 | Thomas Steadman Aldis - 1872 - 84 pages
...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 first and third. AB a harmonic mean between AP and... | |
 | William Chauvenet - Mathematics - 1872 - 382 pages
...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 the definition commonly given in algebra.... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...constant « a iz, and if í is constant sa: f. SECTION V. HARMONIC PROPORTION AND PROGRESSION. 90. Three quantities are in Harmonic Proportion when the...the same order) as the first is to the third. ILL. 6,4, and 3 are in harmonic proportion, since 6 — 4 : 4 — 3 : : G : 8. If а, Ъ, e are in harmonic... | |
 | Encyclopedias and dictionaries - 1874 - 868 pages
...PROPORTION. Three numbers are said to be in harmonic proportion when the first is to the third, аз the difference between the first and second is to the difference between the second and third, otherwise harmonic proportion is that which subsists between the reciprocals of numbers which are in... | |
 | Edward Atkins - 1875 - 410 pages
...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 — b : b — c. We cannot make a formula for... | |
 | 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 Olney - Geometry - 1876 - 354 pages
...transversal to the triangle ILN. SECTION V. HARMONIC PROPORTION AND HARMONIC PENCILS. 053. DEF.—Three quantities are in Harmonic Proportion when the difference...is to the difference between the second and third, as the first is to the third. ILL.—6, 4, 3 are in harmonic proportion, since 6 — 4:4—3::6:3.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...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 first and third. The expression ' harmonical... | |
 | Edward Atkins - Mathematics - 1876 - 378 pages
...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 — b : b — c. We cannot make a formula for... | |
 | Edward Brooks - Arithmetic - 1876 - 588 pages
...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... | |
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... 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. 
