 | Isaac Dalby - 1806 - 526 páginas
...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 ............... | |
 | Isaac Dalby - 1813 - 538 páginas
...that of the second and third by b. m If three numbers are ia musical proportion, the first will be to the third, as the difference between the first and second, is to the difference of the second and third. Let the first number be * ; Then the second will be x + a; And the third ............... | |
 | Charles Hutton - 1815 - 686 páginas
...the 3d is also For 9 x 4 = б X 6 = 36. equal to that of the 4th ; or if the multiple of the first be Harmonical PROPORTION, is when the first term is to the third, as the difference between the 1st and 2d is to the difference between the 2d and 3d ; or, in tour terms, when the 1st is to the 4th,... | |
 | Euclides - 1821 - 294 páginas
...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... | |
 | James Maginness - 1821 - 378 páginas
...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... | |
 | Beriah Stevens - 1822 - 436 páginas
...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 - 1823 - 704 páginas
...is the same thing, to the square of the single mean, when there is but one for : 9x4 = 6x6 = 36. — Harmonical Proportion is when the first term is to the third as the difference between the second and third ; or in four terms, when the first is to the fourth as the difference between the... | |
 | 1823 - 936 páginas
...geometrical series. 3. Harmonic Series is that in which the first of any three of its consecutive terms is to the third, as the difference between the first and second to the difference between the second and third : hence we readily find that putting a and 6 for its... | |
 | James Mitchell - 1823 - 666 páginas
...or between the quotients of the terms. See the preceding article. Ilarmonical PROPORTION, is wh en the first term is to the third as the difference between the 1st and 2d is to the difference between the •>'.! and 3d ; or in four terms, when the 1st is to the... | |
 | James Ryan - 1824 - 550 páginas
...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... | |
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Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression... 
