| Isaac Dalby - Mathematics - 1806 - 526 pages
...and that of the second and third by b. If 3 numbers are in musical proportion, the first wilt he (o the third, as the difference between the first and second, is to the difference of the second and third. Let the first number be i ; Then the second will be * + a; And the third ............... | |
| John Bonnycastle - Algebra - 1813 - 456 pages
...when the first has the same ratio to the third, as the difference between the first and second has to the difference between the second and third. Thus, a, b, c, are harmonically proportional, when a : с : : a—~b : b—-c. 14. And four quantities are in harmonical proportion, when the first has... | |
| James Maginness - Arithmetic - 1821 - 378 pages
...of musical intervals, or the lengths of strings sounding musical notes; and of three numbers it is, when the first is to the third, as the difference...is to the difference between the second and third, as the numbers 3, 4, and 6; for 3 : 6 : : 4 — 3 : 6—4. If the lengths of strings be as the numbers... | |
| James Maginness - Arithmetic - 1821 - 378 pages
...a fifth 2 to 3, and a fourth 3 to 4. Again, between four numbers, when the first is to the fourth, as the difference between the first and second, is to the difference between the third and fourth, as in the numbers 5, 6, 8, 10; for 5 : 10 :: 6—5 : 10—8, and strings of the lengths... | |
| Euclides - 1821 - 294 pages
...3 : 6, permutando 1 : 8 : : 2 : 6 *'. e . the first term of the series is to the second as the dif. between the first and second is to the difference between the second and third ; and since the second term is greater than the first, it follows that the difference between the second... | |
| Beriah Stevens - Arithmetic - 1822 - 436 pages
...a fifth 2 to 3, and a fourth 3 to 4. Again, between four numbers, when the first ie to the fourth, as the difference between the first and second, is to the difference between the third and fourth, as in the numbers 5, 6, 8, 10 : For strings of such lengths will sound an octave... | |
| George Crabb - Industrial arts - 1823 - 704 pages
...as the difference between the second and third ; or in four terms, when the first is to the fourth as the difference between the first and second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion.... | |
| James Ryan - Algebra - 1824 - 550 pages
...and b, when c= ab 491. Four quantities are in harmonica! proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, n, 4, c, </, are in harmonica! proportion, when aid:: a — 6 : c — d, or... | |
| James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...and 6, when c= ah 491. Four quantities are in harmonica! proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. Thus, a, b, c, d, are in harmonical proportion, when a : d : : a — 6 : c — d,... | |
| Sir William Chambers, Joseph Gwilt - Architecture - 1825 - 378 pages
...to the difference between the second and third, or in four terms, where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth, as 6, 4, 3, or with four terms 24, 16, 12, 9; a sesquialteral ratio is that wherein... | |
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