_Demonstration._ Draw the Line EC parallel to AB, and AE parallel to BC in the same _Fig. 9._ and compleat the _Parallelogram_ ABCE, it is evident that the _Area_ thereof may represent the Space, a _Body_ moved equably with the _Velocity_ BC would describe in the Time AB, and the _Triangle_ ABC represents the _Space_ describ'd by the _Fall_ of a _Body_, in the same Time AB, by the second Proposition. Now the _Triangle_ ABC is half of the _Parallelogram_ ABCE, and consequently the Space described by the _Fall_, is half what would have been described by an _equable Motion_ with the _Velocity_ BC, in the same Time; wherefore the _Velocity_ BC at the end of the _Fall_, is double to that _Velocity_, which in the Time AB, would have described the _Space fallen_, represented by the _Triangle_ ABC with an _equable Motion_, _Q. E. D._ _Prop. IV._ All _Bodies_ on or near the Surface of the _Earth_, in their _Fall_, descend so, as at the end of the first Second of Time, they have described 16 Feet, 1 Inch, _London Measure_, and acquired the _Velocity_ of 32 Feet, 2 Inches, in a Second. This is made out from the 25th Proposition of the second Part of that excellent Treatise of Mr. _Hugenius de Horologio Oscillatorio_; wherein he demonstrates the time of the least _Vibrations_ of a _Pendulum_, to be to the Time of the _Fall_ of a _Body_, from the heighth of half the length of the _Pendulum_, as the _Circumference_ of a _Circle_ to its _Diameter_; whence, as a _Corollary_, it follows, That as the _Square_ of the _Diameter_ to the _Square_ of the _Circumference_, so half the length of the _Pendulum_ vibrating _Seconds_, to the _Space_ described by the _Fall_ of a _Body_ in a _Second_ of _Time_: And the Length of the _Pendulum_ vibrating _Seconds_, being found 39, 125, or ⅛ Inches, the _Descent_ in a _Second_ will be found by the aforesaid _Analogy_ 16 Foot and 1 Inch; and, by the third Proposition, the _Velocity_ will be double thereto; and near to this it hath been found by several Experiments, which by reason of the _swiftness_ of the _Fall_, cannot so exactly determine its _Quantity_. The Demonstration of _Hugenius_ being the Conclusion of a long Train of _Consequences_, I shall for brevity sake omit; and refer you to his Book, where these things are more amply treated of. From these Four _Propositions_, all _Questions_ concerning the _Perpendicular Fall of Bodies_, are easily _solved_, and either _Time_, _Height_, or _Velocity_ being assign'd, one may readily find the other two. From them likewise is the Doctrine of _Projects_ deducible, assuming the two following _Axioms_; _viz._ That a _Body_ set a moving, will move on continually in a right _Line_ with an _equable Motion_, unless some other Force or Impediment intervene, whereby it is accelerated, or retarded, or deflected.