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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: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - 186 páginas
...homologous sides, that is, they are the antecedents or the consequents of the ratios. Let ABC, DCB be equiangular triangles, having the angle ABC equal...consequently the angle BAC equal to the angle CDE (2 Cor. 32. 1). The sides about the equal angles of the triangles ABC, DCE are proportional; and those...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 páginas
...angles are homologous sides, that is, are the antecedents or con' sequents 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 BAG equal to the angle CDE. The sides about the equal angles of the triangles ABC,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - 513 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...DEC, and consequently * the angle BAC equal to the a 32. l. angle CDE. The sides about the equal angles of the triangles ABC, DCE are proportionals; and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 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 a the angle BAG equal to the a 32. 1. angle CDE. The sides about the equal angles of the triangles...
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The Element of Geometry

John Playfair - 1836 - 114 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 (5. 2.) the angle BAC equal to the angle CDE. The sides about the equal angles of the triangles ABC,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 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 BAG equal to the angle CDE. The sides about the equal angles of the triangles...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...are the antecedents or consequents of the ratios. Let ABC, DCE, be equiangular triangles, having die angle ABC equal to the angle DCE, and the angle ACB to the angle DEC, and consequently the angle BAG equal to the angle CDE (I. 32). The sides about the equal angles of the triangles ABC, DCE, are...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...angles are homologous sides ; that is, are the antecedents or consequents of the proportions. Let ABC, DCE be equiangular triangles, having the angle ABC...to the angle DEC; and consequently* the angle BAC *mtt- equal to tne angIe CDE. The sides about the 3*AX. equal angles of the triangles ABC, DCE shall...
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The Elements of Euclid

Euclid - 1838 - 416 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 (32. 1.) the angle BAC equal to the angle CDE. The sides about the equal angles of the triangles ABC,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 páginas
...angles are homologous sides, that is, are the antecedents or consequents of the ratios. u 2 Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle * 32.1. ACB to the angle DEC, and consequently* the angle BAC equal to the angle CDE: the sides about...
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