 ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.  The boys' algebra - Page 199by James Cahill (of Dublin.) - 1875 - 209 pagesFull view - About this book
 | James Stormonth - 1879 - 810 pages
...its 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... | |
 | Henry Angel - Geometry, Plane - 1880 - 372 pages
...py^qy (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...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 - 10: 15-12, and... | |
 | Henry Angel - 1880 - 360 pages
...iheieforepy=qy (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...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 - 10: 15-12, and... | |
 | 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. 6,4, and 3 are in... | |
 | 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...is to the difference between the second and third, as in the three numbers 2, 3. and 6. — adv. Harmonically. Harmonics, har-mon'iks, ;.-.//. used as... | |
 | 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...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 as sing,... | |
 | 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 3 are... | |
 | Euclides - 1884 - 434 pages
...of 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 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 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 magnitudes... | |
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