| Euclides - 1861
...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 - 1862
...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... | |
| Robert Potts - 1864
...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,... | |
| Alexander Kennedy Isbister - 1865
...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... | |
| Euclid, Isaac Todhunter - 1867 - 400 pagina’s
...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 - 1867 - 400 pagina’s
...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 - 410 pagina’s
...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 - 1872 - 349 pagina’s
...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.'... | |
| James Martin (of the Wedgwood inst, Burslem) - 1874
...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... | |
| Euclides - 1876
...to one of these, the remaining one B D («) V. 15. (<Z) V. 14. (6) Hypoth. (0 V. Dcf. 5. («) v. 11. **of the first two shall have to the other the same...shall also be proportionals taken soparately, viz. as** AE is to EB so is CFtoFD. DEMONSTRATION. Take of AE, EB, CF, FD any equimultiples whatever GH, HK,... | |
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