 | Euclides - 1821 - 294 pages
...3 : 6, permutando 1 : 8 : : 2 : 6 *'. e . the first term of the series is to the second as the dif. between the first and second is to the difference between the second and third ; and since the second term is greater than the first, it follows that the difference between the second... | |
 | Euclides - 1845 - 546 pages
...segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference...difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion' is derived... | |
 | Elias Loomis - Algebra - 1855 - 356 pages
...are said to be in harmonical proportion when the first is to the third as the difference between tlu. first and second is to the difference between the second and third, Thus, 2, 3, 6 are in harmonical proportion ; for 2 : 6:: 3-2 : 6-3. Let a, b, c be in harmonical proportion... | |
 | Elias Loomis - Algebra - 1858 - 394 pages
...are said to be in harmonical proper tion when the first is to the third as the difference between tin first and second is to the difference between the second and third. Thus, 2, 3, 6 are in harmonical proportion ; for 2:6:: 3-2 : 6—3. Let a, b, c be in harmonical proportion... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference...difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical proportion' is derived... | |
 | Euclides - 1864 - 448 pages
...segments, as the other extreme segment is to the middle part. 'Three lines are in harmonica! proportion, when the first is to the third, as the difference...difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical proportion' is derived... | |
 | Elias Loomis - Algebra - 1864 - 386 pages
...said to be in harmonical proper tion when the first is to the third as the difference between tltt first and second is to the difference between the second and third. Thus, 2, 3, 6 are in harmonical proportion ; for 2:6::3-2 : 6-3. Let a, b, c be in harmonical proportion;... | |
 | Robert Potts - 1865 - 528 pages
...segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference...difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression ' harmonical proportion' is derived... | |
 | Robert Potts - 1868 - 434 pages
...segments, as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference...difference between the second and third ; and the second is called a harmonic mean betwe en the first and third. The expression ' harmonical proportion' is... | |
 | George Hale Puckle - 1868 - 386 pages
...consider AD, AB, AC as the first, second, and third quantities, respectively, equation (2) asserts that the first is to the third as the difference between...to the difference between the second and third, and AD AD AO sin AOD sin C AC BD AO BD AC BO sinD sin BOD sinAOC sin C > BG BO 1 2 BG W sinD sin AOD sin... | |
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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... 
