C ?5 7 ] 
Maxima or Minima, and the Solid of lead Refiftance, 
are refolved without Computations, from the firft 
Fluxions only. There are alfo eafy fynthetic Demon* 
^rations fubjoined, becaufe this Theory is commonly 
efteemed of an abftrufe Nature, and Miftakes have 
been more frequently committed in the Profecution 
of it, than of any other relating to Fluxions. To 
give fome Idea of the Author's Method, fuppofe the 
Gravity to a& in parallel Lines, a to denote the Ve- 
locity acquired at the lowermoft Point of the Curve, 
and u the Velocity acquired at any other Point of the 
Curve. Suppofe the Element of the Curve to be dc- 
feribed by this Velocity u , but the Element of the 
Bafe to be always deferibed by the conftant Velocity 
a. Then it is eafily demonftrated without any Com- 
putation, that the Element of the Ordinate being 
given, the Difference of the Times in which the 
Elements of the Curve and Bafe are thus deferibed is 
a Minimum , when the Ratio of thofe Elements is that 
of a to u ; i. e . when the Sine of the Angle, in which 
the Ordinate interfe&s the Curve, is to the Radius in 
this Ratio . Suppofmg therefore this Property to take 
place over all the Curve, the Excefs of the Time in 
which it is deferibed by the Body defending alongft 
it, above the Time in which the Bafe is deferibed 
uniformly with the Velocity a, mud be a Minimum*, 
and this latter Time being given, it follows that the 
Time of Defcent in this Curve is a Minimum. When 
the Gravity tends to a given Centre, fubftitutc an 
Arc of a Circle deferibed from that Centre through 
the lowermoft Point of the Curve in the Place of the 
Bafe in the former Cafe; and the Property of the 
Line of fwifteft Defcent will be difeovered in the 
2 z 3 fame 
