Citations:noncuple


 * 1557, Robert Record, Whetstone of Witte, sig. Eiiiᵛ
 * 36 vnto 4 is a noncuple proportion.
 * 1570, Henry Billingsley, translating the words of the Comte de Candale, in the former’s translation of Euclid of Alexandria’s Στοιχεῖα, entitled The Elements of Geometrie of the Most Ancient Philosopher Euclide of Megara (therein naming the wrong Euclid), chapter XVI, f. 453ᵛ
 * To proue that a trilater equilater Pyramis, is noncuple to a cube inscribed in it.
 * 1636, Charls Butler, The Principles of Muſik in Singing and Setting: With the two-fold Uſe therof, Eccleſiaſticall and Civil (London: John Haviland), page 25
 * Becaus Sextupla is đe Triple of Minims in Duple Time, and Noncupla đe Triple of Minims in Triple Timʻ; đerʻforʻ we e fall reddily out of Duple Proportion, into Sextupla, as in đe Kings Mask: (alđow g in đe Medley, đis Sextupla dωʻŧ immediatly ſucce e dʻ đe Triple) and out of Triple into Noncupla: as in đe G R O U N D: w i c be e ing ſet to đe Virginal, đe ri g t hand diſcanteŧ in Noncuple uppon đe plain Triple of đe left hand.
 * 1674, Sir William Petty, A Discourse Made before the Royal Society…Concerning the Use of Duplicate Proportion…Together with a new Hypothesis of Springy or Elastique Motion (London), page 117; quoted by Robert Kargon in “ William Petty’s Mechanical Philosophy” (pages 63–66) in Isis (ed. George Sarton; pub. University of Chicago Press on behalf of the History of Science Society), volume 56, № 1 (1965 Spring), pages 65–66
 * [T]ake a Bow and hang any weight to the middle of its string, and observe how low it draweth the said string; Now if you shall quadruple the same weight it will draw down double the first distance, and noncuple will draw it down treble, etc.
 * ante 1690, Samuel Jeake, Λογιστικη Λογια, or Arithmetick Surveighed and Reviewed; in four books (2nd ed., pub. 1696, London), page 182
 * Both triples added together…make the proportion or amounting Ratio Noncuple, or ninefold.
 * 1690, William Leybourn, Cursus Mathematicus (1st ed.), 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; In Four Parts (7th ed., J. Matthews at the Black-Swan in Pater-Noſter-Row), part III: “Of Inſtrumental Arithmetick”, § ii: ‘By Nepair’s Bones’, page 265
 * In the third (againſt the Figure 3) 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 [aut.], John Kersey and George Shelley [eds.], Mr. Wingate’s Arithmetick: Containing a Plain and Familiar Method for Attaining the Knowledge and Practice of Common Arithmetick (13th ed., London: three publishers), chapter VI: “Diviſion by whole Numbers”, 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.
 * 1729, Lt. Gen. Casimir Simienowicz [aut.] and Capt. George Shelvocke [tr.], The Great Art of Artillery (J. Tonſon at Shakeſpear’s Head in the Strand), book III: “Of Rockets”, chapter iv: ‘How to mix the Ingredients, and prepare Compoſitions for all Sorts of Rockets’, page 148
 * In ſhort, from one ℔ to the very leaſt Rocket, 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.
 * 1730, Galileo Galilei [aut.] and Tho[mas?] Weſton [tr.], Mathematical Diſcourſes Concerning Two New Sciences Relating to Mechanicks and Local Motion, in Four Dialogues (J. Hooke at the Flower-de-Luce in Fleet-ſtreet), dialogue III: “Of Motion naturally accelerated”, page 264
 * ‛Tis manifeſt, therefore, from this Computation, that the Spaces run thro’ in equal Times, by a Moveable, which, departing from Reſt, acquires a Velocity conformable to the Increaſe of the Time, are to one another as the uneven Numbers, counting from the Unit, as 1, 3, 5, are: And that the Spaces run thro’ being taken together, 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; and, in a Word, that the Spaces run thro’ are in a duplicate Ratio of the Times, i. e. as the Squares of the Times.
