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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...
Euclidian Geometry - Page 157
by Francis Cuthbertson - 1874 - 349 pages

## The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 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...

## 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 second which the third has to the fourth, when, any equimultiples whatever being taken of the ist and 3rd, and any equimultiples whatever of the 2nd...

## A Text Book of Algebra

William Steadman Aldis - Algebra - 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,...

## 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,...

## The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...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,...

## The Teaching of Elementary Mathematics

David Eugene Smith - Mathematics - 1902 - 418 pages
...Teaching. One has but to read the Euclidean definition of equal ratios to be assured of this fact : " The first of four magnitudes is said to have the same...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...

## First Stage Practical Plane and Solid Geometry

G. F. Burn - Geometry - 1903 - 272 pages
...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...

## Ellen: Or, Whisperings of an Old Pine, Volume 1

Joseph Battell - Force and energy - 1903 - 722 pages
...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...