| Euclid, Micaiah John Muller Hill - 1900 - 165 pages
...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...being taken, and any equimultiples whatsoever of the** second and fourth being taken; if the multiple of the first be less than that of the second, the multiple... | |
| Euclid, Micaiah John Muller Hill - 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,... | |
| David Eugene Smith - 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...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 the... | |
| Joseph Battell - 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... | |
| G. F. Burn - 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... | |
| Australasian Association for the Advancement of Science. Meeting - 1905 - 786 pages
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point: " **The first of four magnitudes is said to have the same...the second which the third has to the fourth when,** if the first be divided into any number whatever of equal parts, and the third be divided into the... | |
| ANZAAS (Association) - 1905 - 782 pages
...geometrically as sound as Euclid's, and infinitely more natural. I need only quote it to enforce the point : " **The first of four magnitudes is said to have the same...the second which the third has to the fourth when,** if the first be divided into any number whatever of equal parts, and the third be divided into the... | |
| Euclid - 1908 - 456 pages
...unnecessary. Simson added, in place of Theon's corollary, the following : " Likewise, if the first has **the same ratio to the second which the third has to the fourth,** then also any equimultiples whatever of the first and third have the same ratio to the second and fourth... | |
| Arthur Schultze - 1912 - 398 pages
...has only to read Euclid's definition* to be convinced that it is utterly unfit for young students. * **"The first of four magnitudes is said to have the...being taken, and any equimultiples whatsoever of the** second and fourth ; if the multiple of the first be less than that The fact that the arithmetical view... | |
| William Calvert Kneale, Martha Kneale - 1962 - 802 pages
...of mathematics. The essence of it is a new definition of the equality of ratios between magnitudes : **'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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