On the ORIGIN of PORISMS. i 



:o 



dertaken. They thought it fufficient to demonftrate the pro- 

 portions, which they knew from Pappus, to have been contained 

 in thofe books*; but they did not follow the ancient method of 

 inveftigation, and few of them appear to have had any idea of 

 the elegant and fimple analyfis by which thefe proportions were 

 originally difcovered, and by which the Greek geometry was 

 peculiarly diftinguifhed.. 



Among thefe few, Fermat and Halle y are to be particu- 

 larly remarked. The former, one of the greateft mathematicians 

 of the laft age, and a man in all refpecls of fuperior abilities, had 

 very juft notions of the geometrical analyfis, and appears often 

 abundantly fkilful in the ufe of it ; yet in his restoration of the 

 Loci Plani, it is remarkable, that in the moft difficult propofi- 

 tions, he lays afide the analytical method, and contents himfelf 

 with giving the fynthetical demonftration. The latter, among 

 the great number and variety of his literary occupations, 

 found time for a moft attentive ftudy of the ancient ma- 

 thematicians, and was an inftance of, what experience (hews 

 to be much rarer than might be expecled, a man equally 

 well acquainted with the ancient and the modern geome- 

 try, and equally difpofed to do juflice to the merit of both. 

 He reftored the books of Apollonius, on the problem De 

 Setlione Spatii, according to the true principles of the ancient 

 analyfis. 



These books, however, are but fhort, fo that the firft re- 

 ftoration of confiderable extent that can be reckoned complete, 

 is that of the Loci Plani by Dr Simson, publifhed in 1749, 

 which, if it differs at all from the work it is intended to re- 

 place, feems to do fo only by its greater excellence. This much 

 at leaft is certain, that the method of the ancient geometers does 

 not appear to greater advantage in the moft entire of their wri- 

 tings, than in the rcftoration above mencioned ; and that 

 Dr Simson has often facrificed the elegance to which his own 

 analyfis would have led, in order to tread more exactly in what 



U 2 the 



