[ 3*8 ] 
blcm they had fhown how* it was to be performed : 
Far lefs did they fuppofc any thing to be done, that 
cannot be conceived to be poflible, as a Line or Series 
to be actually continued to Infinity, or a Magnitude 
to be diminifhed rill it. become infinitely lefs than it 
was. The Elements into which they refolved Mag- 
nitudes were always finite, and fuch as might be con- 
ceived to be real. Unbounded Liberties have been 
introduced of late, by which Geometry (wherein 
every thing ought to be clear) is filled with Myfteries, 
and Philofophy is like wife perplexed. Several In- 
ftanccs of this kind are mentioned. The Series i, 2, 
3,4, 5, 6, 7, &c. is fuppofed by fome to be adually 
continued to Infinity j and, after fuch a Suppofuion, 
we are puzzled with the Queflion, Whether the 
Number of finite Terms in fuch a Series is finite or 
infinite. In order to avoid fuch Suppofitions, and 
their Confequences, the Author chofe to follow the 
Antients in their Method of Demonftration as much 
as poflible. Geometry has been always confidercd 
as our fureft Bulwark againfl: the Subtleties of the 
Sceptics, who are ready to make ufe of any Advan- 
tages that may be given them againfl: it * and it is 
important, not only that the Conclufions in Geo- 
metry be true, but likewife that their Evidence be 
unexceptionable. However, he is far from affirm- 
ing, that the Method of Infinitefimals is without 
Foundation, and afterwards endeavours to juftify a 
proper Application of it. 
The Grounds of the Method of Fluxions are de- 
ferred in Chap. 1. Book I. and again in Chap. 1. 
* See Buykos Dictionary, Article Zeno. 
Book 
