Figurate numbers
Figurate Fig"ur*ate, a. [L. figuratus, p. p. of figurare. See {Figure}.] 1. Of a definite form or figure. [1913 Webster]

Plants are all figurate and determinate, which inanimate bodies are not. --Bacon. [1913 Webster]

2. Figurative; metaphorical. [Obs.] --Bale. [1913 Webster]

3. (Mus.) Florid; figurative; involving passing discords by the freer melodic movement of one or more parts or voices in the harmony; as, figurate counterpoint or descant. [1913 Webster]

{Figurate counterpoint} or {Figurate descant} (Mus.), that which is not simple, or in which the parts do not move together tone for tone, but in which freer movement of one or more parts mingles passing discords with the harmony; -- called also {figural}, {figurative}, and {figured counterpoint} or {descant} (although the term figured is more commonly applied to a bass with numerals written above or below to indicate the other notes of the harmony).

{Figurate numbers} (Math.), numbers, or series of numbers, formed from any arithmetical progression in which the first term is a unit, and the difference a whole number, by taking the first term, and the sums of the first two, first three, first four, etc., as the successive terms of a new series, from which another may be formed in the same manner, and so on, the numbers in the resulting series being such that points representing them are capable of symmetrical arrangement in different geometrical figures, as triangles, squares, pentagons, etc.

Note: In the following example, the two lower lines are composed of figurate numbers, those in the second line being triangular, and represented thus: . 1, 2, 3, 4, etc. . . . 1, 3, 6, 10, etc. . . . . . . . etc. 1, 4, 10, 20, etc . . . . . . . . . . . . [1913 Webster]


The Collaborative International Dictionary of English. 2000.

Look at other dictionaries:

  • figurate numbers — plural noun A series of numbers such that if each be subtracted from the next, and the series so formed be treated in the same way, by a continuation of the process equal differences will ultimately be obtained • • • Main Entry: ↑figure …   Useful english dictionary

  • Figurate — Fig ur*ate, a. [L. figuratus, p. p. of figurare. See {Figure}.] 1. Of a definite form or figure. [1913 Webster] Plants are all figurate and determinate, which inanimate bodies are not. Bacon. [1913 Webster] 2. Figurative; metaphorical. [Obs.]… …   The Collaborative International Dictionary of English

  • Figurate counterpoint — Figurate Fig ur*ate, a. [L. figuratus, p. p. of figurare. See {Figure}.] 1. Of a definite form or figure. [1913 Webster] Plants are all figurate and determinate, which inanimate bodies are not. Bacon. [1913 Webster] 2. Figurative; metaphorical.… …   The Collaborative International Dictionary of English

  • Figurate descant — Figurate Fig ur*ate, a. [L. figuratus, p. p. of figurare. See {Figure}.] 1. Of a definite form or figure. [1913 Webster] Plants are all figurate and determinate, which inanimate bodies are not. Bacon. [1913 Webster] 2. Figurative; metaphorical.… …   The Collaborative International Dictionary of English

  • Figurate number — A figurate number is a number that can be represented as a regular and discrete geometric pattern (e.g. dots). If the pattern is polytopic, the figurate is labeled a polytopic number, and may be a polygonal number or a polyhedral number.The first …   Wikipedia

  • figurate number — noun : any of a progression of numbers formed from an arithmetical progression in which the first term is 1 and the difference an integer by taking the first term, and the sums of the first two, first three, first four, and so on as the… …   Useful english dictionary

  • Figural numbers — Figural Fig ur*al, a. [From {Figure}.] 1. Represented by figure or delineation; consisting of figures; as, figural ornaments. Sir T. Browne. [1913 Webster] 2. (Mus.) Figurate. See {Figurate}. [1913 Webster] {Figural numbers}. See {Figurate… …   The Collaborative International Dictionary of English

  • Triangular numbers — Triangular Tri*an gu*lar, a. [L. triangularis: cf. F. triangulaire.] 1. Having three angles; having the form of a triangle. [1913 Webster] 2. (Bot.) Oblong or elongated, and having three lateral angles; as, a triangular seed, leaf, or stem. [1913 …   The Collaborative International Dictionary of English

  • Polygonal numbers — Polygonal Po*lyg o*nal, a. Having many angles. [1913 Webster] {Polygonal numbers}, certain figurate numbers. See under {Figurate}. [1913 Webster] …   The Collaborative International Dictionary of English

  • Pyramidal numbers — Pyramidal Py*ram i*dal, a. [Cf. F. pyramidal.] [1913 Webster] 1. Of or pertaining to a pyramid; in the form of a a pyramid; pyramidical; as, pyramidal cleavage. [1913 Webster] The mystic obelisks stand up Triangular, pyramidal. Mrs. Browning.… …   The Collaborative International Dictionary of English

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