C 89] 
region always parallel to the Ordinate. Hence he in- 
fers, that the fluxion of the Ordinate is to the Fluxion 
of the Abfcifs, as the Ordinate is to the Subtangent 
of the Curve. 
Having likewife proved from the firft Suppofition, 
that if the defcribing Point, when arrived at any Place 
given, fhould continue to move onwards, with the 
Velocity it has there, it would proceed in a Right 
Line, which would touch the Curve in that Point 5 
he concludes that the Direction of the Force in that 
Place is in the Tangent to the Curve : Confequent- 
ly, the three Directions being known in each Place, 
the Proportion between the Velocities of the urging 
Forces will be likewife known. So that the Nature 
of the Curve being given, the Law obferv'd by thefe 
Velocities may be found 5 and if the Law of the Ve- 
locities be given, the Nature of the Curve may like- 
wife be given. 
Book III. 
In the third and laft Book, we have the inverfe Me- 
thod of Fluxions, with its Application to the feveral 
Problems folvable by it; fuchasthe fuperficial and fa- 
lid Contents, of Curvilineal Figures, the Redification 
of Curve Lines, Centres of Gravity, Ofcillation and 
Percuffion. Here alfo Mr. Cotes s Tables of Fluents 
are explain'd and illuftrated by Examples. 
He finifhes this Book with a great Variety of Pro- 
blems, that are of a Phyfico- Mathematical Nature, fe- 
veral of which are new, and propofed to him by Mr. 
Belidor . Some, indeed, are not fo, having been 
folved by Meffieurs Varignon and Parent but then 
he has folved them after a different, and, as he hopes, 
a more agreeable Manner, the Conftmdion bring 
more fimple, and the Procefs much {hotter. 
M III. Qfa 
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