[ 337 3 
amounts to a certain finite Magnitude (as, while the 
Tangent increafes, the Arc incrcafes, but never 
amounts to a Quadrant) ; this is applied fucceffively 
to the feveral Subje&s mentioned in the Title of the 
Chapter. Let the Figure be concave towards the 
Bale, and fuppofe it to have an Afymptote parallel 
to the Bafe; in this Cafe the Ordinate always in- 
creafes while the Bafe is produced, but never amounts 
to the Diftance between the Afymptote and the Bafe. 
In like manner a curvilineal Area, in a Second Figure, 
may increafe, while the Bafe is produced, and ap- 
proach continually to a certain finite Space, but never 
amount to it: This is always the Cafe, when the 
Ordinate of this latter Figure is to a given right Line, 
as the Fluxion of the Ordinate of the former is to 
the Fluxion of the Bafe ; and of this various Ex- 
amples are given. A Solid may increafe in the fame 
manner, and yet never amount to a given Cube or 
Cylinder, when the Square of the Ordinate of the 
latter Figure is to a given Square, as the Fluxion of 
the Ordinate of the firft Figure is to the Fluxion of 
the Bafe. A Spiral may in like manner approach to 
a Point continually, and yet in any Number of Re- 
volutions never arrive at it; and there are Progrefi 
lions of Fra&ions that may be continued at Pleafure, 
and yet the Sum of the Terms may be always lefs 
than a given Number. Various Rules are demon* 
ftrated, and illuftrated by Examples, for determining 
when a Figure has an Afymptote parallel or oblique 
to the Bafe; when the Area terminated by the Curve 
and the Afymptote has a Limit which it never ex- 
ceeds, or may be produced till it furpafs any aflign- 
able Space ; when the Solid generated by that Area, 
the 
