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" MAGNITUDES which have the same ratio to the same magnitude are equal to one another ; and those to which the same magnitude has the same ratio are equal to one another. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 16
by Thomas Gaskin - 1847 - 263 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...Wherefore, of unequal magnitudes, &c. QED G L C — B FG C-- ]! KHD KD b7.defc 5. PROP. IX. THEOR. see *. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C: A is equal to B: for, if they are not equal, one of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 320 pages
...of A+B by HI, C has a g-eater ratio to A than it has to A+Bb. Therefore, &c. Q, ED PROP. IX. THEOR. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. If A : C : : B : C, A=B. For, if not, let A be greater than B ; then, because A is greater than B,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...than it has to AB. Wherefore, of unequal magnitudes, £?. QED 1 a. b 7 DeC *. PROP. IX. THEOR. SeeN. MAGNITUDES which have the same ratio to the same magnitude are equal to one another; and those.to which the same magnitude has the same ratio are equal to one another. multiple F; and that...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 pages
...than it has to AB. Wherefore, of unequal magnitudes, &c. QED A 6 b 7 Def. 5. PROP. IX. THEOR. s«eN. MAGNITUDES which have the same ratio to the same magnitude...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C; A is equal to B. For, if they are not equal, one of...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...m, C has a sweater ratio to A than it has to A+B (def. 7. 5.). Therefore, &c. Q,ED PROP. IX. THEOR. Magnitudes .which have the same ratio to the same...magnitude has the same ratio are equal to one another. If A : C : : B : C, A=B. For, if not, let A be greater than B ; then, because A is greater than B,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...than it has to A+B (def. 7.5.). Therefore, &c. Q..ED PROP. IX. THEOR, Magnitudes 'which have the stime ratio to the same magnitude are equal to one another...those to which the same magnitude has the same ratio arc equal to one another. If A : C : : B : C, A=B. For, if not, let A be greater than B ; then, because...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 800 pages
...magnitud« has a greater ratio to the less than it has to the rrcaler. Prop. IX. Theor. Maiíiiiludcs u Inch have the same ratio to the same magnitude are equal to one another; and thuse to which the same uiagm» tude has the same ratio are equal to one ani«! magnitudes, arc equal...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...quotient ; and therefore the ratio of C to B is greater lhaa the ratio of C to AQED PROP. IX. THEOR. Magnitudes which have the same ratio to the same magnitude...magnitude has the same ratio, are equal to one another. DEMONSTRATION. 1 . Let A and B have the same ratio to C, it is to be proved that A is equal to B. Because...
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An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...A. s? QED PEOP. IX. THEOR. f.'iX/if'i Magnitudes which have the same ratio to the same magnitude arc equal to one another; and those to which the same magnitude has the same raliu, are equal to one another. DEMONSTRATION. 1. Let A and B have the same ratio to C, it is to be...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...AB. Wherefore, of unequal magnitudes, &c. QED A Г KHDG 1 I LKD PROP. IX. TIIEOR. Magnitudes ichich have the same ratio to the same magnitude are equal to one another ; and those to which the tame magnitude has the tame ratio are equal to one another. L»t A, B hare each of them the same ratio...
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