 | Euclides - 1864 - 448 pages
...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 between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the... | |
 | Robert Potts - 1865 - 528 pages
...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 between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the... | |
 | George Whitefield Samson - Art - 1867 - 852 pages
...and 5th of the first octave, and the 5th of the second octave, arc in the following proportion ; " the first is to the third as the difference between the first and second is to the difference between the second and third ;" or 24 : 72 : : 36—24 : 72—36 ; ie 1 : 3 : : 12 :... | |
 | 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 and second is to the difference between the second and third, or — when the first and third and the said two differences... | |
 | Encyclopedias and dictionaries - 1868 - 872 pages
...in the 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 and second is to the difference between the second and third, otherwise harmonic proportion is that which subsists between... | |
 | Robert Potts - 1868 - 434 pages
...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 between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean betwe en the... | |
 | George Holmes Howison, Joseph Ray - Geometry, Analytic - 1869 - 622 pages
...(Doppelschnittsverhaltniss). 386. Definition. — An Harmonic Proportion subsists between three quantities, 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, if the pencil in the above diagram cut the transversal... | |
 | William Henry Besant - Conic sections - 1869 - 304 pages
...segments of any 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 and second is to the difference between the second and third : and the second magnitude is said to be an harmonic mean... | |
 | George Hale Puckle - Conic sections - 1870 - 382 pages
...AB, AG as the first, 'second, and third quantities, respectively, equation (2) asserts that the lirst is to the third as the difference between the first and second is to the difference between the second and third, anij the quantities are therefore in harmonical progression.... | |
 | William Chauvenet - Geometry - 1871 - 380 pages
...harmonic proportion [2] may be written thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, are^uch 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... | |
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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... 