 * ante 1742, Edmond Halley [aut.] and Eugene Fairfield McPike [ed.], Correspondence and Papers of Edmond Halley: Preceded by an Unpublished Memoir of His Life by One of His Contemporaries and the ‘Éloge’ by d’Ortous de Mairan (1932; Oxford: At the Clarendon Press), page 148
 * […] treble by a Noncuple &c and to bring that to measure, if the Reservatory of Water be 32 foot high, the velocity of the water will be the same as of a body fallen 16 foot, as all bodies do in a second of time, now that velocity is at the rate of 32 foot to a second. and for any other hight as √32 : 32 :: so √ hight to the velocity of the Liquor pressing by its weight out at a Hole[.]
 * 1744–1749, Gottfried Wilhelm von Leibniz (in correspondence with John Bernoulli), “Commercium Literarum” (1696 January), quoted in translation in The Philosophical Transactions of the Royal Society of London, from Their Commencement, in 1665, to the Year 1800; Abridged, eds. Charles Hutton, George Shaw, and Richard Pearson, volume IX: 1744–1749 (1809; C. and R. Baldwin, New Bridge-Street, Blackfriars), by James Jurin in his “Dynamical Principles, or Metaphyſical Principles of Mechanicks”, on page 218
 * If for duple we had substituted triple, quadruple, quintuple, &c. the action would have come out noncuple, sedecuple, 25ple; and generally it appears, that equable, equitemporaneous, moving actions, are to equal moveable, as the squares of the velocities; or, which is the same thing, that in the same or an equal body, the forces are in a duplicate ratio of the velocities.
 * 1760, Francis Maſeres, Elements of Plane Trigonometry: In which is introduced, a Diſſertation on the Nature and Uſe of Logarithms (London: T. Parker and T. Payne in Caſtle-ſtreet near the Mews-gate; J. Whiſton and B. White at Boyle’s-head, Fleet-ſtreet), article 103, 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.
 * 1797, Colin Macfarquhar and George Gleig [eds.], Encyclopædia Britannica: or, A Dictionary of Arts, Sciences, and Miſcellaneous Literature (3rd ed., Colin Macfarquhar and Andrew Bell), volume 15: 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 [editor of the original French], and Charles Hutton [translator], Recreations in Mathematics and Natural Philosophy (printed for G. Kearsley, Fleet Street, by T. Davison, White-Friars), volume 2, part V: “Containing every thing moſt curious in regard to acouſtics and muſic”, article v.2: ‘Ingenious manner in which Rameau expreſſes the relation of the ſounds in the diatonic progreſſion’, pages 395–396
 * The velocity of the vibrations performed by a string, of a determinate length, and distended by different weights, is as the square roots of the stretching weights: quadruple weights therefore will produce double velocity, and consequently double the number of vibrations in the same time; a noncuple weight will produce vibrations of triple velocity, or a triple number in the same time.
 * 1816, Thomas Taylor, Theoretic Arithmetic, in Three Books; containing the substance of all that has been written on this subject by Theo of Smyrna, Nicomachus, Iamblichus, and Boetius. — Together with some remarkable particulars respecting perfect, amicable, and other numbers, which are not to be found in the writings of any ancient or modern mathematicians. Likewise, a specimen of the manner in which the Pythagoreans philosophized about numbers; and a development of their mystical and theological arithmetics. (London: A.J. Valpy, Tooke’s Court, Chancery Lane), book II, chapter xxxviii: “On the aggregate of the parts of the terms of different series.”, page 133
 * In the noncuple series, each term exceeds the octuple of the sum of its parts, by unity.
 * 1835, G. Hervey, Hoyle’s Games, Improved and Enlarged by New and Practical Treatises, with the Mathematical Analysis of the Chances of the Most Fashionable Games of the Day, Forming an Easy and Scientific Guide to the Gaming Table, and the Most Popular Sports of the Field (London: thirteen publishers), part I: “Games of Chance”, § 2: ‘Combinations of Dice’, page 22
 * For nine dice. To have…1 noncuple…[there is] 1…Determinate throw [and] there are…6…Indeterm[inate] throws.
 * 1984, The Journal of Musicological Research (Gordon and Breach), volume 5, page 17
 * The eighth is vacant because there is no noncuple proportion of 9/1 on the monochord, though it is possible in nature — and, we could now add, electronically.