 | Horatio Nelson Robinson - 1844 - 184 σελίδες
...product equal to 576, to find the numbers. NB Three numbers are said to be in harmonical proportion, when the first is to the third, as the difference between...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 this proportion gives... | |
 | Euclides - 1845 - 546 σελίδες
...as the other extreme segment is to the middle part. Three lines are in harmonical proportion, when the first is to the third, as the difference between...is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical... | |
 | William Watson (of Beverley.) - 1845 - 188 σελίδες
...to the difference between the second and third ; or in four terms, when the first is to the fourth as the difference between the first and second is to the difference between the third and fourth ; or the reciprocals of numbers iu Arithmetical Proportion are in Harmonical Proportion.... | |
 | James W. Kavanagh - 1846 - 304 σελίδες
...said to form a harmonica! series when of every three of its consecutive [following] terms the iirst is to the third, as the difference between the first...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. The middle one of... | |
 | Elias Loomis - 1846 - 380 σελίδες
...b. (229.) Four quantities are said to be 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. Thus, 2, 3, 4, 8 are in harmpnical proportion, for 2:8::3 — 2:8 — 4. Let a, b,... | |
 | Samuel Alsop - 1846 - 300 σελίδες
...harmonical proportion. ,. 69. Four quantities are in harmonical proportion where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth. Thus, if a : d : : a — b : с — d, a, b, c, and d are in harmonical proportion.... | |
 | Horatio Nelson Robinson - 1846 - 276 σελίδες
...proportion. (Art. 125.) Four magnitudes are in harmonica! 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. Thus, a, b, c, d, are in harmonical proportion when a : d : : a — b : c — d,... | |
 | Elias Loomis - 1846 - 376 σελίδες
...b. (229.) Four quantities are said to be in harmonical proportion when the first is to the fourth a2 the difference between the first and second is to the difference between the third and fourth. Thus, 2, 3, 4, 8 are in harmonical proportion, for 2:8::3 — 2:8 — 4. Let a, b,... | |
 | John Bonnycastle - 1848 - 334 σελίδες
...PROGRESSION. An harmonical progression is a series of which the first of any three consecutive terms is to the third, as the difference between the first...is to the difference between the second and third. Thus, 1, i,!,*,i, and 2, 2f, 3, 4, 6, 12, are harmonical series, for taking any three consecutive terms... | |
 | Samuel Alsop - 1848 - 336 σελίδες
...in-harmonical proportion. 69. Four quantities are in harmonical proportion where the first is to the fourth as the difference between the first and second is to the difference between the third and fourth. Thus, if a : d : : a — b : с — d, a, b, c, and d are in harmonical proportion.... | |
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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... 
