 | Benjamin Martin - 1747 - 574 σελίδες
...; 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... | |
 | Isaac Dalby - 1806 - 526 σελίδες
...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 - 1813 - 538 σελίδες
...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 ............... | |
 | Euclides - 1821 - 294 σελίδες
...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... | |
 | Beriah Stevens - 1822 - 436 σελίδες
...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... | |
 | Nicolas Pike - 1822 - 536 σελίδες
...number* it is, whcu tlie Jirst is to Ike tltird, ai the difference between, the first and lecond it to the difference between the second and third, as the numbers 3, 4, 6. Thus, if the length* of strings be as these numbers, they will sound an octave 'J to 6, u fifth... | |
 | George Crabb - 1823 - 704 σελίδες
...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.... | |
 | 1823 - 936 σελίδες
...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 - 1824 - 550 σελίδες
...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... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...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,... | |
| |
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... 
