| Euclid - 1859 - 150 pages
...áXX»)Xoiç tari' <cai irpоç а rо aura TOV aiiruv íjcei \oyov, íKtu»a ïffrt «XA//Xiuï iarív. **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... | |
| Eucleides - 1860 - 396 pages
...> 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... | |
| Dugald Stewart - 1860 - 390 pages
...the Fates dispense Pomp, power, and everything but sense. P. 377, n. F, n. 1. — Magnitudes having **the same ratio to the same magnitude are equal to one another.** — Euclid. P. 378, n. G, n. 2. — Those alone that have been mentioned are properly called quantities,... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...it has to AB. (v. def. 7.1 ' Wherefore, of two unequal magnitudes, &c. QED 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.... | |
| Euclides - 1861 - 464 pages
...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 - Geometry, Algebraic - 1862 - 104 pages
...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 - 1864 - 448 pages
...than it has to AB. (v. def. 7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. **Magnitudes which have the same ratio to the same magnitude are equal to one another : and those to which** tlut same magnitude has the same ratio arc equal to one another. Let, A, B have each of them the same... | |
| Euclides - 1865 - 402 pages
...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... | |
| Robert Potts - 1865 - 528 pages
...7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. Magnitudes which have tlie **same ratio to the same magnitude are equal to, one another : and those to** whieh the tame magnitude has the same ratio ar» equal to one another. Let A, B have each of thorn... | |
| John Playfair - Geometry - 1855 - 350 pages
...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 are equal to** on* another ; and those to which the same magnitude has the same ratio are equal to one another. If... | |
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