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Boeken Boek 31 - 40 van 43 over IF magnitudes, taken jointly, be proportionals, they shall also be proportionals....
" 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... "
The Elements of Euclid with Many Additional Propositions and Explanatory Notes - Pagina 51
door Eucleides - 1860
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Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

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...
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The propositions of the fifth book of Euclid proved algebraically

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...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

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,...
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The college Euclid: comprising the first six and the parts of the eleventh ...

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

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,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

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.'...
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The Elements of Euclid, containing the first six books, with a selection of ...

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...
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The Elements of Euclid, with many additional propositions, and explanatory ...

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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