Page:The Analyst; or, a Discourse Addressed to an Infidel Mathematician.djvu/78

68 the Velocities generating in the two firt Moments, from the exces of the Velocity in the third above that in the econd Moment, we obtain the third Fluxion. And after the ame Analogy we may proceed to fourth, fifth, fixth Fluxions, &c. And if we call the Velocities of the firt, econd, third, fourth Moments a, b, c, d, the Series of Fluxions will be as above, a. b - a. c - 2b + a. d - 3c + 3b - a. ad infinitum, i. e. $$\dot{x}. \ddot{x}. \dot{\ddot{x}}. \ddot{\ddot{x}}.$$ ad infinitum.

XLIV. Thus Fluxions may be conidered in undry Lights and Shapes, which eem all equally difficult to conceive. And indeed, as it is impoible to conceive Velocity without time or pace, without either finite length or finite Duration, it mut eem above the powers of Men to comprehend even the firt Fluxions. And if the firt are incomprehenible, what hall we ay of the econd and third Fluxions, &c? He who can conceive the beginning of a beginning, or the end of an end, omewhat before the firt or after the