C w ] 
Second Book, is, that when the Firft Fluxion of the 
Ordinate, with its Fluxions of any fubfequent fuc- 
cefllve Orders, vanifh, and the Number of all thefe 
Fluxions that vanifh is odd, then the Ordinate is a 
Maximum or Minimum , according as the Fluxion 
of the next Order to thefe is negative or pofitive. 
The Ordinate pahes through a Point of contrary 
Flexure, when its Fluxion becomes a Maximum or 
Minimum , fuppofing the Curve to be continued on 
both Sides of the Ordinate. Hence the common 
Rule for finding the Points of contrary Flexure is 
corrected in a iimilar manner. Such a Point is not 
always formed when the Second Fluxion of the Or- 
dinate vanifhes j for if its Third Fluxion likewife 
vanifhes, and its Fourth Fluxion be real, the Curve 
may have its Cavity turned all oneWay. The fame is 
to be faid, when its Fluxions of the fubfequent fuc- 
ceflive Orders vanifh, if the Number of all thofe that 
vanifh be even. Other Theorems are fubjoined re- 
lating to this Subjed. 
The Xth Chapter treats of the Afymptotes of Lines, 
the Areas bounded by them and the Curves, the 
Solids generated by thefe Areas, of fpiral Lines, and 
the Limits of the Sums of Progreilions. The Ana- 
logy there is betwixt thefe Subjeds, induced the Au- 
thor to treat of them in one Chapter, and illuftrate 
them by one another. He begins with Three of the 
molt fimple Inflances of Figures that have Afymptotes* 
In the common Hyperbola, the Ordinate is recipro- 
cally as the Bafe, and therefore decreafes while the 
Bafe increafes, but never vanifhes, becaufe the Red» 
angle contained by it and the Bafe is always a given 
Area, and it is allignable at any allignable Diftance, 
how 
