 | Robert Simson - Trigonometry - 1806 - 546 pages
...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... | |
 | Euclides - 1816 - 588 pages
...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... | |
 | John Mason Good - 1819 - 800 pages
...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;... | |
 | James Ryan - Algebra - 1824 - 550 pages
...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... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...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... | |
 | Euclides - 1826 - 226 pages
...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.... | |
 | Euclid - 1826 - 234 pages
...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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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... | |
 | John Radford Young - Euclid's Elements - 1827 - 228 pages
...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,... | |
 | Perry Fairfax Nursey - Industrial arts - 1834 - 478 pages
...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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Ratios that are the same to the same ratio, are the same to one another. 
