 | 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
...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
...: 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
...121.968175. CON'TRA HARMONICAL PROPORTION. Three terms or quantities arc said to be in contra harmonica! proportion, when the difference between the first...the difference between the second and third, as the third is to the first. CON-VERGE', [b. comtTgo. con, with, and vcrgo, to incline]. To tend or incline... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...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.... | |
 | Horace Mann, Pliny Earle Chase, Phiny Earie Chase - Arithmetic - 1857 - 394 pages
...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 harmonical proportion,... | |
 | Horace Mann, Pliny Earle Chase - Arithmetic - 1857 - 388 pages
...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 harmonical proportion,... | |
 | Elias Loomis - Algebra - 1858 - 394 pages
...are said to be in harmonical proper tion when the first is to the third as the difference between tin first and second is to the difference between the second and third. Thus, 2, 3, 6 are in harmonical proportion ; for 2:6:: 3-2 : 6—3. Let a, b, c be in harmonical proportion... | |
 | John Fair Stoddard, William Downs Henkle - Algebra - 1859 - 538 pages
...a~6 : 6~c. (4O4.) 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. The quantities a, 6, c, and d are in harmonica! proportion when a : d : : a~6 : c~<f.... | |
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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... 
