 | Edward Olney - Algebra - 1882 - 358 pages
...SECTION V. HAEMONIC PROPORTION AND PROGRESSION. 96. 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.... | |
 | Euclides - 1884 - 434 pages
...mathematicians* defined three magnitudes to be in harmonical 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. Now, if AB be cut internally at C and externally at D in the same ratio, AD :DB =AC:CB;... | |
 | Thomas Henry Eagles - 1885 - 404 pages
...DEFINITION. 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 between the first and third.... | |
 | George Hale Puckle - Conic sections - 1887 - 404 pages
...first, second, and third quantities, respectively, equation (2) asserts that 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 quantities are therefore in hannonical progression. The lines KO, KA, KP,... | |
 | Nathan Fellowes Dupuis - Geometry - 1889 - 370 pages
...AP:AQ=AB-AP:AQ-AB. Taking AP, AB, AQ as three magnitudes, we have the statement : — The first is to the third as the difference between the first and second is to the difference between the second and the third. And this is the definition of three quantities in Harmonic Proportion as given... | |
 | Encyclopedias and dictionaries - 1890 - 986 pages
...1C PEOPOETI01T. 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 the reciprocals of numbers... | |
 | Nathan Fellowes Dupuis - Algebra - 1892 - 362 pages
...-• abc bac a _a — b с b — c That is, three quantities are in HP when the first is to the third as the difference between the first and second is to the difference between the second and third. The term Harmonic is derived from the property that a string of a musical instrument... | |
 | Nathan Fellowes Dupuis - Geometry - 1894 - 313 pages
...AQ-AB. Taking AP, AB, AQ as three magnitudes, we have the statement : — The first is to the third as the difference between the first and second is to the difference between the second and the third. And this is the definition of three quantities in Harmonic Proportion as given... | |
 | John Clark Ridpath - Encyclopedias - 1897 - 496 pages
...its name. ' Harmon'ic Proportion. Three numbers are said to be in HP 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 HP is that which subsists between the reciprocals of numbers which are... | |
 | Encyclopedias and dictionaries - 1897 - 844 pages
...physical laws. HARMONIC PROPORTION : that relation of three numbers when the first is to the third, as the difference between the first and second is to the difference between the second and third as in the three numbers 2, 8, 6 ; otherwise harmonic proportion is that which subsists... | |
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Three quantities are said to be 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. 
