| 单词 | figurate arithmetic |
| 释义 | > as lemmasfigurate arithmetic b. figurate numbers: 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., terms as the successive terms of a new series, from which another may be formed in the same manner, and so on. So figurate arithmetic, the science of such numbers.Thus from the arithmetical series 1, 2, 3, 4, etc., a second series 1, 3, 6, 10, etc. (‘triangular’ numbers) is formed as above described; and from this again a third series, 1, 4, 10, 20 (‘pyramidal’ numbers). ΘΚΠ the world > relative properties > number > arithmetic > [noun] > kinds of decimal arithmetic1608 disme1608 decimal1623 vulgar arithmetic1653 logistic1656 figurate arithmetic1666 rhabdology1667 mental arithmetic1766 binary arithmetic1796 the world > relative properties > number > mathematical number or quantity > [noun] > produced in a certain way > figurate or polygonal corporal number1594 figurate numbers1666 polygonal1717 figurate1796 polygon1842 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > progression > numerical elements in or parts of parcel1561 figurate numbers1666 harmonic mean1706 harmonical1796 arithmetical1798 harmonic average1949 1706 W. Jones Synopsis Palmariorum Matheseos 163 The Sums of Numbers in a Continued Arithmetic Proportion from Unity are call'd Figurate..Numbers. 1785 C. Hutton Math. Tables 7 The several orders of figurate numbers, which he [Vieta] calls triangular, pyramidal, etc. 1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 528 Ex. 2 The sum of the x first terms of any progression of figurate numbers being required. < as lemmas |
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