 | 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 Progression,... | |
 | 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. Harmonics, har-mon'iks, ;.-.//.... | |
 | 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. Harmonics, har-mon'iks, n.pl. used... | |
 | 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. 6, 4, and... | |
 | 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...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; AD:AC... | |
 | 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...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. Thus if... | |
 | 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...second 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... | |
 | William Chauvenet - Geometry - 1888 - 826 pages
...proportion [2] may be written thus, AC : AD = AB — AC : AD — AB, or, AC, AB, AD, are such that the firet is to the third as the difference between the first...second is to the difference between the second and third ; that is, they are in harmonic progression, according to the definition commonly given in algebra.... | |
 | Nathan Fellowes Dupuis - Geometry - 1889 - 370 pages
...(305°, Cor.) 308°. Let APBQ be a harmonic range. Then i , AP:PB = AQ:BQ, A ' BQ .'. AP:AQ=AB-AP:AQ-AB. Taking AP, AB, AQ as three magnitudes, we have the...Proportion as given in Arithmetic and Algebra. EXERCISES. i. When three line segments are in harmonic proportion the rectangle on the mean and the sum of the... | |
| |
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... 
