Chap. 3. PHILOSOPHY. 139

gree os curvature, which the figure has in each point of it,and requires a long and complex mathematical reasoning.However I (hall speak a little to the first proposition, whichSir Isaac Newton lays down for this purpose. By thisproposition, when a body is found moving in a curve line, itmay be known, whether the body be kept in its course by apower always pointed toward the same center; and if it be so,where that center is placed. The proposition is this: that ifa line be drawn from some fixed point to the body, and re-maining by one extream united to that point, it be carriedround along with the body; then, if the power, wherebythe body is kept in its course, be always pointed to this fixedpoint as a center, this line will move over equal spaces in equalportions of time. Suppose a body were moving through thecurve line A B C D (in fig. 8 4.) and passed over the arches A B,B C, C D in equal portions of time; then is a point, as E, canbe found, from whence the line E A being drawn to the bodyin A, and accompanying the body in its motion, it shall makethe spaces E A B, E B C, and E C D equal, over which it pas-' ses, while the body describes the arches AB, BC, and CD :and if this hold the lame in all other arches, both great andsmall, os the curve line ABLE), that these spaces are alwaysequal, where the times are equal; then is the body kept inthis line by a power always pointed to E as a center.

30. The principle, upon which SirlsAAcNEWTON hasdemonstrated this, requires but small skill in geometry to com-prehend. I shall therefore take the liberty to close the pre-

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