 | 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
...been living when 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...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 :... | |
 | G. Ainsworth - 1854 - 216 pages
...c=a—b : b—c. Four quantities are said to be in Har. Prog, when the first term is to the fourth term as the difference between the first and second is to the difference between the third and fourth. a, b, c, d are in Har. Prog, when a : d=(b—a) : (d—c). Any series of quantities... | |
 | Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...harrnonial proportion, because 24 : 9 : : 8 : 3. Three quantities are in harmonial proportion when the first is to the third as the difference between...is to the difference between the second and third. Thus, the numbers 6, 4, and 3 are in harmonial proportion, because G : 3 : : 2 : 1. PRO-PöRTION-AL.... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...and 8. (229.) Four quantities are said to be 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, 2, 3, 4, 8 are in harmonical proportion ; for 2:8:: 3—2 : 8-4. Let a, b,... | |
 | Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...PHOPORTIOX HAKMOMAL. Four quantities arc in ii .rni.ini.il 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 24, 10, 12, and 9 are in li.iini.nn.il proportion, because 24 : 9 : : 8 : 3.... | |
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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... 
