 | Euclides - 1855 - 270 pages
...The same demonstration holds in any number of magnitudes, which is here applied to two. Therefore, if any number of magnitudes, be equimultiples of as many others, each of each ; whatsoever multiple any one of them is of its part, the same multiple is all the first magnitudes... | |
 | Euclides - 1860 - 288 pages
...greater than the same multiple of another, is greater than that other magnitude. PROPOSITION I. THEOREM. If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first... | |
 | Eucleides - 1860 - 396 pages
...magnitudes be equimultiples of two others, and if equimultiples of these be taken from the two first. If any number of magnitudes be equimultiples of as many others, each of each. If the first be the same multiple or submultiple of the second that the third is of the fourth. CONSEQUENCES.... | |
 | Euclides - 1863 - 122 pages
...The same demonstration holds in any number of magnitudes, which is here applied to two. Therefore, if any number of magnitudes be equimultiples of as many others, each of each ; whatsoever multiple any one of them is of its part, the same multiple is all the first magnitudes... | |
 | Euclides - 1865 - 402 pages
...greater than the same multiple of another, is greater than that other magnitude. PROP. I.— THEOREM. If any number of magnitudes be equimultiples of as many others, each of each; then what multiple soever any one of them is of its part, the same multiple shall all the first magnitudes... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...that other magnitude. PROPOSITION 1. THEOREM. If any number of magnitudes be equimultiples of a* many, each of each; whatever multiple any one of them is of its part, the same multiple shall all the first magnitudes be of all the other. Let any number of magnitudes AB,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...that other magnitude. PROPOSITION 1. THEOREM. If any number of magnitudes be equimultiples of as many, each of each; whatever multiple any one of them is of its part, the same multiple shall all the first magnitudes be of all the other. Let any number of magnitudes AB,... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pages
...pB. I. Ax. 1. PROPOSITION I. (Eucl. v. 1.) If any number of magnitudes be equimultiples of as many, each of each ; whatever multiple any one of them is of its sub. multiple, (he same multiple must all the first magnitudes, taken together, be of all the other,... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...that other magnitude. PROPOSITION 1. THEOREM. If any number of magnitudes be equimultiples of as many, each of each; whatever multiple any one of them is of its part, the same multiple shall all the first magnitudes be of all the other. Let any number of magnitudes AB,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...other magnitude. J PROPOSITION 1. THEOREM. If any number of magnitudes be equimultiples of at many, each of each; whatever multiple any one of them is of its part, the same multiple shall all the first magnitudes be of all t)ie other. Let any number of magnitudes AB,... | |
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If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest. 
