 | 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 ............... | |
 | Isaac Dalby - Mathematics - 1813 - 538 pages
...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 ............... | |
 | 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... | |
 | Beriah Stevens - Arithmetic - 1822 - 434 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 - 732 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.... | |
 | Encyclopedias and dictionaries - 1823 - 934 pages
...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 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,... | |
 | James Ryan - Algebra - 1824 - 548 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... | |
 | 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... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...when C~2a— 6' „ 10. Four quantities are in harmonical 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 harmonica] proportion, when « : d ;: 0 — 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... 
