[ 5 “ 3 
Sect. 3. Coroll, fir ft '. 
From the Nature of Quantity we may fee what it 
is that gives Mathematics fuch Advantage over other 
Sciences, in Clearnefs and Certainty ; namely, that 
(Quantity admits of a much greater Variety of Re- 
lations than any other Subjed of human Reafoning; 
and at the fame time every Relation or Proportion 
of Quantities may by the Help of Lines and Num- 
bers be fo diftindly defined, as to be eafiiy diftin- 
guifhed from ail others, without any Danger of Mif- 
take. Hence it is that we are able to trace its Re- 
lations through a long Procefs of Reafoning, and 
with a Perfpicuity and Accuracy which we in vain 
exped in Subjeds not capable of Menfurarion. 
Extended Quantities, fuch as Lines, Surfaces and 
Solids, befides what they have in common with all 
other Quantities, have this peculiar, That their Parts 
have a particular Place and Difpofition among them- 
felves : A Line may not only bear any allignable 
Proportion to another, in Length or Magnitude, 
but Lines of the fame Length may vary in the Dif- 
pofition of their Parts; one may be freight, another 
may be Part of a Curve of any Kind or Dimenfi on, 
of which there is an endlefs Variety. The like 
may be faid of Surfaces and Solids. So that ex- 
tended Quantities admit of no lefs Variety with re- 
gard to their Form than with regard to their Mag- 
nitude : And as their various Forms may be exadly 
defined and meafured, no lefs than their Magni- 
tudes, hence it is that Geometry, which treats of ex- 
tended Quantity, leads us into a much greater Com- 
pafs and Variety of Reafoning than any other Branch 
of 
