algebraical Quantity to be an infinitely ſmall or evaneſcent Quantity, and therefore to be neglected, muſt have produced an Error, had it not been for the curvilinear Spaces being equal thereto, and at the ſame time ſubducted from the other Part or Side of the Equation agreeably to the Axiom, If from Equals you ſubduct Equals, the Remainders will be equal. For thoſe Quantities which by the Analyſts are ſaid to be neglected, or made to vaniſh, are in reality ſubducted. If therefore the Concluſion be true, it is abſolutely neceſſary that the finite Space CFH be equal to the Remainder of the Increment expreſſed by &c. equal I ſay to the finite Remainder of a finite Increment.
XXIX. Therefore, be the Power what you pleaſe, there will ariſe on one Side an algebraical Expreſſion, on the other a geometrical Quantity, each of which naturally divides it ſelf into three Members: The algebraical or fluxionary Expreſſion, into one which includes neither the Ex-
