The DICT Development Group
1 definition found
for Figurate numbers
From The Collaborative International Dictionary of English v.0.48 :
Figurate \Fig"ur*ate\, a. [L. figuratus, p. p. of figurare. See
1. Of a definite form or figure.
Plants are all figurate and determinate, which
inanimate bodies are not. --Bacon.
2. Figurative; metaphorical. [Obs.] --Bale.
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.
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
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 . . . . . . . . . . . .
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