 | Thomas Henry Eagles - 1885 - 404 pages
...'curately determined. DEFINITION. 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. Thus if the... | |
 | Thomas Henry Eagles - Conic sections - 1885 - 401 pages
...accurately determined. DEFINITION. 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. Thus if the... | |
 | George Hale Puckle - Conic sections - 1887 - 404 pages
...АО as the first, second, and third quantities, respectively, equation (2) asserts that the first is to the third as the difference between the first...is to the difference between the second and third, and the quantities are therefore in hannonical progression. The lines KO, KA, KP, KB, in the figure... | |
 | 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...second is to the difference between the second and the third. And this is the definition of three quantities in Harmonic Proportion as given in Arithmetic... | |
 | Encyclopedias and dictionaries - 1890 - 986 pages
...Annaltn, 1855. HARMON 1C PEOPOETI01T. 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... | |
 | Nathan Fellowes Dupuis - Algebra - 1892 - 360 pages
...AP, and - = - + -- abc bac a _ a — b cb — c That is, three quantities are in HP when the first is to the third as the difference between the first...is to the difference between the second and third. The term Harmonic is derived from the property that a string of a musical instrument stopped at lengths... | |
 | Nathan Fellowes Dupuis - Geometry - 1894 - 313 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...second is to the difference between the second and the third. And this is the definition of three quantities in Harmonic Proportion as given in Arithmetic... | |
 | Encyclopedias and dictionaries - 1897 - 844 pages
...science founded on physical laws. HARMONIC PROPORTION : that relation of three numbers when the first is to the third, as the difference between the first...is to the difference between the second and third as in the three numbers 2, 8, 6 ; otherwise harmonic proportion is that which subsists between the... | |
 | John Clark Ridpath - Encyclopedias - 1897 - 496 pages
...instrument, etc., whence 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...is to the difference between the second and third ; otherwise HP is that which subsists between the reciprocals of numbers which are in arithmetical... | |
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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... 
