 | Euclides - 1861 - 464 pages
...Ms. together have to one another the same ratio which two others have to one of these, the rem. one of the first two shall have to the other the same ratio which the rem. one of the last has to the other of these. Con. 1. Convertendo. If A : B = C : D, then A : A ~B... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...remaining one of the last two has to the other of these. a, b, c, d. Let a + b : b :: с + d : d ; Then shall a : b : : с : d. Because a + b : b : : с + d... | |
 | Euclides - 1864 - 448 pages
...together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...taken jointly which are proportionals ; that is, as AB to BE, so let CD be to DF. Then they shall also he proportionals taken separately, viz. as AE to EB,... | |
 | Euclides - 1865 - 402 pages
...Jbgether have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...remaining one of the last two has to the other of these. Prop. 18. If magnitudes, taken separately, be proportionals, they shall also be proportionals when... | |
 | Robert Potts - 1865 - 528 pages
...the same ratio which two others have to one of these, the remaining one of the first tu'o shall hare to the other the same ratio which the remaining one...last two has to the other of these. Let AB, BE, CD, DFbe the magnitudes, taken jointly which are proportionals ; that is, as AB to BE, so let CD be to... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...other of these. Let AB, BE, CD, DF be the magnitudes which, taken jointly, are proportionals ; that is, let AB be to BE as CD is to DF: they shall also... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...futue to one of these, the remaining one of the first two shall have to the other the tame ratio ^chich the remaining one of the last two has to the other of these. Let AB, BE, CD, DF be the magnitudes which, taken jointly, are proportionals ; that is, let AB be to BE as CD is to DF: they shall also... | |
 | Robert Potts - 1868 - 434 pages
...together have to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...taken jointly which are proportionals ; that is, as AB to BE, so let CD be to DF. Then they shall also be proportionals taken separately, viz. as AE to EB,... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...them the same ratio which two others have to one of these, the remaining one of the first two must have to the other the same ratio which the remaining...one of the last two has to the other of these. Let A, B together hare the same ratio to B that C, D together have to D. Then must A be to B as C to D.'... | |
 | Euclides - 1874 - 342 pages
...together nave to one of them, the same ratio which two others have to one of these, the remaining one of the first two shall have to the other the same...last two has to the other of these. Let AB, BE, CD, DF\)& the magnitudes, taken jointly, which are proportionals ; that is, as AB to BE, so let CD be to... | |
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IF magnitudes, taken jointly, be proportionals, they shall also be proportionals when taken separately ; that is, if two magnitudes together have to one of them the same ratio which two others have to one of these, the remaining one of the first two shall... 
