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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... "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 339
των James Ryan - 1826 - 383 σελίδες
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The Arithmetical Magazine, Or, Mercantile Accountant: Adapted to the ...

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,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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 :...

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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 :...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

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...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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...

Elements of Geometry: Containing the First Six Books of Euclid: With a ...

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—...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

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«,...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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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