 | Euclides - 1845 - 546 pages
...extreme segment is to the middle part. 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.... | |
 | Samuel Alsop - Algebra - 1846 - 300 pages
...Proportion. . J • . - » 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a — -b : b — c; the magnitudes a, b, and с are... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...124.) When three magnitudes, a,b,c, have the relation of a:c::a — b:b — c; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonica I proportion. (Art.... | |
 | James W. Kavanagh - 1846 - 304 pages
...to form a harmonica! series when of every three of its consecutive [following] terms the iirst is to the third, as the difference between the first and second is to the difference between the second and third ; thus 12, 8, and 6 form a harmonica1 series, for 12 : 6 : : 12—8 :... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...bf : : eg : dh. (228.) Three quantities are said to be 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. Thus, 2, 3, 6 are in harmonical proportion, for 2:6::3 — 2:6 — 3.... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...eg : dh. (228.) Three quantities are said to be \r\ harmonical proportion when the first is to tke third as the difference between the first and second is to the difference, between the second and third. Thus, 2, 3, 6 are in harmonica] proportion, for 2:6::3 — 2:6 — 3.... | |
 | Samuel Alsop - Algebra - 1848 - 336 pages
...Harmonical Proportion. 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a -- о : b — с ; the magnitudes a, b, and care... | |
 | John Bonnycastle - 1848 - 334 pages
...PROGRESSION. An harmonical progression is a series of which the first of any three consecutive terms is to the third, as the difference between the first and second is to the difference between the second and third. Thus, 1, i,!,*,i, and 2, 2f, 3, 4, 6, 12, are harmonical series, for... | |
 | Horatio Nelson Robinson - Algebra - 1848 - 354 pages
...three magnitudes, a, b, c, have the relation of a: c : : a — b : b — c ; that is, the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion. (Art.... | |
 | Pliny Earle Chase - Arithmetic - 1848 - 244 pages
...HARMONICAL PROGRESSION.* WHEN three numbers are such that the first is to the third, as the difference of the first and second is to the difference of the second and third, they are said to be in HAHHONICAL PROPORTION, and a series of numbers in continued harmonical proportion,... | |
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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... 
