 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...DBF. Euclid's test of a proportion is as follows :-•" The first of four magnitudes iä said to have the same ratio to the second which the third has to...equimultiples whatsoever of the second and fourth ; (l ± P] a : \ q/ : 0 ± -) V q/ :b±Р-b \ b : : a : b, Q/ ~T~ — Cz ч Ч : : a : b. "If the multiple... | |
 | James Hamblin Smith - Algebra - 1882 - 414 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 - 442 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 - 466 pages
...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 - 428 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 - 340 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... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 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 - 116 pages
...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 - 616 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 - 986 pages
...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.... | |
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If the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth... 
