 | 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 :... | |
 | Benjamin Greenleaf - Algebra - 1854 - 374 pages
...SECTION XXII. HARMONICAL PROGRESSION. ART. 280i Three numbers are said to be in harmonical progression when the first is to the third as the difference between...the difference between the second and third. Thus th<5 numbers 3, 4, 6, are in harmonical proportion. For ' 3:6:: 4—3 : 6—4. Or a, b, c, are in harmonical... | |
 | 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... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...aeXdh=bfXcg. Hence, by Art. 213, ae : bf : : eg : dh. (228.) Three quantities are said to be in harmonical proportion when the first is to the third as the difference between tlu. first and second is to the difference between the second and third, Thus, 2, 3, 6 are in harmonical... | |
 | James W. Kavanagh - Arithmetic - 1857 - 298 pages
...numbers is said to form a harmonical series when of every three of its consecutive [following] terms the first is to the third, as the difference between...the difference between the second and third ; thus 12, 8, and 6 form a harmonical series, for 12 : 6 : : 12—8 : 8—6. 308. The middle one of three... | |
 | Horace Mann, Pliny Earle Chase - Arithmetic - 1857 - 388 pages
...when he was 500 years old? Ans. 33554430. >. 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,... | |
 | Horace Mann, Pliny Earle Chase, Phiny Earie Chase - Arithmetic - 1857 - 394 pages
...he was 500 years old ? Ans. 33554430. 9O. 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,... | |
 | 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:c: : b±m : cirfcn. (a:c ::m:n ) HARMONICAL PROPORTION. (4O3.) Three quantities are in harmonical proportion, when the first is to the third, as the difference between the first and the second is to the difference between the second and third. The quantities a, 6, and e aro in karmonical... | |
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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... 
