204 On the ORIGIN, &e. 
as a vice that naturally arifes out of the excellence of the mo- 
dern analyfis. The effect which this has had, in concealing 
from us the clafs of propofitions we are now confidering, can- 
not be better illuftrated than by the example of the Porifm 
difecovered by Boscovicn, in the manner related above. 
Though the problem from which that Porifm is derived, was 
refolved by feveral mathematicians of the firft eminence, among 
whom alfo was Sir IsAAc Newron, yet the Porifm which, as it 
happens, is the moft important cafe of it, was not obferved by 
any of them. This is the more remarkable, that Sir Isaac 
NewTon takes notice of the two moft fimple cafes, in which 
the problem obvioufly admits of innumerable folutions, v7z. 
when the lines given in pofition are either all parallel, or all 
meeting in a point, and thefe two hypothefes he therefore ex- 
prefsly excepts. Yet he did not remark, that there are other 
circumftances which may render the folution of the problem 
indeterminate, as wellas thefe ; fo that the porifmatic cafe confi- 
dered above, efcaped his obfervation: And if it efcaped the ob- 
fervation of one who was accuftomed to penetrate fo far into 
matters infinitely more obfcure, it was becaufe he fatisfied him- 
felf with a general -conftruGtion, without purfuing it into its 
particular cafes. Had the folution been conducted after the 
manner of Evciip or Apovtontus, the Porifm in queftion 
muft infallibly have been difcovered. 
Burt I have already extended this paper to too great a length ; 
fo that, leaving the ufe of algebra in the inveftigation of Po- 
rifms, to be treated of on another occafion, I fhall conclude: 
with a remark from Pappus, the truth of which, I would wil- 
lingly flatter myfelf, that the foregoing obfervations have had 
fome tendency to evince: “ Habent autem Porifmata fubtilem 
‘“ et naturalem contemplationem, neceflariam et maxime uni- 
“ verfalem, atque iis, qui fingula perfpicere et invettigare valent, 
* admodum jucundam.” 
VIII. 
_ a 
