Chap. 2. PHILOSOPHY. 57

from A to B; then AC will be to DE in the fame proportion.In particular, is die time os the fall through A C be twice thetime of the sail through A B; then D E will be twice A B, andA C twice DE; or A C sour times A B. But if the time of thefall through A C had been thrice the time of die fall throughAB; DE would have been treble of AB, and AC treble ofD E ; that is, A C would have been equal to nine times A B.

18. I f a body fall obliquely, it will approach the groundby flower degrees, than when it falls perpendicularly. Sup-pose two lines AB, AL sin fig. 9.) were drawn, one perpen-dicular, and the other oblique to the ground D E: then if abody were to descend in the slanting line A C ; because thepower.of gravity draws the body directly downwards, if theline A C supports the body from falling in that manner, itmust take off part of the effect of the power of gravity; sothat ill the time, which would have. been sufficient for thebody to have fallen through the whole perpendicular line A B,the body shall not have pasted in the line A C a length equalto AB ; consequently the line AC being longer than AB,the body shall most certainly take up more time in pastingthrough A C, than it would have done in falling perpendicu-larly down through A B.

19. The geometers demonstrate, that the time, in whichthe body will descend through the oblique straight line AC,bears the fame proportion to the time of its descent throughthe perpendicular AB, as the line it self AC bears to AB.A.nd in respect to the velocity, which the body will have ac-

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