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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... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Seite 149
von Euclides - 1861
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 Seiten
...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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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 Seiten
...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...equimultiples whatsoever of the second and fourth, if, according as the multiple of the first is greater than, equal to, or less than the multiple of the...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...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...equimultiples whatsoever of the second and fourth, if, according as the multiple of the first is greater than, equal to, or less than the multiple of the...
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Notes on algebra

Howard Candler - 1885
...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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A Text Book of Algebra

William Steadman Aldis - 1887 - 588 Seiten
...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 - 515 Seiten
...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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THE CONTENTS OF THE FIFTH AND SIXTH BOOKS OF EUCLID

M. J. M. HILL - 1900
...following manner : — The first of four magnitudes is said to have the same ratio to the second, as the third has to the fourth, when any equimultiples...equimultiples whatsoever of the second and fourth being taken; if the multiple of the first be less than that of the second, the multiple of the third...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - 1900 - 143 Seiten
...Art. 67. Def. 13. EUCLID'S TEST FOR EQUAL RATIOS. Euclid states this Test in the following manner: — The first of four magnitudes is said to have the same ratio to the second, as the third has to the fourth, when any equimultiples whatsoever of the first and third being taken,...
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First Stage Practical Plane and Solid Geometry

G. F. Burn - 1903 - 255 Seiten
...is the equality of two ratios. Four quantities are therefore in true proportion when the first has the same ratio to the second which the third has to the fourth ; thus, since 3 : 6 and 1 : 2 are equal ratios, we have a true proportion in 3 : 6 : : 1 : 2 (read...
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Ellen: Or, Whisperings of an Old Pine, Band 1

Joseph Battell - 1903
...must contain 2, 3 X 3, or 9 times. See Axiom 6. PROPOSITION IV. ' If the first of four magnitudes has the same ratio to the second which the third has to the fourth, and if any equimultiple whatever is taken of the first and third, and any whatever of the second and...
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