 | Euclides - 1838 - 264 pages
...same kind, a multiple of one may be taken so great as to exceed the other. 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 former... | |
 | Euclides - 1840 - 192 pages
...ratio of C to D ; C : D ^TA : B, the ratio of C to D is less than the ratio of A to B. PROP. I. THEOR. 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... | |
 | Oliver Byrne - Mathematics - 1841 - 140 pages
...B, then A с- B; or, let 3 A c- 3 B, then A с- B; or, let m A c=~ m B, then A с- B PROP. I. THEO. 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 shall of the first magnitudes... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...is greater than the same multiple of another, is greater than that other magnitude. PROP. I. THEOR. 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... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...is greater than the same multiple of another, is greater than that other magnitude. PROP. I. THEOR. If any number of magnitudes be equimultiples of as many others, each nf each, what multiple soever any one of the first is of its part, tlte same multiple is the sum of... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...is greater than the same multiple of another, is greater than that other magnitude. PROP. I. THEOR. 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 tlie sum of all the... | |
 | Euclides - 1846 - 292 pages
...than that other magnitude. PROP. I. THEOR. 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 - Geometry - 1853 - 176 pages
...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 muliiple soever any one of them is of its part, the same multiple shall all the first magnitudes... | |
 | William Somerville Orr - Science - 1854 - 534 pages
...be represented by the small letters ; and, in general, by »», », p, q. PROPOSITION I,— THEOREM. If any number of magnitudes be equimultiples of as...others, each of each, whatever multiple any one of the former is of the corresponding one of the latter, the same multiple is the sum of all the former... | |
 | Euclides - 1855 - 230 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.... | |
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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. 
