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 ftated *. 
20. WE 
* Ix 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 Mogioza, 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 fubjeét, and 
each of them with confiderable probability. 
imo, One of the fignifications of xopifw, is to acquire or obtain; and hence Ieescue, 
the thing obtained or gained. Accordingly, Scarura fays, Ef vox a geometris defumpta 
qui theorema aliquid ex demonfirativo Jyllogifmo neceflario fequens inferentes, illud quafi \u- 
crari dicuntur, quod non ex profeffo quidem theorematis hujus inflituta fit demonflratio, fed 
tamen ex demonflratis reGe fequatur. In this fenfe, Evcuip-ufes the word in his Ele- 
ments of Geometry, where he calls the corollaries of his propofitions, Pors/mata. 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 correét a writer as Evcutp, and fo ferupulous in his ule of 
words, fhould employ the fame term to exprefs two ideas which are perfectly different. 
May we not therefore conjeéture, 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 [egicu« might be very properly applied, fince, in the words of 
Scapuxa, already quoted, Non ex profeffo theorematis hujus inflituta fit demonftratio, fed 
tamen ex demonflratis reéte fequatur. i 
2do, Bur though this interpretation agrees fo well with the fuppofed origin of Porifms, 
it is not free from difficulty. The verb agiu has another fignification, to find out, to 
difeover, to devife ; and is ufed in this fenfe by Parrus, when he fays, that the propofi- 
tions called Porifms, afford great delight, rois Ouvepeevors oguy xa mogiCuv, to thofe 
who are able to underfland and wwvesticatEe. Hence comes mogirpos, the act of finding 
out, or difcovering, and from wofieyec, in this fenfe, the fame author evidently confiders 
Tlogicyre as being derived. His words are, Egacay de (4 again) TMopiouc evo to megoteivoe 
pevoy et¢ Tlopizuov outs Te wpOTEWOMEVs, the ancients faid, that a Portfm ts fomething propofed for 
the FINDING OUT, or DISCOVERING of the very thing propofed. t 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 enigmatical 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 
rrutH, but alfo of the meanine of the very thing which was propofed. They may there. 
fore have been called Pori/mata or Invefligations, by way of eminence. 
