( ( '140 ) ' 
ions of Quantities ate proportional to the nafcent Incre- 
anentiof thofe Quantities; in order to underftand that Me- 
thod throughly, I found it-necefiary toconfider well the 
Properties of Increments in general- And from thofe 
Properties 1 (aw it would be ealy to dfaw a perfect Know- 
ledge of the Method of Fluxions : for if in any cafe the 
Increments are fuppofed to vanilh and to become equal to 
: nothing, their Proportions become immediately the lame 
with the Proportions of the Fluxions. In this Method I 
• conlider Quantities, as formed by a continual Addition 
of parts of a finite Magnitude, and thofe parts I call the 
Increments of the Quantities they belong to, becaufe 
that by the. Addition -oE them the Quantities are increa- 
fed . Thefe parts being confider’d as formed in the fame 
•manner by a. continual Addition of other parts ; thence 
follows the Confideracion of fecond Increments; and (o 
on to third, fourth, and other Increments of a higher 
kind. For Example, if x (lands for auy Number 'in the 
Series oil 4 -10^20. 3 in which theNdmbersare 
formed by a continual Addirioh of the Numbers in the 
Series 1. 3. 6 . 10. 15, &c~ them the Numbers in the lat- 
ter Series are call’d the Increments of the Numbers in the 
foregoing Series; thus, for Example, if to the third 
Number (4) in the firft Series, I add the correfponding 
third Number ( 6 ) in the feebnd Series, Ilhall produce the 
next, that is the fourth Number (10) in the jfirlt Series, 
and fo the, reft. Any Number in the firft Series being 
call’d x, the : correfponcfing,Nun?her ,£wliicji its incre- 
ment) in the fecond Series Texprefs by *. And thele Num- 
bers^ being form’d in the fame -rfiaaner by the Numbers 
in the Series 1. x- 3.4, 5, &e. 1 call thefe laft j^umbers *, 
they being the firft Increments of the Numbers *, and the 
fecond increments of the Numbers x ; and foon. Hence 
having, given any Series of Numbers that are call'd by a 
general Chatafter x, their Increments are found by taking 
. . . — 1 -v 1 - 1 . : 
