 | Euclides - 1865 - 402 σελίδες
...CD to DF. (v. def. 5.) If then magnitudes, &c. QED PROP. XIX.— THEOREM. If a whole magnitude be to a whole, as a magnitude taken from the first is to a magnitude taken from the other; then the remainder shall be to the remainder as the whole to the whole. (References — Prop. v. 11,... | |
 | Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...EB is to FD usABistoCD. [V.ll. Wherefore, if a whole &c. QED • COROLLARY. If the whole be to the whole as a magnitude taken from the first is to a...other, the remainder shall be to the remainder as the magnitude taken from the first is to the magnitude taken from the other. The demonstration is contained... | |
 | Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...Definition 5. Wherefore, if magnitudes &c. QED c PKOPOSITION 19. THEOREM. >^ If a whole magnitude be to a whole as a magnitude taken from the first is to...magnitude taken from the other, the remainder shall lie to the remainder as the whole is to the whole. Let the whole AB be to the whole CD as AE, a magnitude... | |
 | Robert Potts - 1868 - 434 σελίδες
...whole AB to the whole CD. (v. 11.) Wherefore, if the whole, tLc. QED COR. — If the whole be to the whole, as a magnitude taken from the first is to a...magnitude taken from the other; the remainder shall likewise be to the remainder, as the magnitude taken from the first to that taken from the other. The... | |
 | Euclides, James Hamblin Smith - 1872 - 376 σελίδες
...A is to B ns C is to D. I V. Def. 5. QBD PROPOSITION XXVI. (EucL v. 19.) If a whole magnitude be to a whole as a magnitude taken from the first is to a magnitude taken from the other, the remainder must be to the remainder as the whole is to the whole. Let A, B together have the same ratio to C,... | |
 | Euclides - 1874 - 342 σελίδες
...the whole AB to the whole CD (V. 11). Wherefore, if the whole, &c. QED Cor. If the whole be to the whole, as a magnitude taken from the first is to a...magnitude taken from the other ; the remainder shall likewise be to the remainder, as the magnitude taken from the first to that taken from the other. The... | |
 | Euclid, Lewis Carroll - 1874 - 80 σελίδες
...and fourth together (c + d) are to the fourth (c?).], ~ L PKOP. XIX. If one magnitude be to another as a magnitude taken from the first is to a magnitude taken from the other : the remainder is to the remainder as the whole is to the whole. Express enunciation . Let a : Ъ : : с : à ; Taking... | |
 | Charles Lutwidge Dodgson - 1874 - 96 σελίδες
...together (c+d) are to the fourth elusion a + b : Ъ : : c+d : d. PROP. XIX. If one magnitude be to another as a magnitude taken from the first is to a magnitude taken from the other : the remainder is to the remainder as the whole is to the whole. Express enunciation . Talcing given proporLet a :... | |
 | Robert Potts - 1876 - 446 σελίδες
...whole AB to the whole CD. (\. 11.) Wherefore, if the whole, &c. QED COR. — If the whole be to the whole, as a magnitude taken from the first is to a...magnitude taken from the other ; the remainder shall likewise be to the remainder, as the magnitude taken from the first to that taken from the other. The... | |
 | Isaac Todhunter - 1880 - 426 σελίδες
...[Hyp. 0\ereforeEBistoFDasABistoCD.[Vn Wherefore, if a whole &c. QEP COROLLARY. If the whole be to the whole as a magnitude taken from the first is to a...other, the remainder shall be to the remainder as the magnitude taken from the first is to the magnitude taken from the other. The demonstration is contained... | |
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If the whole be to the whole, as a magnitude taken from the first is to a magnitude taken from the other ; the remainder... 
