 IF 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...  A Treatise on the Elements of Algebra - Page 128by Bewick Bridge - 1821 - 227 pagesFull view - About this book
 | Charles Lutwidge Dodgson - 1874 - 96 pages
...part, or fraction, of the second, as the third is of the fourth. Quod est tautologicum. PROP. D. If the first be to the second as the third to the fourth : then, if the first be a multiple or part of the second, the third is the same multiple or part of... | |
 | Euclid, Lewis Carroll - Euclid's Elements - 1874 - 80 pages
...part, or fraction, of the second, as the third is of the fourth. Quod est tautologicum. PROP. D. If the first be to the second as the third to the fourth : then, if the first be a multiple or part of the second, the third is the same multiple or part of... | |
 | Euclides - 1874 - 342 pages
...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.... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...Cis to JD. (v. B.) Therefore, if the first be the same multiple, &c. QEII. PROPOSITION D. THEOREM. 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 it the tame multiple, or the tame ].urt... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...taken separately, be proportionals, they si mil also be proportionals when taken jointly; that is, {f 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 toy ether to the fourth.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...taken separately, lie proportionals, they shall also be proportionals when taken jointly; that is, {f 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.... | |
 | Leonard Marshall - 1883 - 184 pages
...fractions ay + bz az + bx ax + by 2 = — . unless x + y + z=0. a + b 14. If the first of 6 quantities be to the second as the third to the fourth, and the fifth to the second as the sixth to the fourth : prove that the first and fifth together will be to... | |
 | Euclid - 452 pages
...pair itself, ie the pair multiplied by unity]. To prove the partial converse we begin with Prop. D. 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... | |
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