, we were led feparately to the conclufions 

 which I have now dated *. 



20. We 



* In an enquiry into the origin of Porifms, the etymology of the term ought not to 

 be forgotten. The queftion indeed is not about the derivation of the word Uc,^tTft,x, for 

 concerning that there is no doubt; but about the reafon why this term was applied to the 

 clafs of propofitions above defcribed. Two opinions may be formed on this fubje£t, and 

 each of them with confiderable probability. 



imo, One of the fignifications of wef»£», is to acquire or obtain; and hence Yloejurpu, 

 the thing obtained or gained. Accordingly, Scapula fays, EJl vox a geometris defumpta 

 qui theorema aliquid ex demonf rativo fyllogifrno neceffario fquens infer entes, illud quaji lu- 

 crari dicuntur, quod non ex profejfo quidem theorematit hujus injlituta Jit demon/1 ratio, fed 

 tamen ex demonjlratis reile fequatur- In this fenfe, Euclid ufes the word in his Ele- 

 ments of Geometry, where he calls the corollaries of his propofitions, Porifmata. This 

 circumftance creates a prefumption, that when the word was applied to a particular 

 clafs of propofitions, it was meant, in both cafes, to convey nearly the fame idea, as it is 

 not at all probable, that fo correct a writer as Euclid, and fo fcrupulous in his ufe of 

 words, mould employ the fame term to exprefs two ideas which are perfectly different. 

 May we not therefore conjecture, that thefe propofitions got the name of Porifms, en- 

 tirely with a reference to their origin. According to the idea explained above, they 

 would in general occur to mathematicians when engaged in the folution of the more 

 difficult problems, and would arife from thofe particular cafes, where one of the con- 

 ditions of the data involved in it fome one of the reft. Thus, a particular kind of theo- 

 rem would be obtained, following as a corollary from the folution of the problem; and to 

 this theorem the term rio^/*" might be very properly applied, fince, in the words of 

 Scapula, already quoted, Non ex profejfo theorematis hujus infituta fit demonf ratio, fed 

 tamen ex demonf ratis recle fequatur. 



2do, But though this interpretation agrees fo well with the fuppofed origin of Porifms, 

 it is not free from difficulty. The verb -bo^u has another fignification, tofndout, to 

 difcover, to devife ; and is ufed in this fenfe by Pappus, when he fays, that the propofi- 

 tions called Porifms, afford great delight, toij lv\-«.y.iioi% o%uv xxi nogi£nr, to thofe 

 ivho are able to underf and and investigate. Hence comes ttojic-^o?, the aci of fnding 

 out, or difcovering, and from wopcyo?, in this fenfe, the fame author evidently confiders 

 JlocKrpx as being derived. His words are, E<pa<rav 3e («< «f%a.oi) Ho^o-/mi ttvai ro -arfOTEivo- 

 (itvov £ij UoptffJLOV auTX ts , CTfOT£ivo l a£V8, the ancients f aid, that a Porifn isfometbing propofd for 

 the finding out, or discovering of the very- thing propofed. It feems fingular, however, 

 that Porifms fhould have taken their name from a circumftance common to them with fo 

 many other geometrical truths ; and if this was really the cafe, it muft have been on ac- 

 count of the aenigmatical form of their enunciation, which required, that in the ana- 

 lyfis of thefe propofitions, a fort of double difcovery fhould be made, not only of the 

 truth, but alfo of the meaning of the very thing which was propofed. They may there, 

 fore have been called Porifmata or Invefigations, by way of eminence. 



