VU 1

PREFACE.

at the proposed Position in which the Fluxion is tobe found : Whence the true Fluxion, itself, will beobtained, without the Assistance of infinitely smallQuantities, or any metaphysical Considerations.

Thus, for Example, the Motion of a Ball, de-scending by the Force of its own Gravity, is con-tinually accelerated ; but to have the Fluxion of theDistance fall’n thro’ at any given Position of theBall, we must 6nd how far the Ball would, uniform-ly, descend, from that Point, in a given Time, if theGravity, or the Earth’s Attraction, from thence,was to cease acting. By which Means we ssiall have asclear an Idea of the Fluxion and the true Measure ofthe Velocity of the Ball, at any Point assigned, as inthose Cases where the jMotion is, aSuallj, uniform.

Again, if a Right-line be supposed to moveparallel to itself with an equable Motion, and toincrease in Length, at the same Time ; the Areagenerated thereby, will increase with an accele-rated Velocity : But the Fluxion thereof, at anygiven Position of the Line, will be had by takingthat Part of the Increment which would , uni-formly, arise, was the Length (as well as theVelocity) of the Line to continue invariable fromthe proposed Position. For, if the Length besupposed to increase, from the said Position, theArea generated, from thence, will be, evidently,greater than That which would uniformly arisein the fame Time ; since the new Parts, produced10 each