 | William M. Finlay - 1803 - 252 σελίδες
...founded on the \9th proposition of the 5th book of Euclid, which says, u If a whole magnitude, be to a whole, as a magnitude taken " from the first, is to a magnitude taken from the other, the re" mainder shall be to the remainder, as the whole to the whole." |C?* See the application of this,... | |
 | John Playfair - 1806 - 311 σελίδες
...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 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 C<A, A— C : B— D :... | |
 | Robert Simson - 1806 - 518 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 other :... | |
 | Euclid - 1810 - 518 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
...second, as the third and fourth together to the fourth. Prop. XIX. Theor. 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. Prop. E. Theor. If four magnitudes be proportionals, they are also proportionals by conversion, that... | |
 | Euclides - 1814
...whole CD : Wherefore, if the whole, &c. QED ^ CoR. If the whole be to the whole, as a mag- BD 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 the other: The... | |
 | Euclides - 1816 - 528 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...shall be to the remainder, as the whole to the whole. o Let the whole AB, be to the whole CD, as AE, a magnitude taken from AB, to CF, a magnitude taken... | |
 | John Playfair - 1819 - 317 σελίδες
...(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 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—... | |
 | John Mason Good - 1819
...the third and fourth together to the fourth. Prop. XIX. Theor. If a whole magnitude be to и n-hole, as a magnitude taken from the first, is to a magnitude taken from the other; the remainder «hall be to the remainder, as the whole to the whole. Prop. E. Theor. If four magnitudes he proportional«,... | |
 | John Playfair - 1819 - 333 σελίδες
...: C+D : D. Therefore, &c. Q, ED HlOP. XIX. THEOR. If a whole,magnit'udebeto a whole, as amagnitude taken from the first is •to a magnitude taken from the other ; the remainder will be. to the remainder as the whole to (he whole. If A : B : : C : D, and if C be less than A, A—... | |
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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... 
