 | William Chauvenet - Geometry - 1872 - 382 pages
...proportion [2] may be written thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, 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; that is, they are in harmonic progression, according to... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...the same pencil, however the transversal be drawn.) DEP. When we have three straight lines 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, the second is said to be the harmome mean between the... | |
 | James Cahill (of Dublin.) - Algebra - 1875 - 230 pages
...their product divided by their sum. Ans. Three quantities are said to be in Tiarmonical 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 four quantities are said to be in harmonical proportion... | |
 | Edward Atkins - 1875 - 410 pages
...28. 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 the first and second is to the difference between the second and third. Thus, if я, b, с be in HP, we must have a : с :: я... | |
 | William Chauvenet - Geometry - 1875 - 466 pages
...proportion [2] may be wiittcn thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, are such that the firet is to the third as the difference between the first and second is to the difference between the second and third ; that is, they are in harmonic progression, according... | |
 | 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 the first and second is to the difference between the second and third. Thus, if а, Ъ, с be in HP, we must have a : с \: a... | |
 | 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 the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the... | |
 | 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 the first and second is to the difference between the second and third. Thus 6, 4, 3 are in harmonic proportion, for 0:3" G—... | |
 | 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 and second is to the difference between the second and third. That they are three terms in Harmonical Progression is... | |
 | 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 the first and second is to the difference between the second and third. angle contained by the straight line drawn from any point... | |
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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... 
