from The Century Dictionary.
- In mathematics, expressed by the square root: as, the subduplicate ratio of two quantities—that is, the ratio of their square roots.
from the GNU version of the Collaborative International Dictionary of English.
- adjective (Math.) Expressed by the square root; -- said of ratios.
- adjective the ratio of the square roots, or the square root of a ratio.
from Wiktionary, Creative Commons Attribution/Share-Alike License.
- adjective mathematics Expressed by the
square root; said of ratios.
from Wiktionary, Creative Commons Attribution/Share-Alike License
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.
 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.
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.
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.
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.
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.
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.”
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