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" IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides. "
Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ... - Page 163
by Euclid, John Keill - 1733 - 397 pages
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894 - 894 pages
...eight question*. The values attached to the questions are shown in brackets. 1. If two triangles have one angle of the one equal to one angle of the other, and the sides about these equal angles proportional, show that the triangles are similar, and that...
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Calendar, for the Year ...

1895 - 142 pages
...given a side of a regular pentagon, construct it. 4. Triangles which are equal in area, and which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. Describe an isosceles triangle equal in area to a given triangle and having...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 344 pages
...perpendicular to the sides of the other, they are similar. (Why ?) Theorem 9. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional. the triangles are similar. Given A A1 B1d, A2B2C2, such that...
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Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1895 - 346 pages
...perpendicular to the sides of the other, they are similar. (Why ?) Theorem 9. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. Given AA^d, A2B2C2, such that ZG!...
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Euclid, Books 1-4

Rupert Deakin - 1897 - 344 pages
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Proceedings of the Edinburgh Mathematical Society

Edinburgh Mathematical Society - Electronic journals - 1899 - 340 pages
...joined, the triangles EAB, DAC are halves of the parallelograms BE, CD. Hence, Two triangles which have one angle of the one equal to one angle of the other have to each other the same ratio as the rectangles contained by the sides about the equal angles. LIST...
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - Examinations - 1899 - 348 pages
...D and AC in E, so that DP may be a fourth part of PE. Dl 44. Prove that equal triangles, which have one angle of the one equal to one angle of the other, have the sides about the equal angles reciprocally proportional ; and state and prove the converse of this...
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New Plane and Solid Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...to the sides of the other, they are similar. PROPOSITION XVIII. 264. Theorem. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. A, Bi Given A AiBiCi, A^B2C^, such...
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New Plane Geometry

Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 265 pages
...other, they are similar. PLANE GEOMETRY. [BK. IV. PROPOSITION XVIII. 264. Theorem. If two triangles have one angle of the one equal to one angle of the other, and the including sides proportional, the triangles are similar. Given AA^Ci, A2B2C2, such that Z Cl...
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The Contents of the Fifth and Sixth Books of Euclid

Euclid, Micaiah John Muller Hill - Euclid's Elements - 1900 - 190 pages
...PROPOSITION XLVIII. (i). (Euc. VI. 14, 1st Part.) ENUNCIATION. Parallelograms having equal areas and having one angle of the one equal to one angle of the other have the sides about the equal angles reciprocally proportional. Let the two parallelograms be placed so...
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