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" The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having... "
Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI - Página 72
por Euclid - 1868 - 141 páginas
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...angles are homologous sides, that is, are the antecedents or consequents of the ratios. Let ABC, DCE\>e equiangular triangles, having the angle ABC equal...angle ACB to the angle DEC; and consequently the angle BA C equal to the angle CDE. (I. 32.) The sides about the equal angles of the triangles ABC, DCE shall...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 382 páginas
...triangles ABC, DCE ? be equiangular ; the angle BAC / \ being equal to the angle CDE, the A/^ \ angle ABC to the angle DCE, and the angle ACB to the angle DEC, then the homologous sides will be proportional, and we shall have BC:CE::AB:CD::AC:DE. For, let the...
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New Elementary Geometry: With Practical Applications; a Shorter Course, Upon ...

Benjamin Greenleaf - 1873 - 176 páginas
...the two triangles ABC, DCE be equiangular ; the angle BAC being equal to the angle CDE, the angle ABC to the angle DCE, and the angle ACB to the angle DEC, then the homologous sides will be proportional, and we shall have BC:CE::AB: CD : : AC : D E. For,...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...equal angles are homologous sides, that is, are the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC...consequently the angle BAC equal to the angle CDE (I. 32). Then the sides about the equal angles of the triangles ABC, DCE shall be proportionals ; and those...
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New Elementary Geometry with Practical Applications

Benjamin Greenleaf - 1874 - 176 páginas
...two triangles ABC, DCE be equiangular ; the angle BAC being equal to the angle CDE, the angle AB C to the angle DCE, and the angle ACB to the angle DEC, then the homologous sides will be proportional, and we shall have BC:CE::AB: CD : : AC : D E. For,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 páginas
...equal angles are homologous sides, that is, are the antecedents or consequents oj the ratios, Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle A CB to the angle DEC; and consequently the angle BA C equal to the angle CDE. (l. 32.) The sides about...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 páginas
...antecedents or the consequents of the ratios. Let the triangle A BC\>e equiangular to the triangleZ>CZ7, having the angle ABC equal to the angle DCE, and the angle ACB equal to the angle DEC, and consequently the angle BA C equal to the angle CDE : the sides about the...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...to the equal angles are homologoui sides, that is, are the antecedents or consequents of the ratios. Let ABC and DCE be equiangular triangles, having the...The sides about the equal angles of the triangles ABCandDCE are proportionals ; and the sides which are opposite to the equal angles are homologous....
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 400 páginas
...antecedents or the consequents of the ratios. Let thetriangle^l.BCbe equiangular to the triangle _DC#, having the angle ABC equal to the angle DCE, and the angle ACB equal to the angle DEC, and consequently the angle BA <7equal to the angle CDE: the sides about the...
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Books 3-9

Euclid - 1908
...angles are proportional, and those are corresponding sides which subtend the equal angles. Let ABC, DCE be equiangular triangles having the angle ABC equal to the angle DCE, the angle BAC to the angle CDE, and further the angle ACB to the angle CED ; I say that in the triangles...
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