 | Benjamin Martin - Science - 1747 - 574 pages
...; and of three Numbers it is, vvhen the Firjt is to the Third, as the Dif'ference between the Firfi and Second is to the Difference between the Second and Third, as the Num2. Now iince the Tending Force F acts upon the String in the Direction DB, it may be reprefented... | |
 | 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 3,... | |
 | 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,... | |
 | 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... | |
 | 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... | |
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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... 
