22. If the Progression be not infinitely continued; but end (suppose) at _N_, and its least Term be _A_ = _MN_; then, out of _V_/(_R_ - 1) = 1/_m_ + 1/_mm_ + 1/_m_³, _&c._ is to be subducted _A_/(_R_ - 1) (as at ¶ 10.) that is (as by Division will appear) _A_/_R_ + _A_/_R_² + _A_/_R_³ &c. That is (in our present Case) _a_/_m_ + _a_/_mm_ + _a_/_m_³ &c. And so the Aggregate will be (1-_a_)/_m_ + (1-_a_)/_mm_ + (1-_a_)/_m_³ &c. = (1-_a_)/_n_. And thus as to the Line of Projection, in which (secluding the Resistance) the Motion is reputed uniform; dispatching equal Lengths in equal Times. Consider we next the Line of Descent. 23. In the Descent of Heavy Bodies, it is supposed that to each Moment of Time, there is superadded a new Impulse of Gravity to what was before: And each of these, secluding the Consideration of the Air's Resistance, to proceed equally (from their several beginnings) through the succeeding Moments. As (in the erect Lines) 1 1 1 1, _&c._ 1 1 1, _&c._ 1 1, _&c._ 1, _&c._ and so continually, as in the Line of Projection.[16] 24. Hence ariseth (in the transverse Lines) for the first Moment 1, for the second 1 + 1, for the third 1 + 1 + 1, and so forth, in Arithmetical Progression: As are the Ordinates in a Triangle, at equal distance. 25. And such are the continual Increments of the Diameter, or of the Ordinates in the exterior Parabola, answering to the interior Ordinates, or Segments of the Tangent, equally increasing; as is known, and commonly admitted. 26. If we take in the Consideration of the Air's Resistance; we are then, for each of these equal Progressions, to substitute a decreasing Progression Geometrical; in like manner (and for the same Reasons) as in the Line of Projection. 27. Hence ariseth, for the first Moment 1/_m_; for the second 1/_m_ + 1/_m_²; for the third 1/_m_ + 1/_m_² + 1/_m_³, _&c._[17] And such is therefore the Descent of a heavy Body falling by its own weight. The several Impulses of Gravity being supposed equal. 28. That is (in the Figure of ¶ 12) as _FL_, _FM_, _FN_, &c. in the Line of Descent, answering to _FL_, _LM_, _MN_, &c. in the Line of Projection. 29. But though the Progressions for the Line of Projection, are like to each of those many in the Line of Descent; it is not to be thence inferred, that therefore 1/_m_ in the one, is equal to 1/_m_ in the other: But in the Line of Projection (suppose) (1/_m_)_f_ (such a Part of the Force impressed, and a Celerity answerable:) in the Line of Descent, (1/_m_)_g_ such a Part of the Impulse of Gravity. 30. Those for the Line of Descent (of the some Body) are all equal, each to other: Because _g_ (the new Impulse of Gravity) in each Moment is supposed to be the same. 31. But what is the Proportion of _f_ to _g_ (that of the Force impressed, to the Impulse of Gravity in each Body) remains to be inquired by Experiment.