 | Euclides - 1884 - 434 σελίδες
...ways. The ancient Greek mathematicians* defined three magnitudes to be in harmonical progression when the first is to the third as the difference between...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; AD:AC = DB... | |
 | Thomas Henry Eagles - 1885 - 404 σελίδες
...cannot be 'curately determined. DEFINITION. Three magnitudes are said to be in harmonic progression when the first is to the third as the difference between...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 - 1887 - 404 σελίδες
...consider AD, AB, АО as the first, second, and third quantities, respectively, equation (2) asserts that the first is to the third as the difference between...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 - 1889 - 370 σελίδες
...AQ:BQ, A ' BQ .'. 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...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... | |
 | 1890 - 986 σελίδες
...Poggendorff's 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...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 - 1892 - 360 σελίδες
...-, - are in 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...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 - 1894 - 313 σελίδες
...APBQ .'. 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...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... | |
 | John Clark Ridpath - 1897 - 496 σελίδες
...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...is to the difference between the second and third ; otherwise HP is that which subsists between the reciprocals of numbers which are in arithmetical... | |
 | 1897 - 844 σελίδες
...Pythagoreans as a science founded on physical laws. HARMONIC PROPORTION : that relation of three numbers when the first is to the third, as the difference between...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... | |
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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... 
