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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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Manual of Euclid: books iv., v., vi., by J.A. Galbraith and S. Haughton

Joseph Allen Galbraith - 1859
...irípi ràç ïaaç yuíviaç, KU¡ «'i/íóXuym ai viro raç iaof ywviaç viroTtívovaai irXeupaí. The sides about the equal angles of equiangular triangles...ACB to the angle DEC ; and consequently the angle BAС equal to the angle CDE (I. 32). The sides about the equal an- д gles of the triangles ABC and...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860
...are homologous sides ; that is, are the antecedents or consequents of the ratios. Given ABC, DCE, two equiangular triangles, having the angle ABC equal...consequently the angle BAC equal to the angle CDE (I. 32) ; to prove that the sides about the equal angles of the triangles ABC, DCE are proportionals; and those...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 páginas
...antecedents or consequents of the ratios. Let ABC, DCEhe equiangular triangles, having the angle ABC tqual to the angle DCE, and the angle ACB to the angle DEC; and ronsequently the angle BA C equal to the angle CDE. (l, 32.) The sides about the equal angles of the...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1861 - 490 páginas
...two triangles AB C, DCE be equiangular ; the angle BAG 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 : DE. For,...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 490 páginas
...triangles ABC, DCE £ be equiangular ; the angle BAG / \ 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 B • CE proportional, and we shall have BC:CE::AB:CD::AC:DE. For,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Robert Potts - 1864
...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...angle ACB to the angle DEC; and consequently the angle BA C equal to the angle CDE. (I. 92.) The sides about the equal angles of the triangles ABC, DCE shall...
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The college Euclid: comprising the first six and the parts of the eleventh ...

Alexander Kennedy Isbister - 1865
...consequents of the ratios. (References— Prop. I. 17, 22, 28, 32, 34 ; v. 7, 16, 22 ; VI. 2.) 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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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - 1866 - 320 páginas
...two triangles ABC, D CE be equiangular ; the angle BAG 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 B t! E proportional, and we shall have BC:CE::AB:CD::AC:DE. For,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...antecedents or the consequents of the ratios. Let the triangle ABCbQ equiangular to the triangle DCE, having the angle ABC equal to the angle DCE, and the angle ACB equal to the angle DEC, and consequently the anele BA C equal to the angle CDE: the sides about the...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...antecedents or the consequents of the ratios. Let the triangle ABCbe equiangular to the triangle DCE, 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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