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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... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Seite 56
von Euclides - 1840
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 Seiten
...to the angle CAD. Wherefore, if the exterior, &c. QED i * PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportional ;...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...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 Seiten
...QED PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...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...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1813 - 714 Seiten
...angles. Prop. IV. Theor. The sides about the equal angle« of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...ratios. Prop. V. Theor. If the sides of two triangles, about each of their angles, be proportionals, the triangles shall be equiangular, and have their equal...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 Seiten
...PROP. IV. THEOR. • X 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 tiie antecedents or consequents of the ratios. Let ABC, DCE he equiangular triangles, havingthe angle...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 Seiten
...QED PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...are the antecedents or consequents of the ratios. LetABC,DCEbeequiangulartriangles,havingtheangle ABC equal to the angle DCE, and the angle ACB to the...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - 1816 - 352 Seiten
...to the three angles of the other, each to each, the sides about the equal angles are proportionals ; and those, which are opposite to the equal angles, are homologous sides. Let the spherical triangles ABC, EDF, be on unequal spheres ; and let the angles A, B, C of the one,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 Seiten
...Q,. ED PROP. IV. THEOR. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to the equal angles are...are the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC wjual to the angle DCE, imd the angle ACB...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 Seiten
...Q, ED PROP. IV. THEQR. 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, arf the antecedents or consequents of the ratios. Let ABC. DCE be equiangular triangles, having the...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 Seiten
...GEOMETRY. PROP. IV. THEOREM. 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, on the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 326 Seiten
...THEOR, The sides about the equal angles of equiangular triangles are proportionals ; and those whieh are opposite to the equal angles are homologous sides, that is, are the anteeedents or eonsequents of the ratios. Let ABC, DCE, be equiangular triangles, having the angle...
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