( i8r ) 
m 
m 
fro pc, fiet a x^=y. Quart e contract ax” —y erit —j— a x tt 
— z Q. E. D. 
By the fame way of working the fecond Rule may be al- 
fo demonftrated. And if any Equation whatever be affix- 
med expreffing the Relation between the Abfcifla and Area of 
a Curve, the Ordinate may be found in the fame manner, as 
is mentioned in the next Words of the Analyfis. And if 
this Ordinate drawn into an Unit be put for the Area of a 
new Curve, the Ordinate of this new Curve may be found 
by the fame Method : And fo on perpetually. And thefe 
Ordinates reprefent the firft, fccond, third, fourth and fol- 
lowing Fluxions of the firft Area. 
This was Mr. Kenton* s Way of working in thofe Days, 
when he wrote this Compendium of his Analjfis. And the 
fame Way of working he ufed in his Book of Quadratures, 
and ftiJl ufes to this Day. 
Among the Examples with which he illuflrates the Method 
of Series and Moments fet down in this Compendium, are 
thefe. Let the Radius of a Circle be i, and the Arc z, and 
the Sine x, the Equations for finding the Arc whofe 
Sine is given, and the Sine whofe Arc is given, will be 
Mr. Collins gave Mr. Gregory jiotice of this Method 
jn Autumn 1669, and Mr. Gregory, by the Help of one of 
Mr. Kentons Series, after a Year’s Study, found the Method 
in December 1670 5 and two Months after, in. a Letter dated 
Feb. 15. 1671. fent feveral Theorems, found thereby, to 
Mr. Collins , with leave to communicate them freely. And 
Kir. Collins was very free in communicating what he had re- 
ceived both from Mr. Nenton and from Mr. Gregory , as ap- 
pears by his Letters printed in the Commercium. Amongfl: 
the Series which Mr Gregory fent in the laid Letter, were 
thefe 
