superparticular

superparticular
Pertaining to a ratio of any whole number to the next below it (i.e. , etc.).

When a number contains the whole of another in itself, and some part of it besides, it is called superparticular. And if the part of the less it contains is the half, it is called sesquialter; if the third part, sesquitertian; if the fourth, sesquiquartan; if the fifth, sesquiquintan. And the like names being employed to infinity, the form of superparticular numbers will also proceed infinitely.


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  • Superparticular — Su per*par*tic u*lar, a. [L. superparticularis. See {Super }, and {Particular}.] (Math.) Of or pertaining to a ratio when the excess of the greater term over the less is a unit, as the ratio of 1 to 2, or of 3 to 4. [Obs.] Hutton. [1913 Webster] …   The Collaborative International Dictionary of English

  • superparticular — “+ adjective Etymology: Late Latin superparticularis, from Latin super + particula small part + aris ar more at particle : of or relating to a ratio in which the greater term exceeds the less by a unit the ratios of 4 to 3 and of 8 to 7 are… …   Useful english dictionary

  • Superparticular number — Superparticular numbers, also called epimoric ratios, are ratios of the form Thus: A superparticular number is when a great number contains a lesser number, to which it is compared, and at the same time one part of it. For example, when 3 and 2… …   Wikipedia

  • superparticular number — noun A number in the form of a ratio where the dividend equals the divisor plus one. 2/1 and 3/2 and 4/3 and 8/7 are all examples of superparticular numbers. Syn: epimoric ratio, superparticular ratio …   Wiktionary

  • superparticular — su·per·particular …   English syllables

  • multiple superparticular — noun The sum of a whole number and a number of the form for a whole number larger than . is a multiple superparticular, as it is …   Wiktionary

  • Størmer's theorem — In number theory, Størmer s theorem, named after Carl Størmer, gives a finite bound on the number of consecutive pairs of smooth numbers that exist, for a given degree of smoothness, and provides a method for finding all such pairs using Pell… …   Wikipedia

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  • Tritone — For other uses, see Tritone (disambiguation). tritone Inverse tritone Name Other names augmented fourth, diminished fifth Abbreviation TT Size …   Wikipedia

  • Carl Størmer — Infobox Scientist name = PAGENAME box width = image width =150px caption = PAGENAME birth date = September 3, 1874 birth place = Skien death date = August 13, 1957 death place = residence = citizenship = nationality = Norwegian ethnicity = field …   Wikipedia

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