 | John Bonnycastle - 1848 - 334 σελίδες
...harmonical progression is a series of which the first of any three consecutive terms is to the third, as the difference between the first and second is to the difference between the second and third. Thus, 1, i,!,*,i, and 2, 2f, 3, 4, 6, 12, are harmonical series, for taking any three... | |
 | Horatio Nelson Robinson - 1848 - 354 σελίδες
...magnitudes, a, b, c, have the relation of a: c : : a — b : b — c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion. (Art. 125.) Four... | |
 | Samuel Alsop - 1848 - 336 σελίδες
...Proportion. 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a -- о : b — с ; the magnitudes a, b, and care in-harmonical... | |
 | Uriah Parke - 1849 - 414 σελίδες
...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... | |
 | Stephen Chase - 1849 - 348 σελίδες
...and 6 are in harmonical proportion, because 2 : 6 ~ 3 — 2 : 6 — 3. 2. Four numbers are said to be in harmonical proportion, when the first is to the fourth, as the difference of the (e) Gr. lipiurvia, joining, harmony. first and second is to the difference of the third and... | |
 | Uriah Parke - 1850 - 402 σελίδες
...numbers, they will sound an octave 3 to 6; a fifth 2 to 3, and a fourth 3 to 4. Again, between 4 numbers, when the first is to the fourth, as the difference between the first and second is to the differ enee between the third and fourth, as in the numbers 5, 6, 8, 10, for strings of such lengths,... | |
 | Horace Mann - 1851 - 384 σελίδες
...33554430. OO. HARMONICAL PROGRESSION.» When three numbers are such that the first is to the third, as the difference between the first and second is to the difference between the second and third, they are said to be in HARMONICAL PROPORTION ; and a series of numbers, in continued... | |
 | John Bonnycastle - 1851 - 288 σελίδες
...~^~ /* 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, 01... | |
 | Benjamin Greenleaf - 1852 - 348 σελίδες
...PROGRESSION. ART. 276. Three numbers are said to be in harmonica! progression, 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, the numbers 3, 4, 6 are in harmonical proportion. For, 3:6:: 4—3 : 6—4.... | |
 | G. Ainsworth - 1854 - 216 σελίδες
...PROGRESSION. Three quantities are said to be in harmonical progression when the first term is to the third as the difference between the first and second is to the difference between the second and third. a, 6, с are in Har. Prog, when a : c=a—b : b—c. Four quantities are said to... | |
| |
C = 2^V 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. 
