 | Euclides - 1864 - 448 pages
...extreme segments, as the other extreme segment is to the middle part. 'Three lines are in harmonica! proportion, when the first is to the third, as the...is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical... | |
 | Elias Loomis - Algebra - 1864 - 386 pages
...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, c,... | |
 | Robert Potts - 1865 - 528 pages
...extreme segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the...is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical... | |
 | Rolla Rouse - 1867 - 228 pages
...Continue dc to g, and eg will give the harmonic mean.t Harmonic proportion is that in which the first term is to the third, as the difference between the first...is to the difference between the second and third, or — when the first and third and the said two differences are in geometric proportion — or, four... | |
 | George Whitefield Samson - Art - 1867 - 852 pages
...those producing the first, third, fifth and eighth are in this proportion; "the first is to the fourth as the difference between the first and second is to the difference between the third and fourth," or 24 : 48 : : 30 — 24 : 48 — 36 ; ie 1 : 2 : : 6 : 12. Again the intervals... | |
 | Encyclopedias and dictionaries - 1868 - 872 pages
...come down to us in the Greek Scholia. HARMO'NIC PROPORTION. Three numbers are said to be in harmonic proportion when the first is to the third, as the...is to the difference between the second and third, otherwise harmonic proportion is that which subsists between the reciprocals of numbers which are in... | |
 | Robert Potts - 1868 - 434 pages
...extreme segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the...is to the difference between the second and third ; and the second is called a harmonic mean betwe en the first and third. The expression ' harmonical... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...segments of any focal chord of a conic. DEP. Three magnitudes are said to be in harmonic progression when the first is to the third as the difference between...is to the difference between the second and third : and the second magnitude is said to be an harmonic mean between the first and third. Let PSP' be... | |
 | George Hale Puckle - Conic sections - 1870 - 382 pages
...AB, AG as the first, 'second, and third quantities, respectively, equation (2) asserts that the lirst is to the third as the difference between the first...is to the difference between the second and third, anij the quantities are therefore in harmonical progression. The lines KO, KA, KP, KB, in the figure... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...harmonic proportion [2] may be written thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, are^uch that the first is to the third as the difference between...is to the difference between the second and third ; that is, they are in harmonic progression, according to the definition commonly given in algebra.... | |
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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... 
