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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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...unequal magnitudes &c. QKI'. G ,. PROPOSITION 9. THEOREM. Magnitudes which have the same ratio to tlie same, magnitude, are equal to one another ; and those...magnitude has the same ratio, are equal to one another. First, let A and B have the same ratio to C: A shall bo equal to B. For, if A is not equal to B, one...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...it has to A B. (v. def. 7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. 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, Then A shall be equal to B. AD CF For, if they are...
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Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 pages
...laa XXqXoij orf ai iгpb & то aiirb TV avril !%и \oyov, lKfva laa aXXqXoi iarv. Magnitudes which have the same ratio to the same magnitude are equal to one another: and magnitudes to which the same magnitude has the same ratio are equal to one another. PART I. Statement....
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...mqA, .'. D has to B a greater ratio than D has to A. V. Def. 7. QED PROPOSITION VIII. (Eucl. v. 9.) Magnitudes, which have the same ratio to the same...magnitude has the same ratio, are equal to one another. Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...has to AB (V. Def. 7). Wherefore, of two unequal magnitudes, <fec. QED PROPOSITION 9. — Theorem. Magnitudes which have the same ratio to the same magnitude...another ; and those to which the same magnitude has the game ratio are equal to one another. Let A, B have each of them the same ratio to C. Then A shall be...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...2, conv.) and, by inversion, C is to A as C is to B, (V. 4. ) QED PROP. VI.— THEOREM. (Euc. V. 9.) Magnitudes which have the same ratio to the same magnitude are equal; and those to which the same magnitude has the same ratio are equal. Let as A is to C so is B to C;...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 382 pages
...a greater ratio than D has to A. V. Def. 7. (JED PROPOSITION VIII. (Eucl. v. 9.) Magnitudes, whidi have the same ratio to the same magnitude, are equal...magnitude has the same ratio, are equal to one another. Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...than it has to AB. (v. def. 7.) Wherefore, of two unequal magnitudes, &c. QED PROPOSITION IX. THEOREM. Magnitudes which have the same ratio to the same magnitude...are equal to one another : and those to which the tame magnitude has the tame ratio a,• equal to one another. Let, A, B have each of them the same...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1879 - 376 pages
...greater ratio than D has to A. V. Def. 7. PROPOSITION VIII. (EucL v. 9.) Magnitudes, which have the so/me ratio to the same magnitude, are equal to one another;...magnitude has the same ratio, are equal to one another. Let A and B have the same ratio to C. Then must A = B. For if A were greater than B, A would have a...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...Definition 7. Wherefore, of unequal magnitudes &c. QED PROPOSITION 9. THEOREM. Magnitudes which hare the same ratio to the same magnitude, are equal to...magnitude has the same ratio, are equal to one another. First, let A and B have the same ratio to C: A shall be equal to B. For, if A is not equal to B, one...
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