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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...
The Elements of Euclid with Many Additional Propositions and Explanatory Notes - Pagina 51
door Eucleides - 1860
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...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...one of the last two has to the other of these. Let A6, BE, CD, DP be the magnitudes, taken jointly, which are proportionals; that is, as AB to BE, so...
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## The Doctrine of Proportion Clearly Developed: On a Comprehensive, Original ...

Oliver Byrne - 1841 - 98 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...remaining one of the last two has to the other of these. then will ф : 0 " 0 : О' Take M ф ^- m 0, to each add M 0, then we have M^ + M 0 c- « 0 + M 0'...
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Robert Simson - 1845 - 199 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...jointly, which are proportionals ; that is, as AB to BE, so is CD to DF : they shall also be proportionals taken separately ; viz. as AE to EB, so CF...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...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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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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...two has to the other of these. Let AB, BE, CD, DF be four magnitudes which, taken jointly, are proportionals, that is, let AB be to BE as CD to DF : they...
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## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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. PROP. XVIII. THEOREM. If magnitudes, taken separately, be proportionals, they shall also be proportionals...
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## The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853
...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...the last two has to the other of these. LET ab, be, С d, df be the magnitudes taken jointly which are proportionals ; that is, as ab to be so is Сd to...
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## The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

...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 ratio which the remaining one of the last lwo has to the other of these. Let AB, BE, CD, DF be the magnitudes, taken jointly, which are proportionals...
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## The Elements of Euclid, with many additional propositions, and explanatory ...

Euclides - 1855
...together have to one of them the same ratio which tieo others hare to one of these, the remaining one of the first two shall have to the other the same...CD to DF ; they shall also be proportionals taken separately, viz. as AE is to EB so is CF to FD. AB ; therefore GK is the same multiple of GA c AB that...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 pagina’s
...together haw 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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