 | Elias Loomis - 1855 - 356 σελίδες
...and 5. Ex. 2. Find a third harmonical proportional to 5 and 8. (229.) Four quantities are said to be in harmonical proportion when the first is to the...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, c, d be in harmonical proportion... | |
 | Charles Davies, William Guy Peck - 1855 - 592 σελίδες
...because 24 : 9 : : 8 : 3. Three quantities arc in harmonial proportion when Ihc 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 6, 4. and 3 are in harmonial proportion, because 6 : 3 . : 2 :... | |
 | Charles Davies, William Guy Peck - 1855 - 628 σελίδες
...HARMONICAL PROPORTION. Three terms or quantities arc said to be in contra harmonica! proportion, when the difference between the first and second is to the difference between the second and third, as the third is to the first. CON-VERGE', [b. comtTgo. con, with, and vcrgo, to incline].... | |
 | Benjamin Greenleaf - 1857 - 398 σελίδες
...4, 6, they will sound an octave 3 to 6, a fifth 2 to 3, and a fourth 3 to 4. 281. Four numbers arc in harmonical proportion when the first is to the...the difference between the third and fourth. Thus the numbers 5, 6, 8, 10, are in harmonic proportion. For 5 : 10 : : 6—5 : 10-8. Strings of such lengths... | |
 | Horace Mann, Pliny Earle Chase, Phiny Earie Chase - 1857 - 394 σελίδες
...33554430. 9O. 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... | |
 | Horace Mann, Pliny Earle Chase - 1857 - 388 σελίδες
...Ans. 33554430. >. 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... | |
 | Horatio Nelson Robinson - 1858 - 372 σελίδες
...said to be in harmonical proportion. (Art. 125.) Four magnitudes are in harmonical proportion «hen the first is to the fourth as the difference between...between the third and fourth. Thus, a, b, c, d, are in harmonical proportion when a : d : : a — b : с — d, or when a : d : : b — a : d — c. An harmonical... | |
 | Horatio Nelson Robinson - 1859 - 368 σελίδες
...third, the quantities a, b, c, are said to be in liarmonical proportion. (Art. 125.) Four magnitudes are in harmonical proportion when the first is to...difference between the third and fourth. Thus, a, b, e, d, are in harmonical proportion when a : d : : a — b : c — d, or when a : d : : b — a : d... | |
 | John Fair Stoddard, William Downs Henkle - 1859 - 538 σελίδες
...and third. The quantities a, 6, and e aro in karmonical proportion when ' о : с : a~6 : 6~c. (4O4.) Four quantities are in harmonical proportion, when...is to the difference between the third and fourth. The quantities a, 6, c, and d are in harmonica! proportion when a : d : : a~6 : c~<f. PROBLEM. (4O5.)... | |
 | James B. Dodd - 1859 - 368 σελίδες
...4—3 : 6—4, and 4 : 12 :I 6—4 : 12—6. An Harmonical Proportion consists of four terms such that the first is to the fourth as the difference between...between the third and fourth. Thus a, b, c, d, are in Harmonical Proportion, if a : d :: a—b : c—d; or a : d :: b — a : d — c. The numbers 16, 8,... | |
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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. 
