| Isaac Dalby - Mathematics - 1806
...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
...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 ............... | |
| Arithmetic - 1821 - 372 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... | |
| William Enfield (M.A.) - Mathematical recreations - 1821 - 276 pages
...in harmonical proportion, when the first is to the last as the difference between the first and the **second is to the difference between the second and third. Thus the numbers 6,** 3, 2, are in harmonical proportion; for 6 is to 2 as 3, the difference between the two first numbers,... | |
| Euclides - 1821
...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 - 372 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 - 423 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
...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
...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 - 516 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,... | |
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