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