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" Three quantities are said to be proportional, when the ratio of the first to the second is equal to the ratio of the second to the third. "
A Course of Mathematics: For the Use of Academies as Well as Private Tuition ... - Page 318
by Charles Hutton - 1831
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A Treatise on Geometry and Its Application in the Arts

Dionysius Lardner - Curves, Plane - 1840 - 386 pages
...divide the product by a, and the quotient will be d. (264.) When three magnitudes are so related that the ratio of the first to the second is equal to the ratio of the second to the third, they are said to be in confirmed proportion; and the third is said to be a third proportional to the...
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Elementary Course of Geometry ...

Charles William Hackley - Geometry - 1847 - 248 pages
...third. As of the three quantities, A = 2, B = 4, C = 8, where \ = £ = \, both the same ratio. 78. Four quantities are said to be proportional when the ratio of the first to the second is the same as the ratio of the third to the fourth. As of the four, A (4), B (2), C (10), D (5), where...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...the other antecedent must be greater than its consequent; if equal, equal; and if less, less. Def. 3. Three quantities are said to be proportional, when...is equal to the ratio of the second to the third; thus, if A, B, and C are in proportion, then A : B : : B : C. In this case the middle term is said...
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The practice and theory of arithmetic

William Frederick Greenfield - 1853 - 228 pages
...product of the extremes is equal to that of the meam, and conversely. Four numbers are proportionals when the ratio of the first to the second is equal to that of the third to the fourth. Hence these ratios must be compared, which is effected by comparing...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...is of course the same as the ratio 4 : 2, or the ratio 2:1. When there are four quantities such that the ratio of the first to the second is equal to the ratio of the third to the fourth, the four quantities are said tobe in proportion: thus, if the four quantities...
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Arithmetic for Schools

Barnard Smith - Arithmetic - 1854 - 366 pages
...and thus those numbers are proportionals. 149. When proportion exists among four numbers, that is, when the ratio of the first to the second is equal to that of the third to the fourth, this proportion or equality is often denoted by writing down the two...
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The Popular Educator, Volume 6

1855 - 424 pages
...that the first divided by the second is equal to the third divided by the fourth — in other words, when the ratio of the first to the second is equal to the ratio of the third to the fourth, the four are said to be in direct proportion. From this definition it will be...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the measured quantity ; hence, the measure of proportion is ratio. Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth ; this relation is expressed algebraically thus, a : b :: с : d. This expression...
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Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and ...

Charles Davies - Algebra - 1857 - 408 pages
...undergo changes of value, then a is said to be proportional to 6. 183i four quantities are in proportion, when the ratio of the first to the second, is equal to the ratio of the third to the fourth. Thus, if b_ d_ ~^~~' the quantities a, b, c and d, are said to be in proportion....
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...other antecedent must be greater than its consequent ; if equal, equal ; and if less, less. Def. 3. Three quantities are said to be proportional, when...second is equal to the ratio of the second to the third ; thus, if A, B, and C are in proportion, then A : B : : B : C. In this case the middle term is said...
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