 | Horatio Nelson Robinson - 1848 - 354 σελίδες
...proportion. (Art. 125.) 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. Thus, a, b, c, d, are in harmonical proportion when a : d : : a — b : c — d,... | |
 | Uriah Parke - 1849 - 414 σελίδες
...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 - 1850 - 402 σελίδες
...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 σελίδες
...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 - 1851 - 288 σελίδες
...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 - 1852 - 348 σελίδες
...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 σελίδες
...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 - 1855 - 628 σελίδες
...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.... | |
 | Charles Davies, William Guy Peck - 1855 - 592 σελίδες
...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.... | |
 | Elias Loomis - 1855 - 356 σελίδες
...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,... | |
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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... 
