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" Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third. "
Elements of Geometry and Conic Sections - Page 37
by Elias Loomis - 1857 - 226 pages
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The Builder's Practical Guide: Containing a Complete Explanation of the ...

John Nicholson (Civil engineer) - Building - 1830 - 238 pages
...obtained by dividing the consequent by the antecedent. 89. Three magnitudes or quantities, A, B, C, are said to be proportional, when the ratio of the first to the second is the same as that of the second to the third. Thus, 2, 4, 8, are proportional, because 4 is contained...
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A New and Easy Introduction to the Mathematics: Containing. A system of ...

Ira Wanzer - Arithmetic - 1831 - 396 pages
...Thus, 3 : 5, denotes the ratio of 3 to 5. Four quantities are said to be in geometrical proportion, when the ratio of the first to the second is equal to the ratio of the third to the fourth. Thus, the four numbers 8, 4, 14, 7, are proportional, because the ratio 8 : 4...
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Mechanics' Magazine, and Journal of the Mechanics' Institute, Volume 4

1835 - 398 pages
...(4), с (8), where two fourths are equal to four eighths, and one half, both the same ratio. 4. 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), в (2), с (10), D (5), where...
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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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The practice and theory of arithmetic

William Frederick Greenfield - 1853
...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: The mathematical sciences

William Somerville Orr - Science - 1854
...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 - 1854
...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
...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 - 630 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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