 | 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
...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. — If each of the mag- A nitudes A and B has to С the same С ratio; I say that... | |
 | 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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...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; then A is equal to B. For since A is to C as B is to C, "4. = ? ; (V.... | |
 | 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... | |
 | 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... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...it has to AB. [V. Dtfnitien 7. Wherefore, of unequal magnitudes &c. QED LKD PROPOSITION 9. THEOREM. Magnitudes which have the same ratio to the same magnitude,...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... | |
 | Euclides - 1884 - 434 pages
...A by m, but does not exceed the multiple of A + B by m ; .-. C: A is greater than C : A + BV Def. 9 Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. First let A : C = B : C : it is required to prove A = B. For if A be greater than B, then A : C is... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Magnitudes which have the same ratio to the same magnitude are equal to one another. (2) Magnitudes to which the same magnitude has the same ratio are equal to one another. PROPOSITION 10. (1)If A: C>B :C, then A>B. v A:C>B:C, there exist multiples mA, mB, nC, such that mA>nC,... | |
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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. 
