45. In an Horizontal or Oblique Projection, having taken 1-a / n f, in the Line of Projection, and thence (at the Angle given) nt - 1 + a / nn g, in the Line of Descent; the Point in the Curve answering to these, is the Place of the Project answering to that Moment.
46. I am aware of some Objections to be made, whether to some Points of the Process, or to some of the Suppositions. But I saw not well how to wave it, without making the Computation much more perplex'd. And in a Matter so nice, and which must depend upon Physical Observations, 'twill be hard to attain such Accuracy, as not to stand in need of some Allowances.
47. Somewhat might have been farther added to direct the Experiments suggested at ¶ 21, and 31. But that may be done at leisure, after deliberation had, which way to attempt the Experiment.
48. The like is to be said of the different resistance which different Bodies may meet with in the same Medium, according to their different Gravities (extensively or intensively consider'd) and their different Figures and Positions in Motion. Whereof we have hitherto taken no account; but supposed them, as to all these, to be alike and equal.
POSTSCRIPT.
49. The Computation in ¶ 41, 42, 43, may (if that be also desired) be thus represented by Lines and Spaces. The Ablatives a, ma, mma, &c. (being the same with the first Column taken backward) are fitly represented by the Segments of NF (beginning at N) in Figure 5 and 6, and therefore by Parallelograms on these Bases, assuming the common height of Fh, or NQ; the Aggregate of which is Nh, or FQ. And, so many times 1, by so many equal Spaces, on the same Bases, between the same Parallels, terminated at the Hyperbola: The Aggregate of which is hFNQn. From whence if we subduct the Aggregate of Ablatives FY; the remaining Trilinear hQn, represents the Descent.
50. If to this of Gravity, be joined a projecting Force; which is to the Impulse of Gravity as hK to hF (be it greater, less, or equal) taken in the same Line; the same Parallels determine proportional Parallelograms, whose Aggregate is KQ.
51. And therefore if this be a perpendicular Projection downwards; then hKkn (the Sum of this with the former) represents the Descent.
52. If it be a Perpendicular upwards; then the difference of these two represents the Motion; which so long as KQ is the greater, is Ascendent; but Descendent, when hQn becomes greater; and it is then at the highest when they be equal.
53. If the Projection be not in the same Perpendicular, (but Horizontal, or Oblique) then KQ represents the Tangent of the Curve; and hQn the Ordinates to that Tangent, at the given Angle.