C 408 3 
Logarithm from its Number, and converfely the Sine,' 
Tangent, or Secant, from the Arc, and the Number 
from its Logarithm. 
The inverfe Method is profecuted farther in the 
Third Chapter, by reducing Fluents to others of a 
more fimple Form, when they are not aflignable by 
a finite Number of Algebraic Terms. When a 
Fluent can be afligned by the Quadrature of the 
Conic Sedions, (and confequently by circular Arcs or 
Logarithms) this is confidered as the fecond Degree- 
of Refolution ; and this Subjed is treated at Length. 
An Illuftration is premifed of the Analogy betwixt 
Elliptic and Hyperbolic Sedors formed by Rays 
drawn from the Centres of the Figures: The Pro- 
perties of the latter are fometimes more eafily dis- 
covered becaufe of their Relation to Logarithms, and 
lead us in a brief manner to the analogous Properties 
of Elliptic Sedors, and particularly to fome general 
Theorems concerning the Multiplication and Divi- 
fion of circular Sedors or Arcs. When Two Points 
are afiiimed in an Hyperbola, and alfo in an Ellipfis, 
fo that the Sedors terminated by the Semi-axis ; and 
the Two Semi-diameters, belonging to thofe Points, 
are in the fame given Ratio in both Figures, then the 
Relation betwixt the Semi-axis and the Two Ordinates 
drawn from thofe Points to the other Axis, is always 
defined by the fame, or by a fimilar Equation in both 
Figures. This Propofition ferves for demonftrating 
Mr. Cotess celebrated Theorem, as it is extended by 
M. ‘De Moivre , by which a Binomial or Trinomial 
is refolved into its quadratic Divifors, and various 
Fluents are reduced to circular Arcs and Logarithms. 
The Demonfirations are alfo rendred more eafy of 
the 
