 | John Playfair - Mathematics - 1806 - 320 pages
...of A+B by HI, C has a g-eater ratio to A than it has to A+Bb. Therefore, &c. Q, ED PROP. IX. THEOR. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. If A : C : : B : C, A=B. For, if not, let A be greater than B ; then, because A is greater than B,... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...Wherefore, of unequal magnitudes, &c. QED G L C — B FG C-- ]! KHD KD b7.defc 5. PROP. IX. THEOR. see *. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C: A is equal to B: for, if they are not equal, one of... | |
 | Euclides - 1814 - 560 pages
...SeeN. MAGNITUDES which have the same ratio to the same magnitude are equal to one another; and those.to which the same magnitude has the same ratio are equal to one another. multiple F; and that D is greater than • 5 Def. 5. F; E shall also be greater than F a ; but Let... | |
 | Euclides - 1816 - 588 pages
...than it has to AB. Wherefore, of unequal magnitudes, &c. QED A 6 b 7 Def. 5. PROP. IX. THEOR. s«eN. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C; A is equal to B. For, if they are not equal, one of... | |
 | John Playfair - 1819 - 354 pages
...m, C has a sweater ratio to A than it has to A+B (def. 7. 5.). Therefore, &c. Q,ED PROP. IX. THEOR. Magnitudes .which have the same ratio to the same...magnitude has the same ratio are equal to one another. If A : C : : B : C, A=B. For, if not, let A be greater than B ; then, because A is greater than B,... | |
 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...quotient ; and therefore the ratio of C to B is greater lhaa the ratio of C to AQED PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude...to B. Because A and B have, by hypothesis, the same AB ratio to C, therefore we have the equalit) -^=g-, and therefore by multiplication A = B. 2. Because... | |
 | Euclides - 1826 - 226 pages
...be taken greater than p). It is 5. evident that ^* > - f , and £ < i. QED PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude,...magnitude has the same ratio are equal to one another. the same ratio« to c, but they have: therefore • 8.5. Again, let c have the same ratio to A and... | |
 | Euclid - 1826 - 234 pages
...Def.?. 5. evident that -* > -, and ? < £. QED ppmn PROPOSITION IX. THEOREM. Magnitudes which hate the same ratio to the same magnitude, are equal to...magnitude has the same ratio are equal to one another. For let each of the magnitudes A, B, have the same ratio to c : then is A equal to B. 129 the same... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...Magnitudes whieh have the same ratio to the same magnitude are equal to one another ; and those to whieh the same magnitude has the same ratio are equal to one another. If A. : C ". B : C, A=B. For, if not, let A be greater than B; then, beeause A is greater than B, two... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...magnitudes, &c. QED PROP. IX. THEOR. Magnitudes which have the same ratio to the same mag- See N. nitude are equal to one another : and those to which the...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C: A shall be equal to B. For, if they are not equal,... | |
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MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another. 
