ON NATURAL MOTIONS caused by Gravity

Chapter 2. On the moments The measure of a weight's tendency to produce motion or rotation around an axis. of heavy bodies floating in a fluid.

Y in the second case, and raised up to V; then indeed the center of gravity of the aforementioned water, when established horizontally, will fall precisely on the center of suspension M. This is because as the base V is to the base A, or as the aqueous cylinder A volume of fluid with a fixed cross-section. GLV is to the cylinder AEF of equal height in the first case, or to CEF in the second, the distance EM was reciprocally to ML. It must now be shown that the points A, Q, R, S, and M are on the same parabolic line A specific type of curve where every point is equidistant from a fixed point and a fixed straight line.. Because the mass of water TX is equal to the mass of water GHI, therefore, XBF together with GHI is equal to the mass of water TAF. Indeed, the mass of water XBF together with GHI was to GHI as the line HB is to BQ, or (with QN drawn parallel to AE) as LE is to EN. Therefore, FAT to TX, and its half FA to its half AB, will have the same proportion as LE to EN. Furthermore, EA is to AF as MA is to AG, or as ME is to EL. Therefore, from ordered equality, EA to AB will have the same proportion as ME to EN. By the conversion of the ratio, EA to EB will be as EM to MN, or as EB to NQ. Therefore, the three continuous proportionals A series of numbers where the ratio of the first to the second is the same as the second to the third. EA, EB, and NQ will be in the same ratio as that which EM has to MN. For this reason, the square of EM to the square of MN will have that proportion which

A geometric woodcut diagram illustrating a parabolic curve. On the left is a vertical axis labeled with points T, Z, B, c, p, E, and F. A curved line, identified in the text as a parabola, originates at point A and passes through points Q, R, and S, terminating at point M. Horizontal lines connect points B, c, p, and E on the axis to the corresponding points Q, R, S, and M on the curve. From these points, vertical lines extend down to points N, O, P, and L on a horizontal base. To the right of the curve is a separate vertical bar or container containing segments labeled G, H, I, K, L and the number 2.