 | James Maginness - 1821 - 378 σελίδες
...upon prop. 19. Euclid, book 5., which says, "If a whole magnitude, be to a whole, as a magnitude Y taken from the first, is to a magnitude taken from...shall be to the remainder as the whole to the whole." The preceding question worked by proportion, d. Flem. d.Flem. Jra. francs. First. 54 : 240OO : : 3... | |
 | James Ryan, Robert Adrain - 1824 - 542 σελίδες
...that „,_=__. and therefore A+B : B : : C + D : : DQEDPROP. XIX. THEOR. If a whole magnitude be to a whole, as a magnitude taken from the first is to...and C, D. the magnitudes taken from them. So that by hypothesis A : B : : C : D, we are to prove that A : B . : A— C : B — D. 4 B By Prop. XVI. we have... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...л к the whole AB to the whole CD : Wherefore, if the whole, &C. QED Сов. If the whole be to the whole, as a magnitude taken from the first, is to a magnitude taken from the other ; the remainder likewise is to the remainder, as the magnitude taken from the first to that taken from the other :... | |
 | Robert Simson - 1827 - 546 σελίδες
...whole CD. Wherefore, if the whole, &c. QED COR.- If the whole be to the whole, as a mag- B E> nitude 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, Dionysius Lardner - 1828 - 542 σελίδες
...d are unequal, contrary to hyp. MB, N E PROPOSITION XIX. THEOREM. (496) 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 is to the remainder as the whole to the whole. Let the whole AB be to the whole CD as AE a magnitude... | |
 | Pierce Morton - 1830 - 584 σελίδες
...[21] Cor.) PROP. 22. (Eue. v. 19.) If one magnitude be to another as a magnitud« taken from the first to a magnitude taken from the other, the remainder shall be to the remainder in the same ratio. Sec the demonstration of [22] Cor. \. If there be any number of magnitudes A, B,... | |
 | Euclides - 1834 - 518 σελίδες
...t, as the whole AB to the whole CD. Wherefore, if the whole, &c. o. ED Con. If the whole be to the whole, as a magnitude taken from the first, is to...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... | |
 | John Playfair - 1835 - 336 σελίδες
...m(C+D)£nD; therefore (def. 5. 5.}, A+ B : B : : C+D : D. PROP. XIX. THEOR. If a whole magnitude be to a whole, as a magnitude taken from the first is to a magnitude taken from the other ; t/ie remainder will be to the remainder as the whole to the whole. If A : B : : C : D, and if C be... | |
 | 1835 - 684 σελίδες
...[21] Cor.) PROP. 22. (Eue. v. 19.) If one magnitude be to another as a magnitude taken from the first to a magnitude taken from the other, the remainder shall be to the remainder in the same ratio. See the demonstration of [22]. Cor. 1. If there be any number of magnitudes A, B,... | |
 | Euclid - 1835 - 540 σελίδες
...whole CD: Wherefore, " if the whole," &c. QED COR. If the whole be to the whole, as a mag- -n nitude taken from the first, is to a magnitude taken from the other -, the remainder likewise is to the remainder, as the magnitude taken from the first to that taken from tlie other:... | |
| |
If the whole be to the whole, as a magnitude taken from the first is to a magnitude taken from the other ; the remainder... 
