 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...  Chauvenet's Treatise on Elementary Geometry - Page 201by William Chauvenet - 1888 - 322 pagesFull view - About this book
 | 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 - 842 pages
...of the first octave, and the 5th of the second octave, are in the following proportion; "the first is to the third as the difference between the first...is to the difference between the second and third ;" or 24 : 72 : : 36—24 : 72—36 ; ie 1 : 3 : : 12 : 36. These proportions coming within the two... | |
 | 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... | |
 | Robert Potts - 1868 - 434 pages
...other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference between the first...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... | |
 | Encyclopedias and dictionaries - 1868 - 872 pages
...Greek Scholia. HARMO'NIC PROPORTION. Three numbers are said to be in harmonic proportion when the first is to the third, as the difference between the first...is to the difference between the second and third, otherwise harmonic proportion is that which subsists between the reciprocals of numbers which are in... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...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 the first...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... | |
 | William Chauvenet - Mathematics - 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...THEOREM. 43. In a complete quadrilateral, each diagonal ii divided harmonically by the other two. Let ABCDEF be a complete quadrilateral (4), and L, M, N,... | |
 | 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...mean between the extremes AC and AD. PROPOSITION" X.—THEOREM. 43. In a complete quadrilateral, each diagonal ix divided harmonically by the other two.... | |
 | Thomas Steadman Aldis - 1872 - 84 pages
...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...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... | |
 | 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.... | |
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