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" 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... "
Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an ... - Page 458
by Sir John Leslie - 1809 - 493 pages
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Elementary algebra. To which is now added an appendix

James Hamblin Smith - 1883 - 466 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : \ " The first of four magnitudes is said to have the same...being taken and any equimultiples whatsoever of the second and fourth : " If the multiple of the first be less than that of the second, the multiple of...
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Elements of Geometry

George Albert Wentworth - 1882 - 268 pages
...17 QED 272. DBF. Euclid's test of a proportion is as follows :-•" The first of four magnitudes iä said to have the same ratio to the second which the...being taken, and any equimultiples whatsoever of the second and fourth ; (l ± P] a : \ q/ : 0 ± -) V q/ :b±Р-b \ b : : a : b, Q/ ~T~ — Cz ч Ч :...
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Elementary Algebra

James Hamblin Smith - 1882 - 414 pages
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : " The first of four magnitudes is said to have the same...the fourth, when any equimultiples whatsoever of the f1rst and third being taken and any equimultiples whatsoever of the second and fourth : " If the multiple...
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Elements of Plane and Solid Geometry

George Albert Wentworth - 1882 - 442 pages
...±Pa : b ± ?-b : : a : b. Ч Ч QED 272. DEF. Euclid's test of a proportion is as follows : — " The first of four magnitudes is said to have the same...second which the third has to the fourth, when any equimultiplos whatsoever of the first and third being taken, and any equimultiples whatsoever of the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 pages
...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, that the third has to the fourth, when any equimultiples whatever of the first and the third being...
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Notes on algebra

Howard Candler - 1885 - 116 pages
...fourth, that is, д, l>, c, d are said to be proportionals if — = b а The geometrical definition is 2. The first of four magnitudes is said to have the same...the third has to the fourth, when, any equimultiples whatever being taken of the ist and 3rd, and any equimultiples whatever of the 2nd and 4th, if the...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 340 pages
...ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples...being taken, and any equimultiples whatsoever of the second and fourth, if, according as the multiple of the first is greater than, equal to, or less than...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 pages
...ratio and its reciprocal is unity." v. The first of four magnitudes has to the second the same ratio which the third has to the fourth, when any equimultiples...being taken, and any equimultiples whatsoever of the second and fourth, if, according as the multiple of the first is greater than, equal to, or less than...
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A Text Book of Algebra

William Steadman Aldis - 1887 - 616 pages
...f3,ft This condition is evidently equivalent to the definition 5 of the Fifth Book of Euclid, viz.— The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples whatever of the first and third being taken,...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...number of metres may make, a greater length can always be found containing an exact number of yards. 5. The first of four magnitudes is said to have the ' same ratio ' to the second that the third has to the fourth, when, any equimultiples whatever of the first and third being taken,...
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