 | Jeremiah Day - 1814 - 304 σελίδες
...389. 6. Then a:ar::ar—a:arz—ar::arx—ar:ar'—ar*, &c. That is, the first term is Ui liu- second, as the difference between the first and second, to the difference between the second and third; and as tn« difference between the second and third, to the difference between the... | |
 | James Maginness - 1821 - 378 σελίδες
...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 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... | |
 | George Crabb - 1823 - 704 σελίδες
...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 between the first and second is to the difference between the third and the fourth ; the reciprocals of an arithmetical proportion... | |
 | 1823 - 936 σελίδες
...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 two first terme, its general... | |
 | James Ryan - 1824 - 550 σελίδες
...6)c], is a third harmonical proportion to a 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,... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...6)c], is a third harmonical proportion to a 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,... | |
 | John Bonnycastle - 1825 - 336 σελίδες
...a third harmonical proportion to a and b, when 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,... | |
 | Sir William Chambers, Joseph Gwilt - 1825 - 378 σελίδες
...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 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... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...'.ar — a : ar3 —ar'.-'.ar3 — ar : ar3 — ar3, &c. That is, the first term is to the second, as the difference between the first and second, to the difference between the second and third ; and as the difference between the second and third, to the difference betAveen the... | |
 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...DBF. — Three magnitudes are said to be in harmonical progression, when the first is to the third as the difference between the first and second to the difference between the second and third. *#* (531) DBF. — A right line AB is said to be cut harmonically at two points CD,... | |
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Four magnitudes 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. 
