a. Math. [SUB- 10.]
1. Of a ratio or proportion: Being that of the square roots of the quantities; thus, 2 : 3 is the subduplicate ratio of 4 : 9.
1656. trans. Hobbes’ Elem. Philos., 121. A Proportion is said to be Divided, when between two quantities are interposed one or more Means in continual Proportion, and then the Proportion of the first to the second is said to be Subduplicate of that of the first to the third, and Subtriplicate of that of the first to the fourth.
1670. Boyle, Usef. Exp. Nat. Philos., II. iii. 15. The times are in Subduplicate Proportion to the lengths of the Pendulums.
1674. Perry, Disc. Dupl. Prop., 21. The First Instance, Wherein Duplicate, and Sub-duplicate Ratio or Proportion is considerable, Is In the Velocities of two equal and like Ships; which Velocities … are the square Roots of the Powers which either drive or draw them.
1706. W. Jones, Syn. Palmar. Matheseos, 288. The Times in which a Body runs thro’ those Planes, shall be in a Subduplicate Ratio of their Altitudes.
1798. Hutton, Course Math., II. 358. The bodies descend by nearly uniform velocities, which are directly in the subduplicate ratio of the diameters.
¶ 2. = SUBDUPLE. (A misuse.)
1656. Hobbes, Six Lessons, Wks. 1845, VII. 277. It is the same fault when men call half a quantity subduplicate.
1755. Johnson, Subduplicate,… containing one part of two.
