Volume 1

A system of natural philosophy, being a course of lectures in mechanics, optics, hydrostatics, and astronomy / By T. Rutherforth.

  • Rutherforth, T. (Thomas), 1712-1771.
Date:
1754
Catalogue details

Licence: Public Domain Mark

Credit: A system of natural philosophy, being a course of lectures in mechanics, optics, hydrostatics, and astronomy / By T. Rutherforth. Source: Wellcome Collection.

    145/566 (page 109)
    dined plane is lefs than the accelerating force of perpendicular defcent, in the proportion of the planes height to its length. 122. The velocity, which a heavy body acquires in any given time upon an inclined plane, is to the velocity, which it would acquire in the fame time by perpendicular defcent, as the height of the plane is to its length. In an uniformly accelerated motion the velocities produced in equal times are as the caufes, which produce them, that is, as the accelerat¬ ing forces. But, by propofition 120, the accelerating force upon an in¬ clined plane is to the accelerating force in perpendicular defcent as the height of the plane to the length of it. Therefore the velocities pro¬ duced in equal times are in the fame proportion. 123. The fpace, which a heavy body defcribes in a given time upon an in¬ clined plane, is to the fpace, which it woidd defcribe in the fame time by falling perpendicularly, as the height of the plane is to the length of it. The fpaces defcribed in a given time are as the velocities, by propo¬ rtion 10. And the velocities produced in a given time in two bodies, one of which falls upon an inclined plane and the other perpendicularly, are,, by the foregoing propofition, as the height of the plane to the length of it. This therefore will likewile be the proportion of the fpaces, which they defcribe in the fame time. Let AB, Plat. IV. fig. 5. be an inclined plane and fuppofe a heavy body was to fall perpendicularly from A to C, or through a fpace equal to the height of the plane. How far would another heavy body fall in the mean time upon the plane from A towards B ? The fpaces defcri¬ bed in the fame time will be to each other as the height of the plane to the length of it. Therefore the fpace fought is to AC, or to the fpace defcribed by the body which falls perpendicularly, as the fame line AC Is to AB, or as the height of the plane is to the length of it. Now the angle ACB is always a right one j becaufe CB is an horizontal plane, and AC is the perpendicular height of the inclined one. And, if from the angle C in the rightangled triangle ACB you draw the line CD per¬ pendicular to AB, then ADC is fimilar to ACB ; Eucl. b.VI. pr. 8. and AD is to AC as AC to AB. Eucl. b.VI. pr. 4. Therefore AD is the fpace fought. So that, if the two bodies were let fall from A at the fame inftant, when one had fallen perpendicularly to C, the other would have fallen upon the plane no farther than D, 124.