 | Nicolas Vilant - 1798 - 196 σελίδες
...r=*« > * Then от C> r=or > .г т+я XD And v Def. V. A : B=C : D. PROPOSITION XIX.— THEOREM. If a whole magnitude be to a whole as a magnitude taken from the firit is to a magnitude taken from the other, the remainder ihail be to the re,, maindcr as the whole... | |
 | Alexander Ingram - 1799 - 374 σελίδες
...BE, fo b is CD to DF. fore, &.c. Q^ED BOOK V. N i A IP IS b5.Def.5. ca. 5C Where. PROP. XIX. THEOR. IF a whole magnitude be to a whole, as a magnitude taken from the firft is to a magnitude taken from the other ; the remainder mall be to the remainder, as the whole... | |
 | John Playfair, Euclid - 1804 - 468 σελίδες
...therefore c, A+B : B : : C+D : D. Therefore, &c. Q_ ED c S- def. s. ,' Ls PROP. Book V, PROP. XIX. THEOR. IF a whole magnitude be to a whole, as a magnitude taken from the firft, is to a magnitude taken from the other ; the remainder fhall be to the remainder, as the whole... | |
 | John Playfair - 1806 - 320 σελίδες
...A+B : B : : C+D : Dc. Therefore, &c. QED c S.Def.5. Book V. a 16. 5. r. 5. c 11. 5. PROP. XIX. THEOR. IF a whole magnitude be to a whole, as a magnitude...first is to a magnitude taken from the other, the remainder will be to the remainder as the whole to the whole. If A : B : : C : D, and C<A, A— C :... | |
 | Robert Simson - 1806 - 546 σελίδες
...remainder DF, as the whole AB to the whole CD. 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 likewise is to the remainder, as the magnitude taken from the first to that taken from the... | |
 | Euclid - 1810 - 554 σελίδες
...DF, as the whole AB to the whole CD: Wherefore, if the whole, &c. Q. E D. CoR If the whole be to the whole, as a magnitude taken from the first, is to a magnitude taken 5 I , from the other; the remainder likewise is to the remainder, as the magnitude taken from the first... | |
 | John Mason Good - 1813 - 714 σελίδες
...together shall he to the second, as the third and fourth together to the fourth. Prop. XIX. Theor. If a whole magnitude be to a whole, as a magnitude...first, is to a magnitude taken from the other; the remainder shall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes... | |
 | Euclides - 1814 - 560 σελίδες
...f , as AB is to BE, so is CD to DF. If then magnitudes, &c. QED r; PROP. XIX. THEOR. I) F C M N Ira whole magnitude be to a whole, as a magnitude taken...first, is to a magnitude taken from the other; the remainder shall be to the remainder, as the whole to the whole. Let the whole AB, be to the whole CD,... | |
 | Euclides - 1816 - 588 σελίδες
...magnitudes, &c. QED D F M N PROP. XIX. XHEOR. IF a whole magnitude be to a whole, as a magni- See N, tude taken from the first, is to a magnitude taken from the other ; the remainder shall be to the remainder, as the whole to the whole. o Let the whole AB, be to the whole... | |
 | John Playfair - 1819 - 354 σελίδες
...mfA+B-)ZnB, m(C+D)^nD ; therefore (def. 5. 5.), A+B : B : : C+D : D. Therefore, &c. Q, ED PROP. XIX. THEOK. If a whole magnitude be to a whole, as a magnitude...first is to a magnitude taken from the other; the remainder will be to the remainder as the whole to the whole. If A : B : : C : D, and if C be less... | |
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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 shall be to the remainder, as the whole to the whole. 
