 | Samuel Alsop - Algebra - 1846 - 300 pages
...harmonical proportion. ,. 69. Four quantities are in harmonical proportion where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth. Thus, if a : d : : a — b : с — d, a, b, c, and d are in harmonical proportion.... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...b. (229.) Four quantities are said to be in harmonical proportion when the first is to the fourth a2 the difference between the first and second is to the difference between the third and fourth. Thus, 2, 3, 4, 8 are in harmonical proportion, for 2:8::3 — 2:8 — 4. Let a, b,... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...quantities are said to be in harmonical progression, when any three successive terms are so related, that the first is to the third as the difference between the first and the second is to the difference between the second and third. Thus if a, b, c are in harmonical progression,... | |
 | John Bonnycastle - 1848 - 334 pages
...PROGRESSION. An harmonical progression is a series of which the first of any three consecutive terms is to the third, as the difference between the first...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 consecutive terms... | |
 | Samuel Alsop - Algebra - 1848 - 336 pages
...in-harmonical proportion. 69. Four quantities are in harmonical proportion where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth. Thus, if a : d : : a — b : с — d, a, b, c, and d are in harmonical proportion.... | |
 | Uriah Parke - Arithmetic - 1849 - 414 pages
...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 difference between the third and fourth, as in the numbers 5, 6, 8, 10, for strings of such lengths, will sound an octave... | |
 | Uriah Parke - Arithmetic - 1850 - 402 pages
...musical intervals, or the lengths of strings sounding musical notes ; and of three numbers it is when the first is to the third, as the difference between...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 will sound an octave... | |
 | Horace Mann - 1851 - 384 pages
...he was 500 years old? Ans. 33554430. OO. HARMONICAL PROGRESSION.» When three numbers are such that the first is to the third, as the difference between...is to the difference between the second and third, they are said to be in HARMONICAL PROPORTION ; and a series of numbers, in continued harmonical proportion,... | |
 | John Bonnycastle - Algebra - 1851 - 288 pages
...when ab C = 2^H>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, 5, c, d, are in harmonical proportion, when aid : ia — b : c — cZ, or... | |
 | Benjamin Greenleaf - Algebra - 1852 - 348 pages
...and a fourth 3 to 4. 277. Four numbers 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, the numbers 5, 6, 8, 10 are in harmonic proportion. For, 5 : 10 : : 6—5 :... | |
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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... 
