 | Henry Angel - 1880 - 360 pages
...yz=p<i". (3). Three quantities are said 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. Taking the numbers 10, 12, and 15, for example, they form a HP; for 10 : 15 :: 12... | |
 | Edward Olney - Algebra - 1880 - 354 pages
...SECTION V. HARMONIC PROPORTION AND PROGRESSION. 90. 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.... | |
 | James Mackean - 1881 - 510 pages
...terms, and also to infinity 1 217. Geometrical Progression is sometimes called Equirational Progression. difference between the first and second is to the difference between the second and third, — the differences being taken in the same order. Thus, 3, 4, 6, 12 are in Harmonical... | |
 | William Chambers, Andrew Findlater - English language - 1882 - 628 pages
...: recurring periodically.— Harmonic Proportion, proportion in which the first i • 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, 3. and 6. — adv. Harmonically. Harmonics, har-mon'iks,... | |
 | Chambers W. and R., ltd - 1882 - 618 pages
...concordant : recurring periodically.— Harmonic Proportion, proportion in which the first U 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 a, 3, and CL — adv. Harmonically. Harmonics, har-mon'iks,... | |
 | 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 - History - 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... | |
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... 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 the numbers 3, 4, 6. 
