Noncuple

1557, Robert Record, Whetstone of Witte, sig. Eiii 36 vnto 4 is a noncuple proportion.

Both triples added together […] make the proportion or amounting Ratio Noncuple, or ninefold.

Let the Saltpeter be taken together with the Gun-powder in ſeveral Degrees of Superparticular and Superpartient, as Sextuple, Septuple, Octuple, Noncuple and Decuple; or Sixfold, Sevenfold, Eightfold, Ninefold and Tenfold.

The eighth is vacant because there is no noncuple proportion of 9/1 on the monochord.

To proue that a trilater equilater Pyramis, is noncuple to a cube inscribed in it.

The Space run thro’ in the double Time, is quadruple to that ran thro’ in a ſubduple Time; that run thro’ in the triple Time is noncuple.

If for duple we had substituted triple, quadruple, quintuple, &c. the action would have come out noncuple, sedecuple, 25ple.

1797, Colin Macfarquhar and George Gleig (editors), Encyclopædia Britannica (3rd edition) XV (Plant–Rana), page 544, “Projectiles” As the height neceſſary for acquiring any velocity increaſes or diminiſhes in the duplicate proportion of that velocity, it is evident that all the ranges with given elevations will vary in the ſame proportion, a double velocity giving a quadruple range, a triple velocity giving a noncuple range, &c.

The velocity of the vibrations performed by a string […] is as the square roots of the stretching weights: […] a noncuple weight will produce vibrations of triple velocity, or a triple number in the same time.

In the following odd multiples above the ſeptuple arc, the mean arc may be greater than three quadrants: Thus, for inſtance, in the caſe of the noncuple arc, in which the three equidifferent arcs are the quintuple, ſeptuple, and noncuple arcs, ‛tis evident the greateſt magnitude of the ſeptuple, or mean, arc, or that which it has when the noncuple arc is equal to a whole circle, is ⁷⁄₉, or ²⁸⁄₃₆, of the whole circumference, which is greater than ²⁷⁄₃₆ or ¾ of the whole circumference, or three quadrants; and ſince this is true in the noncuple arc, it follows a fortiori that it will be true in all higher multiples.

In the noncuple series, each term exceeds the octuple of the sum of its parts, by unity.

Ðe rigt hand diſcanteŧ in Noncuple uppon đe plain Triple of đe left hand.

And so on to the ninth and last [row], in which you shall find the noncuple of the number given.

In the third […] you ſhall find the triple thereof. In the fourth the Quadruple thereof. In the fifth the Quintuple; and ſo on the ninth and laſt the Noncuple of the Number given.

Again adding 2124 (the triple of the Diviſor) to the Diviſor 708, I find 2832 for the quadruple of the Diviſor, which quadruple I ſubſcribe under the Triple, and proceeding in like manner, at laſt the Table is finiſh’d, which readily ſhews the Diviſor, with the duple, triple, quadruple, quintuple, ſextuple, ſeptuple, octuple, and noncuple of the Diviſor.

For nine dice, to have 1 noncuple [... there is one] determinate throw [... and six] indeterminate throws.

If you shall quadruple the same weight it will draw down double the first distance, and noncuple will draw it down treble, etc.