 | Euclides - 1848 - 52 pages
...other; the remainder shall be to the remainder, as the whole to the whole. 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. PROP.... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...v.), as the whole AB to the whole CD. Wherefore, if the whole, etc. 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 other. The... | |
 | Euclides - Geometry - 1853 - 176 pages
...ia m С d to df If then magnitudes, &c. QED PROPOSITION XIX. — THEOREM. If a whole magniiude be to a whole as a magnitude taken from the first is to a magnitude taken from the otlier, the remainder shall be to tlie remainder as the whole to the whole. LET the whole ab be to... | |
 | Euclides - 1855 - 230 pages
...magnitudes be proportionals. If magnitudes, taken jointly, be proportionals. If a whole magnitude be to a whole as a magnitude taken from the first is to a magnitude taken from the other. Idem . If magnitudes have a ratio to one another. If magnitudes have the same ratio to the same magnitude.... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...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... | |
 | Eucleides - 1860 - 396 pages
...magnitudes be proportionals. If magnitudes, taken jointly, be proportionals. If a whole magnitude be to a whole as a magnitude taken from the first is to a magnitude taken from the other. Idem . If magnitudes have a ratio to one another. If magnitudes have the same ratio to the same magnitude.... | |
 | Euclides - 1861 - 464 pages
...: A = C+D : C: .-. invert. (A, V.) A:A + B=C:C + D. Pnor. XIX.— THEOn. If a whole magnitude be to a whole, as a magnitude taken from, the first is to a magnitude talcen from the other ; the remainder shall be to the remainder as the whole to the whole. " If a whole... | |
 | George Sturton Ward - Geometry, Algebraic - 1862 - 104 pages
...therefore , = T ; о — d о and therefore a — с : b — d : : a : 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 is to that taken. from the other.... | |
 | Euclides - 1864 - 448 pages
...whole AB to the whole CD. fv. 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... | |
 | Robert Potts - 1865 - 528 pages
...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... | |
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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... 
