t 4*° ] 
Ratio , and increafing or diminilbing the Angles con- 
tained by them and the Perpendicular in the fame 
Ratio . From any Figure of this kind a Series of 
Figures is derived by determining the Interfedions of 
the Tangents of the Figure with the Perpendiculars 
from the Centre. Every Series of this kind gives 
Two diflind fort of Fluents; and any one Fluent 
being given, all the other Fluents taken alternately 
from it in the Series depend upon it, or are mea- 
fured by it; but it does not appear, that the Fluents 
of one fort can be compared with thofe of the other 
fort, or with thofe of any different Series of this 
kind. 
The inverfe Method is profecuted farther in the 
4th Chapter, by various Theorems concerning the 
Area when the Ordinate is expreffed by a Fluent, or 
when the Ordinate and Bafe are both exprefled by 
Fluents. The Firft is the Xlth Propofition of Sir 
Ifaac Newtons Treatife of Quadratures. In Art. 
819, 820 , &c. the Author fuppofes the Ordinate 
and Bafe to be both exprefled by Fluents, and fhews, 
in many Cafes, that the Area may be afligned by the 
Produd of Two Ample Fluents, as of Two circular 
Arcs, or of a circular Arc and a Logarithm. This 
Subjed deferves to be profecuted, becaufe the Refo* 
lution of Problems is rendered more accurate and 
Ample, by reducing Fluents to the Produds of Flu- 
ents already known, than by having immediately 
recourfe to infinite Series. One of the Examples in 
Art. 822. may be eafily applied for demonflrating, 
that the Sum of the Fradions which have Unit for 
their common Numerator, and the Squares of the 
Numbers 1, 2, 3, 4, 5, 6, &c. in their natural Order, 
