 | Horatio Nelson Robinson - 1844 - Liczba stron: 184
...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 the first and second, is to the difference between the second and third. Thus a, x, b, are in harmonical proportion, when a ; b... | |
 | Euclides - 1845 - Liczba stron: 546
...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 the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the... | |
 | William Watson (of Beverley.) - 1845 - Liczba stron: 188
...Progression is 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... | |
 | Horatio Nelson Robinson - 1846 - Liczba stron: 276
...Harmonical Proportion. (Art. 124.) When 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... | |
 | Elias Loomis - 1846 - Liczba stron: 380
...Art. 213, ae : bf : : eg : 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... | |
 | Samuel Alsop - 1846 - Liczba stron: 300
...Harmoràcal Proportion. . J • . - » 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... | |
 | James W. Kavanagh - 1846 - Liczba stron: 304
...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 and second is to the difference between the second and third ; thus 12, 8, and 6 form a harmonica1 series, for 12 :... | |
 | Harvey Goodwin - 1846 - Liczba stron: 500
...quantities are said to be in harmonical progression, when any three successive terms are so related, that the first is to the third as the difference between the first and the second is to the difference between the second and third. Thus if a, b, c are in harmonical progression,... | |
 | Horatio Nelson Robinson - 1848 - Liczba stron: 354
...PROPORTION. (Art. 124.) When 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 harmonical proportion.... | |
 | Samuel Alsop - 1848 - Liczba stron: 336
...SECTION IV. . Harmonical Proportion. 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 -- о : b — с ; the magnitudes... | |
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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... 
