...by the radius vector in a double time is double, and triple in a triple time, &c. Hence, in general, the areas described by the radius vector are proportional to the times employed in their description. 2d. As the products of the squares of two radii vectores, by. the angle each describes...

...protakes in moving from S to A. Hence results that re-'1 markable law, first pointed out by Kepler, that the areas described by the radius vector are proportional to the times. Suppose the sun to describe SS' in one day, and SA in 20 days, then the area SES' is to the area SEA...

...the laws of Kepler, gave the most complete evidence to the system of gravitation. Theirs* law, that the areas described by the radius vector are proportional to the times in which they are described, is the result of the motions produced by an original impulse impressed...

...Such is the variation in the angular motion of the sun. The fundamental law of this motion is that the areas described by the radius vector are proportional to the times. If the sun's orbit were circular and without eccentricity, equal areas would correspond to equal angles,...

...confine ourselves to an exposition of the consequences he deduced from Kepler's laws. From the law that the areas described by the radius vector are proportional to the times, Newton draws this conclusion, supported by calculation, that the force acting on the planète is directed...

...as the square of its distance from the earth. 3. The real velocity is inversely as the distance. 4. The areas described by the radius vector are proportional to the times of description. (76.) We have several times mentioned, that, as far as appearances are concerned, it...

...instants, are equal. But the areas in any two consecutive instants being equal, the areas described in any two equal intervals of time must also be equal,...through the fixed point. For, employing the preceding figure, let C be the fixed point and M'M", M"M'" the infinitely small spaces described in two consecutive...

...generally, the areas described in any two intervals of time are proportional to the intervals. Thus token a material point describes a curve, in virtue of a...through the fixed point. For, employing the preceding figure, let C be the fixed point and M'M", M"M'" the infinitely small spaces described in two consecutive...

...planet describe® its orbit is directed to the center of the sun. For, by the first of Kepler's laws, the areas described by the radius vector are proportional to the times, and when this is the case, by Art. 351, the force must be directed to the point about which this equable...

...planet describes ite orbit is directed to the center of the sun. For, by the first of Kepler's laws, the areas described by the radius vector are proportional to the times, and when this is the case, by Art. 351, the force must be directed to the point about which this equable...