( 57 8 )

33. Is in a Perpendicular Projection Upwards; it Afcends in the. Rate ofthe former, Abated by that of the latter. Becaufe here the Impulse of Gra-vity is contrary to the Force Imprefled.

34. When therefore this latter (continually Increasing) becomes Equalto that former, (continually Decreasing) it then ceafeth to Aseend ; and doththenceforth Deseend at the Rate wherein the latter continually Exceeds theformer.

35-. In an. Horizontal or Oblique Projection: If to a Tangent wnosc

Increments are as F L, L M, M N, t£c. tliat is, as —— /, ßc. be fitted

m

Ordinäres (at a given Angle) whose Increments are as FL, FM, FN, ß c

that is, as-g, t£c. The Curve answering to the Compound of thefe

m

Motions, is that svherein the Project is to move.

36. This Curve (being hitherto without a Name) may be called LineaProjeilorum, the Line of Projects, or things Projected; which resembles aParabola Deformcd.

37. The Celerity and Tcndcncy, as to each Point of this Line, is deter-mined by a Tangent at that Point.

3 8. And that against which it makes the greatest Stroke or Percullion, isthat which (at that point) is at Right Angles to that Tangent.

39. If the Projection (at P. ay.) be not Infinitely Continued, but Ter-minate (soppose) at N, so that the last Term in the first Column or SeriesErect, be a ; and consequently in the second, m a ; in the third m m a, (fc.(each Series having one Tcrm fewer than that before it :) . then (for thefime Reasons as at P, zo.) the Aggregata of the severa! Columns (or Erect

-,-,-, and fo fbrrh, till (the Multi*

n n n

ple of a becoming = 1,) the Progression expire.

40. Now all the Abatements here, a, ma, ntm a, ßc. are the fame wirhtheTermsof the first Column taken back ward. For a is the last, ma thenext before it; and so of the rest.

41. And the Aggregate of all the Numerators is so many times 1, as isthe number of Terms (suppose t,) wanting the first Column ; that is.

Series) will be

1 — a

nt — 1 H- a

t —

or

; and this again divided by the common Dcno-

nt — I-+rf nt — 1

jmnaror «, becomes-> And therefore, -

n n

nn

Line of Defcent by its own Gravity.

a

is the

4.x. If