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" Ratios that are the same to the same ratio, are the same to one another. "
A new supplement to Euclid's Elements of geometry, by the author of 'A new ... - Pagina 63
door Joseph Denison - 1840 - 84 pagina’s
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 pagina’s
...evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer that those ratios which are the same to the same ratio, are the same to one another ; but explicitly demonstrates this in prop. 11, of book 5. The demonstration we have given of the 10th...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pagina’s
...most.evident axiom when understood of magnitudes ; yet Euclid does not make use of it to infer, that those ratios, which are the same to the same ratio, are the same to one another; but explicitly .demonstrates this in Prop. 11. of Book 5. * The demonstration we have given of the...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819
...ratio than it has uuto another magnitude i» the leiser oí the two. Prop. XT. Tlieor. Ratios that are the same to the same ratio, are the same to one another. Prop. XII. Tli*or. If any number of magnitudes he proportional.-, as one of the antecedents is 10 it;...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - 1824 - 516 pagina’s
...that B must be less than A. £> Q- E- D. . ' • «"*. PROP. XI. THEOH. «•*•/'**> Ratios that are the same to the same ratio, are the same to one another. DEMONSTRATION. Let A be to B as C to D, and also E to F as C to D ; it is to be shown that A is to...
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 pagina’s
...oftener than C contains A, it is manifest that B must be less than A. QED PROP. XI. THEOR. Ratios that are the same to the same ratio, are the same to one another. DEMONSTRATION. Let A be to B as C. to D, and also E to F as C to D ; it is to be shown that A is to...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...but it has not: whence n is not greater than m, nor does и = m; .-. n < m. PROPOSITION XI. THEOREM. Ratios which are the same to the same ratio are the same to one another. For let A be to в as c is to D, and as c is to л so is E to F : then as A is to в so is E to F....
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pagina’s
...but it has not : whence n is not greater than m, nor does n = m; .'. n < m. PROPOSITION XI. THEOREM. Ratios which are the same to the same ratio are the same to one anot/ier. For let A be to в as c is to D, and as c is to D so is E to F : then as A is to в so is...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 pagina’s
...evident axiom when understood of magnitudes; yet Euclid does not make use of it to infer, that those ratios, which are the same to the same ratio, are the same to one another, but explicitly demonstrates this in Prop. 11. of Book 5. The demonstration we have given of the 10th...
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Elements of Geometry: With Notes

John Radford Young - 1827 - 208 pagina’s
...consequent as all the antecedents are to all the consequents, AE will be to CF as AB is to CD. But ratios, which are the same to the same ratio, are the same to each other ; whence AB will be to CD as EB is to FD ; and, alternately, AB to EB as CD to DF. Again,...
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Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volume 20

Perry Fairfax Nursey - 1834
...fool, then Euclid must have been ; for he positively asserts, aye and pretends to demonstrate too, that ratios which are the same to the same ratio, are the same to one another. (Book 5, prop. 11.) Now Mr. Editor, I need scarcely inform you, that the proof of the llth proposition,...
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