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⁄m2; for the third 1⁄m + 1⁄m2 + 1⁄m3, &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.
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⁄m3, &c. of f, (the impressed Force) increased by 1⁄m, 1⁄m + 1⁄m2, 1⁄m + 1⁄m2 + 1⁄m3, &c. of g the impulse of Gravity, (by ¶ 7, and ¶ 27) Because both Forces are here united.