About the Book
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1752 Excerpt: ...of any One of the said Particles of Time, is an exact Mean between the Velocities at the two Extremes thereof, the corresponding Particle of the Distance AB may be therefore considered as described with that mean Velocity: And so, the Spaces As, cd, de, ef, (sfc. being, respectively, equal to the abovementioned Quantities-, -3--, ' 2 2 2 &c. it followi, by the continual Addition of 2 These, that the Spaces Ac, Ad, As, A/, &c, fallen thro' from the Beginning, will be expreslted by i?, SUL, lL, WL, Which are, evi. 2 2 2 2 2 dently, to one another in proportion, as 1, 4, 9, 16, 25, fcfs. that is, as the Squares of the Times. Si-E. D, Corol, Corollary. Seeing the Velocity acquired in any Number (, n) of the aforefaid, equal, Particles of Time (measured by the Space that would be described in one single Particle) is represented by n time m, or n m, it will therefore be, as i Particle of Time, is to n such Particles, so.is nm, the faid Distance answering to the former Time, to the Distance, nm, corresponding to the Latter, with the fame Celerity, acquired at the End of the faid - Particles. Whence it appears that the Space (found above) thro' which the Ball 2 falls, in any given Time -, is just the Half of That (nm) which might be uniformly described with the last, or greatest, Celerity, in the fame Time. Scholium. It is found, by Experiment, that any heavy Body, near the Earth's Surface (where the Force of Gravity may be consider'd as uniform) descends about 16 Feet, from Rest, in the first Second of Time. Therefore, as the Distances fallen thro' are proved above to be, in Proportion, as the Squares of the Times; it follows that, as the Square of r Second, is to the Square of any given Number of Seconds, so is 16 Feet, to the Number of Feet a hea.
