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Books Books 61 - 70 of 96 on The first of four magnitudes is said to have the same ratio to the second, which....
" The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple... "
A system of practical mathematics; being no.xvi. of a new series of school-books - Page 111
1845
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Elements of geometry, with ... trigonometry

André Darré - 1872
...only one hitherto devised that applies equally to commensurable and incommensurable quantities ; " the first of four magnitudes is said to have the same...the third has to the fourth, when any equi-multiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...nB as mC is to nD. V. Def. 5. QED PROPOSITION XVIII. (Bucl. v. A.) If the first of four magnitudes have the same ratio to the second that the third has to the fourth, then, if the first be greater than the second, the third must be greater than the fourth ; and if equal,...
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Euclid, Book V.: Proved Algebraically So Far as it Relates to Commensurable ...

Euclid's Elements - 1874 - 62 pages
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second...
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Euclid, book v. proved algebraically, so far as it relates to commensurable ...

1874
...third is also greater than that of the fourth. The Algebraical Definition answering to this would be ' The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when the first is the same multiple, part, or fraction of the second...
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Euclidian geometry

1874
...: QD as &AQC : .-. &AQC : &BQCas &AQC : &AQD; (v. 3) Euclid's test of proportion is the following : The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatever of the first and third being taken...
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The Elements of Euclid, containing the first six books, with a selection of ...

James Martin (of the Wedgwood inst, Burslem) - 1874
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. 5. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 403 pages
...said to have a ratio to one another, when the less can be multiplied so as to exceed the other. x V. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 398 pages
...q/ or ai ~ а : fr i ~ b : : a : b. QED 272. DEF. Euclid's test of a proportion is as follows : — "The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...two magnitudes of the same kind to one another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second, which the third has to the fouitl', when any equimultiples whatsoever of the first and third i being...
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Elementary Algebra: With Brief Notices of Its History, Volumes 1-12

Robert Potts - Algebra - 1879
...Eue. Vu., def. 20. Hence it follows that a, b, c, d are proportionals by Eue. V., def. 5, namely : — The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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