Sir I s a A c N e vv T o n’s Book I.

1^,2

wife as the time, in which the body moves over A D E, isequal to the time of its moving over E G H, and to the timeof its moving over H IK ; the space CADE will be equal tothe space CEGH, and to the space CHIK. In the samemanner as the time, in which the body moved over A D E Gis equal to the time of its moving over G H IK, so the spaceC A D E G will be equal to the space C G HIK.

34,. From this principle SirlsAAcNEWTON demonstratesthe proposition mentioned above, by that method of arguingintroduced by him into geometry, whereof we have beforetaken notice a , by making according to the principles of thatmethod a transition from this incurvated figure composed osstraight lines, to a figure of continued curvature ; and byshewing, that since equal spaces are described in equal timesin this present figure composed os straight lines, the same re-lation between the spaces described and the times of their de-scription will also have place in a figure os one continuedcurvature. He also deduces from this proposition the reverseos it; and proves, that whenever equal spaces are continu-ally described ; the body is acted upon by a centripetal forcedirected to the center, at which the spaces terminate.

* § <1.

Chap.