 | Wales Christopher Hotson - 1842 - 306 pages
...a series of quantities of which, if any three consecutive terms be taken, the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a,, a.2, a3, a4, &c. be the consecutive terms of an harmonical progression,... | |
 | Horatio Nelson Robinson - Algebra - 1844 - 184 pages
...numbers. NB Three numbers are said to be 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. Thus a, x, b, are in harmonical proportion, when a ; b : : a — x : x — 6. And... | |
 | William Watson (of Beverley.) - 1844 - 200 pages
...erenceofthesecond 卑 ndth 汁 d ・ Supposea ， & ， 巳 ndcinhamonic 卑 lproport 士 on ， theL Four quantities are in harmonical proportion, when the first is to the fourth ㏄ the difference of the first and second is to the difference of the third and fourth・ Ifthe ぬ... | |
 | Euclides - 1845 - 546 pages
...segment is to the middle part. 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... | |
 | William Watson (of Beverley.) - 1845 - 188 pages
...formed by multiplication or division. 13. Harmonical Proportion, is when 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 in four terms, when the first is to the fourth as the difference between the... | |
 | James W. Kavanagh - 1846 - 304 pages
...harmonica! series when of every three of its consecutive [following] terms the iirst is to the third, as the difference between the first and second is to the difference between the second and third ; thus 12, 8, and 6 form a harmonica1 series, for 12 : 6 : : 12—8 : 8—6. 308.... | |
 | Elias Loomis - Algebra - 1846 - 380 pages
...dh. (228.) Three quantities are said to be 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. Thus, 2, 3, 6 are in harmonical proportion, for 2:6::3 — 2:6 — 3. Let o, b, c... | |
 | Horatio Nelson Robinson - Algebra - 1846 - 276 pages
...three magnitudes, a,b,c, have the relation of a:c::a — b:b — c; that is, 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 harmonica I proportion. (Art. 125.) Four... | |
 | Samuel Alsop - Algebra - 1846 - 300 pages
...• . - » 68. Three quantities are said to be in harmonical proportion, if the first is to the third as the difference between the first and second is to the difference between the second and third. Thus, if a : с : : a — -b : b — c; the magnitudes a, b, and с are in harmonical... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...dh. (228.) Three quantities are said to be \r\ harmonical proportion when the first is to tke third as the difference between the first and second is to the difference, between the second and third. Thus, 2, 3, 6 are in harmonica] proportion, for 2:6::3 — 2:6 — 3. Let a' b, с... | |
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C = 2^V 10. Four quantities are in harmonical proportion, when the first is to the fourth, as the difference between the first and second is to the difference between the third and fourth. 
