C 35; 1 
Terms increafe with accelerated Motions. The Ve- 
locities of the Points that deferibe thofe Lines being 
compared, it is demonftrated from the Axioms by 
common Geometry, that the Fluxions of any Two 
Terms are in a Ratio compounded of the Ratio of 
the Terms, and of the Ratio of the Numbers that 
exprefs how many Terms precede them in the Pro- 
grellion. 
In the Vlth Chapter, the Nature and Properties of 
Logarithms are deferibed after the celebrated In- 
ventor j and it is ebferved, that he made ufe of the 
very Terms Fluxus and Fluat on this Occafion. A 
Line is faid to increafe or decreafe proportionally, 
when the Velocity of the Point, that describes it, is 
always as its Diftance from a certain Term of the 
Line ; and if in the mean time another Point deferibes 
a Line with a certain uniform Motion, the Space 
deferibed by the latter Point is always the Logarithm 
of the Diftance of the former from the given Term. 
Hence the Fluxion of this Diftance is to the Fluxion 
of its Logarithm as that Diftance is to an invariable 
Line ; and the Fluxions of the Quantities that have 
their Logarithms in an invariable Ratio , are to each 
other in a Ratio compounded of this invariable 
Ratio , and of the Ratio of the Quantities them- 
felves. Some Proportions are demonftrated, that 
relate to the Computation of Logarithms, but this 
Subjed is profecuted farther in the Second Book. 
The Logarithmic Curve is here deferibed, with the 
Analogy betwixt Logarithms and Hyperbolic Ratios. 
In the Vllth Chapter, after a general Definition of 
Tangents, it is demonftrated, that the Fluxions of the 
Bafe, Ordinate, and Curve, are in the fame Propor- 
U u 2 tion 
