...orbit, are proportional to the times. (3.) The squares of the times of revolution of any two planets are proportional to the cubes of their mean distances from the sun. These laws were verified by Newton in his Principia, in a course of mathematical reasoning, the foundation...

...moves over Equal Areas in Equal Times ; and (3) that tho Squares of the Periodic Times of the Planets are Proportional to the Cubes of their Mean Distances from the Sun. But these Laws were not universally accepted as the real expression of the phenomena before Newton...

...planet describes equal areas m equal times. III. The squares of the times of revolution of the planets are proportional to the cubes of their mean distances from the sun. The following is an outline of the course of reasoning followed by Newton. In the first place the proposition...

...understood—36, 69, 95, 144, 490, 900, 1,800, 2,800. The squares of the periodic times of the planets are proportional to the cubes of -their mean distances from the sun. Hence, as the distance of the earth from the sun has been found by the transits of Venus to be about...

...proportional to the times of description ; while the squares of the periodic times of the various planets are proportional to the cubes of their mean distances from the sun. These are Kepler's laws ; they are yet, however, only empirical. We know them to be true, but we cannot...

...proportional to the times of description ; while the squares of the periodic times of the various planets are proportional to the cubes of their mean distances from the sun. These are Kepler's laws ; they are yet, however, only empirical. We know them to be true, but we cannot...

...sun. This law is expressed as follows : — " The squares of the times of revolution of the planets are proportional .to the cubes of their mean distances from the sun." To give an illustration of this law, we may take the planets Venus and the Earth, whose times of revolution...

...The squares of the periodic times (the periods of complete revolution round the sun) of two planets are proportional to the cubes of their mean distances from the sun. These laws were discovered from calculations on Tycho Brahe's observations; they enabled Newton to...

...proportional to the times of description ; while the squares of the periodic times of the various planets are proportional to the cubes of their mean distances from the sun. These are Kepler's laws ; they are yet, however, only empirical. We know them to be true, but we cannot...

...over equal areas in equal times ; the third, that the squares of the periodic times of the planets are proportional to the cubes of their mean distances from the sun. The first two laws were discovered by Kepler in the course of a laborious examination of the theory...