 | Euclid, Dionysius Lardner - 1828 - 542 σελίδες
...A, but not greater than m (A + B), C : A is greater than C : A + B. PROPOSITION IX. THEOREM. (486) Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. I,et A, B have each of them the same ratio to C : A is equal toB. For, if they are not equal, one of... | |
 | Euclid - 1835 - 540 σελίδες
...Wherefore, " of unequal magnitudes," &c. QED 0 B K A C GB LKHD b 7. def. 5. PROP. IX. THEOR. D See N. 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 will A be equal to B : For, if they are not... | |
 | Robert Simson - 1835 - 544 σελίδες
...THEOR. D See N Magnitudes which have the same ratio to the same magnitude are equal to one anotlier ; 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 will A be equal to B : For, if they are not... | |
 | 1836 - 488 σελίδες
...the less has ; and the same magnitude has a greater ratio to the less than it has to the greater. IX. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. X. That magnitude, which has a greater ratio than another has to the same magnitude, is the greatest... | |
 | Andrew Bell - 1837 - 290 σελίδες
...the multiple of A + B by m, C has a greater ratio to A than it has to A + B. PROPOSITION IX. THEOREM. Magn-itudes which have the same ratio to 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 numbers,... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...magnitudes, &c. PROP. IX. THEOR. 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 A, B have each of them the same ratio to C : A is equal to B. For, if they be not equal, one of... | |
 | Robert Simson - 1838 - 434 σελίδες
...ratio (7. def. 5.) than it has to AB. Wherefore, of unequal magnitudes, &c, Q,. ED PROP. IX. THEOR. 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 : A is equal to* B : for if they be not equal, one of... | |
 | Euclides - 1840 - 192 σελίδες
...exceed the multiple of A + B by TO, C has a greater ratio to A than it has to A + B. PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. IfA:C::B:C; A=B. For, if not, let A be greater than B ; then, because A is greater than B, two numbers,... | |
 | Euclides - 1841 - 378 σελίδες
...greater ratio* than it has to AB. Wherefore, of unequal * 7 Def. magnitudes, &c. QED 5 PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Let A and B have each of them the same ratio to C: A shall be equal to B. For, if they are not equal,... | |
 | Oliver Byrne - 1841 - 140 σελίδες
...of this important book. PROP. IX. THEO. Magnitudes which have the same ratio to the same magnitudes are equal to one another ; and those to which the...magnitude has the same ratio are equal to one another. then 0 = For, if not, let (У c~ (_), then will O=D-О=П (8B.V.), which is absurd according to the... | |
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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. 
