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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. "
An Elementary Treatise on Algebra: Theoretical and Practical ... - Σελίδα 335
των James Ryan - 1826 - 383 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 σελίδες
...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,...

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

Robert Simson - 1806 - 518 σελίδες
...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...

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

Euclides - 1814
...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 D is greater than • 5 Def. 5. F; E shall also be greater than F a ; but Let...

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

Euclides - 1816 - 528 σελίδες
...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...

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

John Playfair - 1819 - 317 σελίδες
...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,...

An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 σελίδες
...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...to B. Because A and B have, by hypothesis, the same AB ratio to C, therefore we have the equalit) -^=g-, and therefore by multiplication A = B. 2. Because...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...be taken greater than p). It is 5. evident that ^* > - f , and £ < i. QED PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude,...magnitude has the same ratio are equal to one another. the same ratio« to c, but they have: therefore • 8.5. Again, let c have the same ratio to A and...

Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 σελίδες
...Def.?. 5. evident that -* > -, and ? < £. QED ppmn PROPOSITION IX. THEOREM. Magnitudes which hate the same ratio to the same magnitude, are equal to...magnitude has the same ratio are equal to one another. For let each of the magnitudes A, B, have the same ratio to c : then is A equal to B. 129 the same...

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

Euclid, John Playfair - 1826 - 320 σελίδες
...Magnitudes whieh have the same ratio to the same magnitude are equal to one another ; and those to whieh 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, beeause A is greater than B, two...

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

Robert Simson - 1827 - 513 σελίδες
...magnitudes, &c. QED PROP. IX. THEOR. Magnitudes which have the same ratio to the same mag- See N. nitude are equal to one another : and those to which the...magnitude has the same ratio are equal to one another. Let A, B have each of them the same ratio to C: A shall be equal to B. For, if they are not equal,...




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