32. This Proportion being found as to one known Force; the same is thence known as to any other Force (whose Proportion to this is given) in the same uniform _Medium_. 33. And this being known, as to one _Medium_; the same is thence known as to any other _Medium_, the Proportion of whose Resistance to that of this is known. 34. If a heavy Body be projected downward in a perpendicular Line; it descends therefore at the Rate 1/_m_, 1/_mm_, 1/_m_³, _&c._ of _f_, (the impressed Force) increased by 1/_m_, 1/_m_ + 1/_m_², 1/_m_ + 1/_m_² + 1/_m_³, _&c._ of _g_ the impulse of Gravity, (by ¶ 7, and ¶ 27) Because both Forces are here united. 35. If in a perpendicular Projection upwards; it ascends in the rate of the former, abated by that of the latter. Because here the impulse of Gravity is contrary to the Force impressed. 36. When therefore this latter (continually increasing) becomes equal to that former (continually decreasing) it then ceaseth to ascend; and doth thenceforth descend at the rate wherein the latter continually exceeds the former. 37. In an Horizontal, or Oblique Projection: If to a Tangent, whose Increments are as _FL_, _LM_, _MN_, &c. that is as (1/_m_)_f_, &c. be fitted Ordinates (at a given Angle) whose Increments are as _FL_, _FM_, _FN_, &c. that is, as (1/_m_)_g_, &c. The Curve answering to the Compound of these Motions, is that wherein the Project is to move. 38. This Curve (being hitherto without a Name) may be call'd _Linea Projectorum_; the Line of Projects, or things projected; which resembles a Parabola deform'd. 39. The Celerity and Tendency, as to each Point of this Line, is determined by a Tangent at that Point. 40. And that against which it makes the greatest Stroke or Percussion, is that which (at that Point) is at right Angles to that Tangent. 41. If the Projection (at ¶ 27) be not infinitely continued, but terminate (suppose) at _N_, so that the last Term in the first Column or Series erect be _a_; and consequently in the second, _ma_; in the third, _mma_, &c. (each Series having one Term fewer than that before it:) Then (for the same Reasons, as at ¶ 22) the Aggregates of the several Columns (or erect Series) will be (1 - _a_)/_n_, (1 - _ma_)/_n_, (1 - _mma_)/_n_, and so forth, till (the Multiple of _a_ becoming = 1) the Progression expire. 42. Now all the Abatements here, _a_, _ma_, _mma_, &c. are the same with the Terms of the first Column taken backward. For _a_ is the last, _ma_ the next before it; and so of the rest. 43. And the Aggregate of all the Numerators is so many times 1, as is the Number of Terms (suppose _t_,) wanting the first Column; that is _t_ - (1 - _a_)/_n_, or (_nt_ - 1 + _a_)/_n_; and this again divided by the common Denominator _n_, becomes (_nt_ - 1 + _a_)/_nn_. And therefore ((_nt_ - 1 + _a_)/_nn_)_g_, is the Line of Descent by its own Gravity.