 | Benjamin Martin - 1747 - 574 Seiten
...between four Numbers is, when the Firft is to the Fourth as the Difference between the Firft and Sfcond is to the Difference between the Third and Fourth, as in the (See Annotation XXII.) alfo that the Force of moving Bodies is as the Quantity of Matter and Velocity... | |
 | Isaac Dalby - 1806 - 526 Seiten
...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 ............... | |
 | James Maginness - 1821 - 378 Seiten
...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 between the first...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 10 will sound an octave 5 to 10;... | |
 | James Maginness - 1821 - 378 Seiten
...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... | |
 | Nicolas Pike - 1822 - 536 Seiten
...firnt is lo the fourth, at the difference between the Jirst and lecond i» In tlie difference betteeen the third and fourth, as in the numbers 5, 6, 8, 10 ; for strings of sjich lengths will sound an octare 5 to 10 ; u sixth greater, 6 to 10 ; a third greater 8 to 10 ; a... | |
 | George Crabb - 1823 - 704 Seiten
...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 between the first...second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion are in harmonica) proportion. Proportion... | |
 | James Ryan - 1824 - 550 Seiten
...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, Robert Adrain - 1824 - 542 Seiten
...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... | |
 | Sir William Chambers, Joseph Gwilt - 1825 - 378 Seiten
...is the same as 6 divided by 4, each being 1£ ; harmonical, wherein the first term is to the third as the difference between the first and second is to the difference between the second and third, or in four terms, where the first is to the fourth as the difference between the... | |
 | John Bonnycastle - 1825 - 336 Seiten
...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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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... 
