| James Maginness - Arithmetic - 1821 - 378 pages
...lengths of strings sounding musical notes; and of three numbers it is, when the first is to the third, as the difference between the first and second, 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... | |
| 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... | |
| James Maginness - Arithmetic - 1821 - 378 pages
...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 - 436 pages
...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
...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
...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
...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,... | |
| John Bonnycastle - Algebra - 1825 - 336 pages
...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... | |
| Sir William Chambers, Joseph Gwilt - Architecture - 1825 - 378 pages
...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... | |
| Thomas Curtis - Aeronautics - 1829 - 798 pages
...article PROPORTION, that if three numbers be in harmonical proportion the first is to the third as ty-five leagues from St. Louis, ascending the Senegal, * Foulah, into which the waters of th Let a, b, and x be three terms in harmonical proportion ; then a ; x '. '. a — b '. Ь — x. whence... | |
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