On the ORIGIN of PORISMS. 155 
dertaken. They thought it fufficient to demonftrate the pro- 
pofitions, 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 propofitions were 
originally difcovered, and by which the Greek geometry was 
peculiarly diftinguifhed., 
Amone thefe few, FERmMAT and Hattey are to be particu- 
larly remarked. The former, one of the greateft mathematicians - 
of the laft age, and a man in all refpects of fuperior abilities, had 
very juft notions of the geometrical analyfis, and appears often 
abundantly fkilful in the ufe of it; yet in his reftoration of the 
Loci Plani, itis 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 fhews 
to be much rarer than might be expected, a man equally 
well acquainted with the ancient and the modern geome- 
try, and equally difpofed to do juftice to the merit of both. - 
He reftored the books of ApoLttonius, on the problem De 
SeEtione Spati, 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 Plant by Dr Simson, publithed 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 
_ Mot appear to greater advantage in the moft entire of their wri- 
_ tings, than in the reftoration above mentioned; and that 
_ Dr Simson has often facrificed the elegance to which his own 
: c, analyfis would have led, in order to tread more exactly in what 
U2 the 
