202 On the ORIGIN and 
has it arifen, that propofitions which are in themfelves fo im- 
portant, and that aétually occupied fo confiderable a place in 
the ancient geometry, have been fo little remarked in the mo- 
dern? It cannot indeed be faid, that propofitions of this kind 
were wholly unknown to the moderns before the reftoration of 
what Evctip had written concerning them ; for befide M. Bos- 
covicu’s propofition, of which fo much has been already faid, the 
theorem which afferts, that in every fyftem of points there is a” 
centre of gravity, has been fhewn above to bea Porifm ; and we 
fhall fee hereafter, that many of the theorems in the higher geo- 
metry belong to the fame clafs of propofitions. We may add, that 
fome of the elementary propofitions of geometry want only the 
proper form of enunciation to be perfect Porifms. It is not there- 
fore ftriatly true, that none of the propofitions called Porifms have 
been known to the moderns; but it is certain, that they have 
not met, from them, with the attention they met with, from 
the ancients, and that they have not been diftinguifhed as 
a feparate clafs of propofitions. The caufe of this difference is - 
undoubtedly to be fought for in a comparifon of the methods 
employed for the folution of geometrical problems in ancient, | 
and in modern times. 
In the folution of fuch problems, the geometers of antiquity 
proceeded with the utmoft caution, and were careful to remark 
every particular cafe, that is to fay, every change in the con- 
ftruction, which any change in the ftate of the data could pro- 
duce. . The different conditions from which the folutions were 
derived, were fuppofed to vary one by one, while the others 
remained the fame; and all their poffible combinations being 
thus enumerated, a feparate folution was given, wherever any 
_confiderable change was obferved to have taken place. 
This was fo much the cafe, that the /ectio rationis, a geo- 
metrical problem of no great difficulty, and one of which the 
folution would be difpatched, according to the methods of the 
modern geometry, in a fingle page, was made, by APoLLo- 
NIUS, 
