 | James Stormonth - 1879 - 810 pages
...third and perfect fifth; the common chord: harmonlcal proportion, that relation of three numbers, when the first is to the third, as the difference between the first and second is to the dili'erence between the second and third, as in the three numbers 2, 3, and 6. harmotome, n. Mr'niu-tOm... | |
 | Rolla Rouse - 1879 - 400 pages
...mean, continue c to g, and eg will be that mean. 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, the third, and the said two differences... | |
 | Henry Angel - Geometry, Plane - 1880 - 372 pages
...(Euclid iii. 3), and xy, yz=pq*. (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... | |
 | Henry Angel - 1880 - 360 pages
...(Euclid iii. 3), and xy, 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... | |
 | Chambers W. and R., ltd - 1882 - 618 pages
...musical : 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.... | |
 | William Chambers, Andrew Findlater - English language - 1882 - 628 pages
...: concordant : 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.... | |
 | Euclides - 1884 - 434 pages
...ways. The ancient Greek 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... | |
 | Thomas Henry Eagles - 1885 - 404 pages
...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 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 - 1887 - 404 pages
...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 the first and second is to the difference between the second and third, and the quantities are therefore in hannonical progression.... | |
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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... 
