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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. - Page 72
by Euclid - 1868
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - Logarithms - 1723 - 444 pages
...Sides which are fubtended under the equal Angles, are homologous, or of like Ratio. . -• ' ' TETABC. DCE, be equiangular Triangles, •*-' having the Angle ABC equal to the Angle DCE; the Angle A CB equal to the Angle DEC, and the Angle BAC equal to the Angle CDE. I fay, the Sides that...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1762 - 488 pages
...equal angles are homologous fides, that is, are the antecedents or confequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC...angle DCE, and the angle ACB to the angle DEC, and confequently " the angle BAC equal to the angle CDE. The fides "• 3*- 1• about the equal angles...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - Geometry - 1772 - 462 pages
...Sides, which are fubtended under the equal Angles, are homologous ', or of like Ratio. TET ABC, DEC, be equiangular Triangles, -*~' having the Angle ABC equal to the Angle DCE, the Angle. ACB equal to the Angle D EC, >„ and the Angle BAC equal to the Angle CD £. I fay, the...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - Trigonometry - 1775 - 534 pages
...equal angles are homologous fides, that is, are the antecedents or confequents of the ratios. Let AEC, DCE be equiangular triangles, having the angle ABC...angle DCE, and the angle ACB to the angle DEC, and confequently * the angle BAC equal to the angle » 3*. '• CDE. The fides about the equal angles of...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...angles are homologous fides, that is, e the antecedents or confequents of the ratios. po ar Let ABC, DCE be equiangular triangles, having the angle ABC...angle DCE, and the angle ACB to the angle DEC, and confequently' the angle BAC equal to the angle » 3». ». CDE. The fides about the equal angles of...
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The Elements of Euclid: With Dissertations Intended to Assist and Encourage ...

Euclid, James Williamson - Euclid's Elements - 1781 - 324 pages
...proportionals; and thofe fides are of like fatio which are extended under the equal angles. Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE; and the angle ACB equal to the angle DEC; and befides the angle BAC equal to the angle CDE : I fay that the fides about...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...equal angles are homologous fides, that is, are the antecedents or corifequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DCE, and the angle ACB to the a"gle DEC, and ronfequently » the angle BAC equal to the a yi.i. angle CDE. The fides about the equal...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...equal angles, are homologous fides, that is, are the antecedents or confequents 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 a 3»- l• DEC, and confequently • the angle BAC equal to the angle CDE. The fides about the equal...
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Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - Circle-squaring - 1804 - 468 pages
...equal angles are homologous fides, that is, are the antecedents or confequcnts of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC...angle DCE, and the angle ACB to the angle DEC, and confequently a the angle BAG equal to the » 34. i» angle CDE. Ths fides about the equal angles of...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 1804 - 530 pages
...equal angles are homologous fides, that is, are the antecedents or confequents of the ratios. Let ABC, DCE be equiangular triangles, having the angle ABC equal to the angle DC1 ., and the angle ACB to the angle DEC, and confequently a the angle BAC equal to the angle CDE....
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