C 1*7 3 
chiefly in the Geometry of Curve-lines. As firft, he 
determines the maxima and minima of Quantities in 
all Cafes, and propofes (ome elegant Problems to il- 
luftrate this Do&rine. Then he teaches us to draw 
Tangents to Curves, whether Geometrical or Media- 
nical, and that after a great Variety of Ways, or how- 
ever the Nature of the Curve may be defined. Here 
likewife he propofes fome Queftions, to exercife and 
improve the Learner : Then is very particular upon 
finding the Quantity of Curvature, at any Point of 
a given Curve, whether Geometrical or Mechanical, 
or in determining the Centre and the Radius of 
Curvature : To which feveral other curious Specula- 
tions are fub join'd of a like Nature. Here he com- 
municates a very elegant and intirely new Problem, 
for determining die Quality of the Curvature, at any 
Point of a given Curve ; or how the Curvature pro- 
ceeds in refped of its greater or lefs Inequability. 
Afterwards he goes on to the Quadrature of Curves,, 
which chiefly gives occafion to apply the inverfe Me- 
thod of Fluxions. And firft he (hews how, by the 
direft Method, to find as many Curves as you pleafe, 
(or to determine their Equations) the Areas of which; 
fhall be capable of an exad Quadrature. Then he 
(hews how to find as many Curves as you pleafe, 
which, tho' not capable of a juft Quadrature, yet 
their Areas may be compared to thofe of the Conic 
Se&ions, or of fuch other Curves as (hall be aflignkh. 
Laftly, He (hews how to determine in general the 
Area of any Curve that fhall be propofed, chiefly by 
the Method of Infinite Series 5 where many curious 
and ufeful Speculations are occafionally introduced, 
and inferted As how to afcertain the Limits of aa 
Area, 
