 | Euclid, James Thomson - 1845 - 382 σελίδες
...: A : : D : C ; and inversely (V. B) A : B : : C : D. If, therefore, &c. ABC i' PROP. D. THEOB.— If the first be to the second as the third to the fourth, and if the first be a multiple, or a part of the second ; the third is the same multiple, or part of the fourth. Let A : B : : C : D;... | |
 | Euclid - 1845 - 218 σελίδες
...taken separately, be proportionals, they shall also be proportionals when taken jointly ; that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth.... | |
 | Euclides - 1845 - 546 σελίδες
...(v. B.) Therefore, if the first be the same multiple, &c. QED PROPOSITION D. THEOREM. //' the Jlrsl be to the second as the third to the fourth, and if tJic Jirst be a multiple, or a part of the second ; the third is the same multiple, or the same part... | |
 | Dennis M'Curdy - 1846 - 166 σελίδες
...hypothesis ; (b) p. 3, 5 ; (c) def. 5, 5 ; (d) p. B, 5. D Th. If the first be to the second as the third is to the fourth, and if the first be a multiple or part of the second, the third is the same multiple or part of the fourth. Let A, B, C, D be four magnitudes, in order; so that A is to B as C is to D. First,... | |
 | Euclides - 1846 - 292 σελίδες
...taken separately, be proportionals, tItey shall also be proportionals when taken jointly : that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth.... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...magnitudes, taken separately, be proportionals, they will also be proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together will be to the second as the third and fourth together to the fourth.... | |
 | Euclides - 1848 - 52 σελίδες
...magnitudes, taken separately, be proportionals, they shall also be proportionals when taken jointly; that is, if the first be to the second, as the third to the fourth, the first and second together shall be to the second, as the third and fourth together to the fourth.... | |
 | University of Durham - 1851 - 222 σελίδες
...To describe an isosceles triangle having each angle at the base double the angle at the vertex. 1 2. If the first be to the second as the third to the fourth, and if the first be a multiple or a part of the second, the third is the same multiple or part of the fourth. 13. Give Euclid's definition... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...taken separately, be proportionals, they shall ^ also be proportionals when taken jointly ; that is, if the first be to the second as the third to the fourth, the first and second together shall be to the second as the third and fourth together to the fourth.... | |
 | Euclides - 1853 - 176 σελίδες
...taken separately, be proportionals, they shall also bе proportionals when taken jointly, that is, if the first be to the second as the third to the fourth, the first and second together shall be to the second as the third and fourth together to the fourth.... | |
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IF the first be to the second as the third to the fourth, and if the first be a multiple, or part of the second; the third is the same multiple, or the same part of the fourth... 
