 | 1836 - 488 σελίδες
...will be to the second as the third and fourth together to the fourth. XIX. 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 will be to the remainder as the whole to the whole. D. If four magnitudes be proportionals, they are... | |
 | Andrew Bell - 1837 - 290 σελίδες
...nB, m (C + D) ^ nD ; therefore A + B:B::C + D:D. PROPOSITION XIX. THEOREM. If a whole magnitude be to a whole, as a magnitude taken from the first, is to...shall be to the remainder, as the whole to the, whole. If A : B : : C : D, and if C be less than A, A — . C : B — D : : A : B. Because A : B : : C : D,... | |
 | Robert Simson - 1838 - 434 σελίδες
...DF, as the whole AB to the whole CD : Wherefore, if the whole, &c. QED B 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 other: the... | |
 | Euclides - 1840 - 192 σελίδες
...D)^s"nD ; therefore, A + B : B : : C + D : D (v. Def. 5). 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, the remainder will be to the remainder as the whole to the whole. t If A : B : : C : D, and if C be less than A,... | |
 | Euclides - 1841 - 378 σελίδες
...whole AB to the * " whole CD.* Wherefore, if the whole, Sic. QED * 11. 5. COR. If the whole be to the whole, as a magnitude taken from the first, is to...other; the remainder shall be to the remainder, as the magnitude taken from the first to that taken from the other. The demonstration is contained in the... | |
 | Oliver Byrne - 1841 - 144 σελίδες
...hypothesis, a + Ь : с + d :: Ъ : d, and .'. a : с :: a + Ь : с + d. 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 other. The... | |
 | John Playfair - 1842 - 332 σελίδες
...wi(C+D)/nD ; therefore (def. 5. 5.), A+ B:B :: CfD : 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 ; the remainder will be to the remainder as the whole to the whole. If A : B : : C : D, and if C be less than A, A—... | |
 | Euclides - 1845 - 546 σελίδες
...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 - 1845 - 218 σελίδες
...DF§, as the whole AB to the whole CD. Wherefore, if the whole, &c. QED BD 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 other. The... | |
 | Euclides - 1846 - 292 σελίδες
...BE as CD to DF. Wherefore, If four magnitudes %c. QED 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, then the remainder shall be to the remainder as the whole to the whole. Let the whole AB, be to the... | |
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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... 
