204 On the ORIGIN, &c. 



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 proportions we are now considering, can- 

 not be better illuftrated than by the example of the Porifm 

 difcovered by Boscovich, 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 Newton, yet the Porifm which, as it 

 happens, is the mod 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 mod fimple cafes, in which 

 the problem obvioufly admits of innumerable folutions, viz. 

 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 well as 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 conftrudlion, without purfuing it into its 

 particular cafes. Had the folution been conducted after the 

 manner of Euclid or Apol-lonius, the Porifm in queftion 

 muft infallibly have been difcovered. 



But 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 (hall 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. 



