 Three quantities are said to be 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.  The University Algebra - Page 390by John Fair Stoddard, William Downs Henkle - 1866 - 528 pagesFull view - About this book
 | Isaac Dalby - Mathematics - 1806 - 526 pages
...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 ............... | |
 | Charles Butler - 1814 - 582 pages
...difference of the first and second to the difference of the second and third ; and four terms are said to be in harmonical proportion, when the first is to the fourth, as the difference of the first and second to the. difference of the third and fourth. Thus, if a : c :: a—b : b—c,... | |
 | William Nicholson - Natural history - 1819 - 394 pages
...wlu-n the first, the third, and the said two differences, are in geometrical proportion. Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth. Thus 2, 3, 6, are in harmonicaI... | |
 | James Maginness - Arithmetic - 1821 - 378 pages
...they will sound an octave S to 6, 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...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 5, 6, 8, and... | |
 | 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... | |
 | Beriah Stevens - Arithmetic - 1822 - 436 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, 6. Thus, if the lengths of strings be as these numbers, they... | |
 | George Crabb - Industrial arts - 1823 - 704 pages
...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...second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion. Proportion... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...PROGRESSION. 490. Three quantities are said to be 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. Thus, a, 6, c, are harmonically proportional, when a : c : : a — b : b — c, or... | |
 | James Ryan - Algebra - 1824 - 550 pages
...PROGRESSION. 490. Three quantities are said to be 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. Thus, a, 6, c, are harmonically proportional, when a : c : : a — b : b — c, or... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...1— r 9. Three quantities are said to be 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. Thus, a, b, c, are harmonically proportional, when a:c ;;a— b : b — c, or a :... | |
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