subduplicate

It is at the equinoxes that the earth changes her distances from the sun most rapidly, and whether she is passing from her perihelion or from her aphelion, the density of the ether externally is changing in the subduplicate ratio of these distances and consequently at these times there will be the greatest disturbance of the electric equilibrium.

Outlines of a Mechanical Theory of Storms Containing the True Law of Lunar Influence T. Bassnett

[3] If the periodic times are in the sesquiplicate ratio of the radii, and therefore the velocities reciprocally in the subduplicate ratio of the radii, the centripetal forces will be in the duplicate ratio of the radii inversely; and the converse.

The World's Greatest Books — Volume 15 — Science Various 1909

And that they move in orbits very nearly parabolical, I infer from their velocity; for the velocity with which a parabola is described is everywhere to the velocity with which a comet or planet may be revolved about the sun in a circle at the same distance in the subduplicate ratio of 2 to 1; and, by my computation, the velocity of comets is found to be much about the same.

The World's Greatest Books — Volume 15 — Science Various 1909

And if the satellite did gravitate towards the sun with a force, lesser in the proportion of e to d, the distance of the centre of the satellite's orb from the sun would be less than the distance of the centre of Jupiter from the sun in the subduplicate of the same proportion.

A History of Science: in Five Volumes. Volume II: The Beginnings of Modern Science 1904

The orbital paths of the planets are in the simple ratio of the distances; the weights or quantities of matter in different planets are in the subduplicate ratio of the same distances, as has been already proved; so that with every increase of distance a planet has more matter and therefore is moved more slowly, and accumulates more time in its revolution, requiring already, as it did, more time by reason of the length of the way.

Kepler Bryant, Walter W 1920

If at equal distances from the sun any satellite, in proportion to the quantity of its matter, did gravitate towards the sun with a force greater than Jupiter in proportion to his, according to any given proportion, suppose d to e; then the distance between the centres of the sun and of the satellite's orbit would be always greater than the distance between the centres of the sun and of Jupiter nearly in the subduplicate of that proportion: as by some computations I have found.

A History of Science: in Five Volumes. Volume II: The Beginnings of Modern Science 1904

The third and fourth causes compensate each other in a comparison of different planets; the simple and subduplicate proportion compound the sesquiplicate proportion, which therefore is the ratio of the periodic times.”

Kepler Bryant, Walter W 1920