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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... "
Report on Foreign Systems of Naval Education - Page 242
by James Russell Soley - 1880 - 335 pages
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 546 pages
...if the outward, &c. QED PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...QED i * PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportional ; 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 angle ABC equal to .the...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813 - 714 pages
...into two equal angles. Prop. IV. Theor. The sides about the equal angle« of equiangular triangles are proportionals ; and those which are opposite to...homologous sides, that is, are the antecedents Or consequents of the ratios. Prop. V. Theor. If the sides of two triangles, about each of their angles,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 pages
...'~~*~~' outward, &c. QED 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 pages
...v-~v-*> outward, &c. QED PROP. IV. THEOR. THE sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to...homologous sides, that is, are the antecedents or consequents of the ratios. LetABC,DCEbeequiangulartriangles,havingtheangle ABC equal to the angle DCE,...
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A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ...

Daniel Cresswell - Geometry - 1816 - 352 pages
...of the one be equal 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 - Circle-squaring - 1819 - 350 pages
...the exterior, &c. Q,. ED PROP. IV. THEOR. The sides about the equal angles of equiangular triangles are proportionals ; and those which are opposite to...homologous sides, that is, are the antecedents or consequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC wjual to the...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...the exterior, &c. 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 pages
...&c. QED OF 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 - Euclid's Elements - 1826 - 326 pages
...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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