| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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... | |
| Robert Potts - 1868 - 434 pages
...it has to A B. (v. def. 7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. **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, Then A shall be equal to B. AD CF For, if they are... | |
| Euclid - 1868 - 138 pages
...laa àXXqXoij íorf «ai iгpbç & то aiirb TÔV avril» !%и \oyov, lKfîva laa aXXqXoi£ 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 I. Statement.... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...mqA, .'. D has to B a greater ratio than D has to A. V. Def. 7. QED PROPOSITION VIII. (Eucl. v. 9.) **Magnitudes, which have the same ratio to the same...magnitude has the same ratio, are equal to one another.** Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a... | |
| Euclides - 1874 - 342 pages
...has to AB (V. Def. 7). Wherefore, of two unequal magnitudes, <fec. QED PROPOSITION 9. — Theorem. **Magnitudes which have the same ratio to the same magnitude...another ; and those to which the same magnitude has the** game ratio are equal to one another. Let A, B have each of them the same ratio to C. Then A shall be... | |
| Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...2, conv.) and, by inversion, C is to A as C is to B, (V. 4. ) QED PROP. VI.— THEOREM. (Euc. V. 9.) **Magnitudes which have the same ratio to the same magnitude are equal;** and those to which the same magnitude has the same ratio are equal. Let as A is to C so is B to C;... | |
| Euclides, James Hamblin SMITH - 1876 - 382 pages
...a greater ratio than D has to A. V. Def. 7. (JED PROPOSITION VIII. (Eucl. v. 9.) Magnitudes, whidi **have the same ratio to the same magnitude, are equal...magnitude has the same ratio, are equal to one another.** Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a... | |
| Robert Potts - Geometry - 1876 - 446 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 the** tame magnitude has the tame ratio a,• equal to one another. Let, A, B have each of them the same... | |
| Euclides, James Hamblin Smith - 1879 - 376 pages
...greater ratio than D has to A. V. Def. 7. PROPOSITION VIII. (EucL v. 9.) Magnitudes, which have the so/me **ratio to the same magnitude, are equal to one another;...magnitude has the same ratio, are equal to one another.** Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...Definition 7. Wherefore, of unequal magnitudes &c. QED PROPOSITION 9. THEOREM. Magnitudes which hare **the same ratio to the same magnitude, are equal to...magnitude has the same ratio, are equal to one another.** First, let A and B have the same ratio to C: A shall be equal to B. For, if A is not equal to B, one... | |
| |