 | Euclides - Euclid's Elements - 1881 - 236 pages
...they cannot be said to be of the same kind, and so cannot have any ratio to each other. T. The Brst of four magnitudes is said to have the same ratio...of the first be less than that of the second, the mu'tiple of the third is also less than tlint of the fourth : or, if the multiple of the first be equal... | |
 | George Albert Wentworth - Geometry, Modern - 1882 - 268 pages
...17 QED 272. 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...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
...representing the ratios must be equal. Euclid's test is given in Book v. Def. 5, where it stands thus : " The first of four magnitudes is said to have the same...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
...±Pa : b ± ?-b : : a : b. Ч Ч QED 272. DEF. Euclid's test of a proportion is as follows : — " The first of four magnitudes is said to have the same...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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 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... | |
 | 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... | |
 | 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... | |
 | 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 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
...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,... | |
 | 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,... | |
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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... 
