 | John Playfair - 1855 - 340 σελίδες
...multiple of A+B by m, C has a greater ratio to A than it has to A+B (def. 7. 5.). 15 PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude...to which the same magnitude has the same ratio are tqual to one another. If A: C :: B: C, A=B. For if not, let A be greater than B ; then because A is... | |
 | Euclides - 1855 - 230 σελίδες
...: A. C . C PROPOSITION IX. THEOREM.—If magnitudes have the same ratio to the same magnitude, they are equal to one another: and those to which the same...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C ; then A shall be equal to B. ^ DEMONSTRATION. For,... | |
 | Euclid - 1859 - 150 σελίδες
...Magnitudes which have the same ratio to the same magnitude are equal to one another: and magnitudes to which the same magnitude has the same ratio are equal to one another. PART L Statement — If each of the mag- A — nitudes A and B has to С the same ^ ratio; I say that... | |
 | Eucleides - 1860 - 396 σελίδες
...> C i A. PROPOSITION IX. THEOBEM. — If magnitudes have the same ratio to the same magnitude, they 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 ; then A shall be equal to B. DEMONSTRATION. For, if... | |
 | Robert Potts - 1860 - 380 σελίδες
...PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude are equal lo tme another : and those to which the same magnitude has the same ratio an tqual to one another. Let, A, B have each of them the same ratio to C. Then A shall be equal to... | |
 | Euclides - 1861 - 464 σελίδες
...10. Hence 3 (5+4) > (3—1) 10. bnt3 X 5 > (3—1) 10, Л 5 + 4 : 10 > 5 : 10. PROP. IX.— THEOn. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Cox. Pst. 1, V. DRM. 8, V.— Def. 7, V.— Dei. 5, V. E. l Hyp. 1. ,, 2Cone. Let A : C = B : C ; or... | |
 | George Sturton Ward - 1862 - 104 σελίδες
...ba greater ratio than с has to a. Therefore, of unequal magnitudes, &c. — (¿. ED PROPOSITION IX. Magnitudes which have the same ratio to the same magnitude,...magnitude has the same ratio, are equal to one another. a, b, c. Because a : с : : b : c, .. fab therefore - = - j с с and therefore a = b. Secondly, let... | |
 | Euclides - 1865 - 402 σελίδες
...than it has to AB. (T. def. 7.) Wherefore, of unequal magnitudes, &c Q, E. T>. PROP. EX.— THEOREM. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. (Reference — v. def. 5.) Let A and B have each of them the same ratio to C. Then A shall be equal... | |
 | John Playfair - 1855 - 350 σελίδες
......... 15 PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude are equal to on* another ; and those to which 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, two... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...unequal magnitudes &c. QKI'. G ,. PROPOSITION 9. THEOREM. Magnitudes which have the same ratio to tlie same, magnitude, are equal to one another ; and those...magnitude has the same ratio, are equal to one another. First, let A and B have the same ratio to C: A shall bo equal to B. For, if A is not equal to B, one... | |
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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. 
