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" In a direct proportion, the first term has the same ratio to the second, as the third has to the fourth. "
Euclid, book v. proved algebraically, so far as it relates to commensurable ... - Side 2
av Charles Lutwidge Dodgson - 1874
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An Introduction to Algebra: With Notes and Observations: Designed for the ...

John Bonnycastle - 1811 - 230 sider
...ar, 6r, 6 are in inverse proportion. A series of quantities are said to be in geometxical progression when the first has the same ratio to the second as the second to the third, the third to the fourth, &c. Thus, 2, 4, 8, 16, 32, 64, We. and a, ar, ar2, ar>,...
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A Course of Mathematics ...: Composed for the Use of the Royal Military ...

Charles Hutton - 1811 - 406 sider
...geometrical progression, or continuous proportion, when every two terms have always the same ratio, or when the first has the same ratio to the second as the second to the third, and the third to the fourth, &c. Thus, 2, 4, 8, 16, 32, 64, &C, and a, ar^ at*-j...
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A Course of Mathematics: For the Use of Academies as Well as Private Tuition

Charles Hutton - 1812 - 620 sider
...geometrical progression, or continuous proportion, when every two terms have always the same ratio, or when the first has the same ratio to the second as the second to the third, and the third to the fourth, &c. Thus, 2, 4, 8, 16, 32, 64, Sec, and a, ar, ar3,...
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A Course of Mathematics: For the Use of Academies, as Well as Private ...

Charles Hutton - 1822 - 616 sider
...geometrical progression, or continuous proportion, when every two terms have always the same ratie, or when the first has the same ratio to the second, as the second to the third, and the third to the fourth, &c. Thus, 2,4, 8, 16, 32, 64, &c, and a, ar, ara,ar3,...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 516 sider
...Proportion cannot consist in less than three terms. 9. Three magnitudes, are said to be proportional, when the first has the same ratio to the second, as the second has to th«" third. 10. Of three proportional magnitudes, the middle one, is said to be, a mean...
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The Complete Practical Arithmetician: Containing Several New and Useful ...

Thomas Keith - 1822 - 354 sider
....— The ttule of Three Direct teaches, by three given numbers, to find a fourth, which shall have the same ratio to the second as the third has to the first ; that is, if the first be greater than the third, the second will be greater than the fourth...
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A New and Complete System of Arithmetick: Composed for the Use of the ...

Nicolas Pike - 1822 - 562 sider
...The Rule of Three Direct teaches, by having three numbers* given, to find A fourth, which shall have the same ratio to the second, as the third has to the jirst. The Kule of Three Inverse teaches, by having three numbers given, to find a fourth, which shall...
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Letters to the Hon. William Prescott, LL.D., on the Free Schools of New ...

James Gordon Carter - 1824 - 150 sider
...catching the truth by legerdemain. To assign as a reason for such statement, that the " first term has the same ratio to the second, as the third has to the fourth," is, if possible, more unphilosophical. It is not only ridiculous, but absurd. A ratio, that is, any...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 sider
...multiplied by the number of the first ratios. PROPOSITION XIV. THEOREM. If the first magnitude have the same ratio to the second, as the third has to the fourth, if the first be greater than the third, the second will also be greater than the fourth ; if equal,...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 sider
...multiplied by the number of the first ratios. PROPOSITION XIV. THEOREM. If the first magnitude have the same ratio to the second, as the third has to the fourth, if the first be greater than the third, the second ivilL also be greater than the fourth ; if equal,...
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