 | 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...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... | |
 | 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...is to the difference between the second and third; that is, they are in harmonic progression, according to the definition commonly given in algebra. Of... | |
 | Edward Olney - Geometry - 1872 - 562 pages
...HARMONIC PROPORTION AND HARMONIC PENCILS. 957- DEF- — Three quantities are in Harmonic Proportion when the difference between the first and second 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 0 — 4:4 — 3::6:8.... | |
 | Edward Olney - Geometry - 1872 - 96 pages
...HARMONIC PROPORTION AND HARMONIC PENCILS. 95V. DEF. — Three quantities are in Harmonic Proportion when the difference between the first and second 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... | |
 | Edward Olney - Geometry - 1872 - 102 pages
...HARMONIC PROPORTION AND HARMONIC PENCILS. 957- DBF.—Three quantities are in Harmonic Proportion when the difference between the first and second 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: :... | |
 | Edward Olney - Algebra - 1873 - 354 pages
...SECTION V. HARMONIC PROPORTION AND PROGRESSION. 90. 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... | |
 | 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... | |
 | Chambers W. and R., ltd - 1874 - 870 pages
...come down to us in the Greek Scholia. HARMO'KIC PROPORTION'. Three numbers are said to be in harmonic proportion when the first is to the third, as the difference between the firut and second is to the difference between the second and third, otherwise harmonic proportion ia... | |
 | 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 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 the... | |
 | 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...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... 
