| 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... | |
| Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 143 pages
...multiple of the third is also equal to that of the fourth : and, if the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth. The statement of the above Test in symbols has already been given... | |
| David Eugene Smith - Mathematics - 1900 - 312 pages
...OF ELEMENTARY MATHEMATICS equal to that of the fourth ; or, if the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth."1 The other extreme is the purely algebraic plan, the one adopted... | |
| James Harrington Boyd - Algebra - 1901 - 777 pages
...multiple of the third is also equal to that of the fourth, and if the multiple of the first be greater **than that of the second, the multiple of the third is also** greater than that of the fourth." (Euclid, Book V.) ac For, let a : b = c ; d; then — oa £2=£5.... | |
| G. F. Burn - Geometry - 1903 - 255 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... | |
| Joseph Battell - Force and energy - 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... | |
| ANZAAS. - Science - 1905
...natural. I need only quote it to enforce the point: " The first of four magnitudes is said to have **the same ratio to 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) - Science - 1905
...natural. I need only quote it to enforce the point : " The first of four magnitudes is said to have **the same ratio to 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 - Mathematics, Greek - 1908
...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 - Mathematics - 1912 - 370 pages
...convinced that it is utterly unfit for young students. * "The first of four magnitudes is said to have **the same ratio to the second, which the third has...fourth ; if the multiple of the first be less than that** The fact that the arithmetical view of ratio leads to a product of two lines is no serious objection,... | |
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