 | James Cahill (of Dublin.) - Algebra - 1875 - 230 pages
...third. And 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 a, 6, and с are in harmonical proportion when a : с : : a — 6 : b — с... | |
 | Edward Atkins - Mathematics - 1876 - 378 pages
...131. Quantities are said to be in Harmonical Progression when any three consecutive terms being taken, the first is to the third as the difference between...is to the difference between the second and third. Thus, if а, Ъ, с be in HP, we must have a : с \: a — b : b — c. We cannot make a formula for... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...as the other extreme segment is to the middle part. Three lines are in, Jiarmonical proportion, when the first is to the third, as the difference between...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... | |
 | Edward Brooks - Arithmetic - 1876 - 588 pages
...inversely as two other quantities. An Harmonieni Proportion is one in which the first term is to the last as the difference between the first, and second is to the difference between the last and the one preceding the last. We have also Partitii-e and Medial Proportion, which will be defined... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...PROPORTION AND HARMONIC PENCILS. 92. Def. Three quantities are said to be in harmonic proportion when the first is to the third as the difference between...is to the difference between the second and third. Thus 6, 4, 3 are in harmonic proportion, for 0:3" G— 4 : 4—3. PROPOSITION I. 93. When a straight... | |
 | D. Tierney - 1877 - 126 pages
...-7 are three consecutive terms in a a - bb ' a ' a + 5b Harmonic Progression, since the first term is to the third as the difference between the first...is to the difference between the second and third. That they are three terms in Harmonical Progression is also obvious, since they are the reciprocals... | |
 | James White - Conic sections - 1878 - 160 pages
...follows also from Euc., Bk. VI., Prop. 3 and Cor.: taking this definition of harmonic progression, the first is to the third as the difference between...is to the difference between the second and third. angle contained by the straight line drawn from any point to an extremity and one point in the line... | |
 | Edward Olney - 1878 - 360 pages
...SECTION V. HARMONIC PROPORTION AND PROGRESSION. 96. Three quantities are in Harmonic Proportion when the difference' between the first and second is to the difference between the second and third (the differences being taken in the same order) as the first is to the third. ILL. 6, 4, and 3 are in harmonic... | |
 | James McDowell - 1878 - 310 pages
...magnitudes are in Harmonical Progression when the first is to the third as the .difference between the B _K first and second is to the difference between the second and third. (4) When a series of magnitudes is such that every three consecutive magnitudes are in arithmetical,... | |
 | Rolla Rouse - 1879 - 400 pages
...mean, continue c to g, and eg will be that mean. 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, the third, and the said two differences are in geometric proportion ; or, four... | |
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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... 
