 | Euclid - 1892 - 460 σελίδες
...same magnitude are equal to one another. That IB, if A : C = B : C. then A = B. (ii) Those magnitudes to which the same magnitude has the same ratio are equal to one another. That is, if C : A = C : B. then A = B. PROPOSITION 8. Magnitudes have the same ratio to one another... | |
 | Irving Stringham - 1893 - 164 σελίδες
...because nC > mR while nC is either < m A, or at most = m A, .-. C : B > C : A. (Def. 7.) PROPOSITION 6. "Magnitudes which have the same ratio to the same...magnitude has the same ratio are equal to one another. ' ' That is, A, B, C being three magnitudes of the same kind ; if A : C : : B : C, then A = B. and... | |
 | Joseph Battell - 1903 - 722 σελίδες
...— will hold a greater number of pints than quarts. No demonstration necessary. PROPOSITION IX. ' Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another.' '• Still another proposition that needs not demonstration. PROPOSITION X. "Ratio being the number... | |
 | Cora Lenore Williams - 1905 - 122 σελίδες
...same magnitude has a greater ratio to the less of two magnitudes than it has to the greater. Prop. 26. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Prop. 27. That magnitude which has a greater ratio than another has to the same magnitude is the greater... | |
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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. 
