18. IF a body fall obliquely, it will approach the ground by slower degrees, than when it falls perpendicularly. Suppose two lines A B, A C (in fig. 9.) were drawn, one perpendicular, and the other oblique to the ground D E: then if a body were to descend in the slanting line A C; because the power of gravity draws the body directly downwards, if the line A C supports the body from falling in that manner, it must take off part of the effect of the power of gravity; so that in the time, which would have been sufficient for the body to have fallen through the whole perpendicular line A B, the body shall not have passed in the line A C a length equal to A B; consequently the line A C being longer than A B, the body shall most certainly take up more time in passing through A C, than it would have done in falling perpendicularly down through A B. 19. THE geometers demonstrate, that the time, in which the body will descend through the oblique straight line A C, bears the same proportion to the time of its descent through the perpendicular A B, as the line it self A C bears to A B. And in respect to the velocity, which the body will have acquired in the point C, they likewise prove, that the length of the time imployed in the descent through A C so compensates the diminution of the influence of gravity from the obliquity of this line, that though the force of the power of gravity on the body is opposed by the obliquity of the line A C, yet the time of the body’s descent shall be so much prolonged, that the body shall acquire the very same velocity in the point C, as it would have got at the point B by falling perpendicularly down. 20. IF a body were to descend in a crooked line, the time of its descent cannot be determined in so simple a manner; but the same property, in relation to the velocity, is demonstrated to take place in all cases: that is, in whatever line the body descends, the velocity will always be answerable to the perpendicular height, from which the body has fell. For instance, suppose the body A (in fig. 10.) were hung by a string to the pin B. If this body were let fall, till it came to the point C perpendicularly under B, it will have moved from A to C in the arch of a circle. Then the horizontal line A D being drawn, the velocity of the body in C will be the same, as if it had fallen from the point D directly down to C.