# noncuple
## English
### Etymology

First attested in adjectival use in 1557, in nominal use in 1636, and in verbal use in 1674; from the post-Classical Latin noncuplus (“nine times larger than”), from the Classical Latin nōnus (“ninth”) + -cuplus; compare nonuple.

### Pronunciation

* (Received Pronunciation) enPR: nŏnʹkyo͞opl, IPA: /ˈnɒnkjuːpl/

### Adjective

noncuple (not comparable)
* Ninefold.
** (of a ratio or proportion) Nine-to-one; (in 1729 quot.) imprecisely, with any number of aliquot parts over.
*** 1557, Robert Record, Whetstone of Witte, sig. Eiii
    36 vnto 4 is a noncuple proportion.
*** ante 1690, Samuel Jeake, Λογιστικη Λογια, or Arithmetick Surveighed and Reviewed (second edition, published in 1696), page 182
    Both triples added together […] make the proportion or amounting Ratio Noncuple, or ninefold.
*** 1729, Lt. Gen. Casimir Simienowicz (author), Capt. George Shelvocke, transl., The Great Art of Artillery, page 148: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.
*** 1984, The Journal of Musicological Research, V, page 17:The eighth is vacant because there is no noncuple proportion of 9/1 on the monochord.
** (construed with to) Nine times greater or larger than.
*** 1570, Henry Billingsley tr. Comte de Candale in The Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara, f. 453
    To proue that a trilater equilater Pyramis, is noncuple to a cube inscribed in it.
*** 1730, Galileo Galilei, translated by Thomas Weſton, Mathematical Diſcourſes Concerning Two New Sciences Relating to Mechanicks and Local Motion, page 264: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.
** Nine times as great or as numerous.
*** 1744–1749, Gottfried Wilhelm von Leibniz (author) and James Jurin (translator), “Commercium Literarum” (1696) in The Philosophical Transactions of the Royal Society of London (1665–1800) IX (1809), page 218
    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.
*** 1803, Jacques Ozanam (author), Jean-Étienne Montucla [Fr. ed.], and Charles Hutton (translator), Recreations in Mathematics and Natural Philosophy II, pages 395–396
    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.
** (mathematics, rare) Divided into nine equal segments.
*** 1760, Francis Maſeres, Elements of Plane Trigonometry, page 109: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.
** (rare, of a series of numbers) Proceeding by powers of nine with exponents in integral succession (i.e.: 9$^1$, 9$^2$, 9$^3$, 9$^4$, ... = 9, 81, 729, 6,561, ...).
*** 1816, Thomas Taylor, Theoretic Arithmetic, page 133:In the noncuple series, each term exceeds the octuple of the sum of its parts, by unity.

### Noun

noncuple (plural not attested)
* (rare, music) Nine beats per measure.
** 1636, Charls Butler, The Principles of Muſik in Singing and Setting, page 25:Ðe rigt hand diſcanteŧ in Noncuple uppon đe plain Triple of đe left hand.
* The product of multiplying a given number by nine.
** 1690, William Leybourn, Cursus Mathematicus, 1st edition, page 181:And so on to the ninth and last [row], in which you shall find the noncuple of the number given.
** 1700, William Leybourn, Arithmetick: Vulgar, Decimal, Inſtrumental, Algebraical, 7th edition, page 265: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.
** 1713, Edmund Wingate (author), John Kersey and George Shelley (editors), Mr. Wingate’s Arithmetick (13th ed.), page 45
    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.
* (rare, of dice) A throw in which all of nine dice show the same value (an event whose probability of occurring is 1,679,616 to 1).
** 1835, G. Hervey, Hoyle’s Games, page 22:For nine dice, to have 1 noncuple [... there is one] determinate throw [... and six] indeterminate throws.

### Verb

noncuple
* (transitive, rare) Make nine times greater; multiply by nine.
** 1674, Sir William Petty, A Discourse made before the Royal Society […] concerning the Use of Duplicate Proportion, page 117:If you shall quadruple the same weight it will draw down double the first distance, and noncuple will draw it down treble, etc.

#### Derived terms

* noncuplication (obsolete, rare)

### References

* “†Noncuple” listed on page 193 of volume VI, part II (M–N), § ii (N) of A New English Dictionary on Historical Principles [1st ed., 1908] †Noncuple, a. and sb. Obs. [f. L. nōnus ninth + -uple as in quadruple, with c inserted on the analogy of decuple.] A. adj. Ninefold. Noncuple to: nine times as great as. B. sb. A quantity nine times as great as another. [¶] 1557 Recorde Whetst. E iij b, 36 vnto 4 is a noncuple proportion. 1570 Billingsley Euclid xvi. prop. 30. 454 To proue that a trilater equilater Pyramis, is noncuple to a cube inscribed in it. 1674 Petty Disc. Dupl. Proportion 22 A quadruple Sail is requisite to double Swiftness, and noncuple to treble. 1674 Jeake Arith. (1696) 182 Both triples added together..make the proportion or amounting Ratio Noncuple, or ninefold. 1690 Leybourn Curs. Math. 181 And so on to the ninth and last [row], in which you shall find the noncuple of the number given. [¶] Hence †Noncuplica·tion, multiplication by nine. [¶] 1674 Jeake Arith. (1696) 25 Noncuplication, or to multiply by 9.
* “†noncuple, a. and n.” listed in the Oxford English Dictionary [2nd edition, 1989]
* “† noncuple, adj. and n.” listed in the Oxford English Dictionary [3rd edition, December 2003]