| James Hamblin Smith - Algebra - 1882 - 398 pages
...test is given in Book v. Def. 5, where it stands thus : " 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** f1rst and third being taken and any equimultiples whatsoever of the second and fourth : " If the multiple... | |
| George Albert Wentworth - Geometry - 1882 - 398 pages
...DEF. Euclid's test of a proportion is as follows : — " The first of four magnitudes is said to have **the same ratio to the 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... | |
| James Hamblin Smith - 1883
...multiple of the third is also 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." We shall now show, first, how to deduce Euclid's test of the equality... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 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. When four magnitudes are proportionals it is usually expressed by... | |
| 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... | |
| Euclid, John Casey - Euclid's Elements - 1885 - 312 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...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... | |
| Howard Candler - 1885
...proportionals if — = b а The geometrical definition is 2. 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** whatever being taken of the ist and 3rd, and any equimultiples whatever of the 2nd and 4th, if the... | |
| William Steadman Aldis - Algebra - 1887 - 588 pages
...when any equimultiples whatever of the first and third being taken, and any equimultiples whatever **of the second and fourth, if the multiple of the first...of the third is also less than that of the fourth,** and if the multiple of the first be equal to that of the second, the multiple of the third is also... | |
| Encyclopedias and dictionaries - 1890
...whatever of the second and fourth, according as the multiple of (he first is greater, equal to, or **less than that of the second, the multiple of the third Is also** greater, equal to, or less than that of the fourth — ie, A, B, C, D are proportionals, when, if mA.... | |
| Encyclopedias and dictionaries - 1897
...whatever of the second and fourth, according as the multiple of the first is greater, equal to, or **less than that of the second, the multiple of the third is also** greater, equal to, or less than that of the fourth — ie, A, B, C, D are proportionals, when if mA... | |
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