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" IF the first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth... "
Elements of Algebra with Exercises - Page 354
by George Egbert Fisher, Isaac Joachim Schwatt - 1899 - 478 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...when divided by the fourth, we say of these magnitudes, as we did of the numbers above described, that the first is to the second as the third is to the fourth. There are only two more circumstances necessary to be considered, in order -to bring us precisely to...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...first be the same multiple of the second, or the same part of it, that the third is of the .fourth ; the first is to the second as the third is to the fourth. Let the first A be the same multiple of B the second, that C the-third is of the fourth D : A is to...
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Easy Introduction to Mathematics, Volume 2

Charles Butler - 1814 - 582 pages
...PROPORTION. 83. The foregoing articles treat of the properties of what is called DIRECT PROPORTION, where the first is to the second as the third is to the fourth ; but when the terms are so arranged, ' It must he understood, tbat what we have delivered on proportion,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...first be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth. Let the first A be the same multiple of B the second, that C the third is of the fourth D : A is to...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...magnitudes be the same multiple of the second, or the same part ofit, that the third is of the fourth, the first is to the second, as the third is to the fourth. First, let A •= pB, and C = pD ; then A : B :: C:D. Let there be taken of A and C any equi-multiples...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...first be the satne multiple of the second, or 1he same part of it that the third is of the fourth ; the first is to. the second as the third is to the fourth. DEMONSTRATION. I. Supposing m to be any integer greater than unity, let mA the first be the same multiple...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...first be (lie same multiple of the second,' or the same part of it that the third is of the fourth ; the first is to the second as the third is to the fourth. DEMONSTRATION. t 1. Supposing m lo be any integer greater than unity, let w»A the lirst be the same...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...(482) If the first be the same multiple or submultiple of the second, that the third is of the fourth ; the first is to the second as the third is to the fourth. Let the first A be the same multiple of the second B that the third C is of the fourth D ; A : B =...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...magnitudes be the same multiple of the second, or the same part of it, that the third is of the fourth ; the first is to the second, as the third is to the fourth. Let the first A be the same multiple of B the second, that C the third is of the fourth D; then A is...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 524 pages
...of the first divided by the second is equal to the quotient of the third divided by the fourth, then the first is to the second as the third is to the fourth, or the ratio of the first and second is equal to the ratio of the third and fourth ; because these...
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