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

John Playfair - 1842 - 317 páginas
...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...and the angle ACB to the angle DEC, and consequently (4. Cor. 32. 1.) the angle BAC equal to the angle CDE. The sides about the equal angles of the triangles...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...equal angles are homologous sides, that is, the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC...and the angle ACB to the angle DEC; and consequently (32.1.) the angle BAC equal to the angle CDE: the sides about the equal angles of the triangles ABC,...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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...sides about the equal angles of the triangles ABC, DCE shall be proportionals; and those shall be the homologous sides which are opposite to the equal...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 páginas
...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...equal to the angle DCE, and the angle ACB to the angle • 32. i. and DEC; and consequently* the angle 3 Ax. BAC equal to the angle CDE : the sides about...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 : then the sides about the equal angles of the triangles, ABC, DCE, shall be proportionals, those being...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 páginas
...angles are homologous sides, that is, are the antecedents or consequents of the ratios Let ABC, DCE,be equiangular triangles, having the angle ABC equal...and the angle ACB to the angle DEC, and consequently (4. Cor. 32. 1.) the angle BAC equal to the angle CDE. The sides about the equal angles of the triangles...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1849 - 317 páginas
...angles are homologous sides, that is, are the antecedents or consequents of the ratios Let ABC, DCE,be equiangular triangles, having the angle ABC equal...and the angle ACB to the angle DEC, and consequently (4. Cor. 32. 1.) the angle BAC equal to the angle CDE. The sides about the equal angles of the triangles...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 páginas
...angles are homologous sides, that is, are the antecedents or consequents oftlie ratios. LET abc, dce he equiangular triangles, having the angle abc equal...and the angle acb to the angle dec, and consequently (i. 32) the angle bac equal to the angle cd e. The sides about the equal angles of the triangles abc,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...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 equal to the angle DCE, and the angle ACB F to the angle DEC ; and consequently (32. i. and 3 Ax.) the angle BAC equal to the angle CDE : the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1853 - 317 páginas
...or consequents of the ratios Let ABC, DCE, be equiangular triangles, having the angle ABC equal (o the angle DCE, and the angle ACB to the angle DEC, and consequently (4. Cor. 32. 1.) the angle BAC equal to the angle CDE. The aides about the equal angles of the triangles...
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