3

of FLUXIONS.

to continue invari-able from the Posi-tion RS, the Rect-angle RnS wouldthen be uniformlygenerated, with thevery Celerity where-with it begins to begenerated, or withwhich the SpaceA inn is increased inthat Position.

5. f rom what has been hitherto said it will appear,that the Fluxions of Quantities are , always , as theCelerities by -which the quantities themselves increase inMagnitude: Whence it will not be difficult to form aNotion of the Fluxions of Quantities otherwise generated;as well such as arise from the Revolution of Right-linesand Planes, as those by parallel Motion: But of this here-after. I come now to strew the Manner of determin-ing the Fluxions of algebraic Quantities ; by which allothers, of what Kind soever, are explicable. But firstof all it will be requisite to premise the following Ob-servations.

I. That the snal Letters u, w, x, y, z of the Alpha-bet are commonly put for variable Quantities ; and the ini-tial Letters a, b, c, d, Sic. for invariable ones: Thusthe Diameter as a given Circle may be denoted by a,and the Sine of any Arch thereof (considered as varia-ble) by x.

II. Toat the Fluxion of a Quantity represented by asingle Letter , is ujually expressed by the fame Letter witha Dot or Full-poini over it: Thus the Fluxion of x isrepresented by x, and that of y by y.

III. That the Fluxion of a Qiiantity which decreases,inf sad of increasing, is to be considered as negative.

B a

PRO-