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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 161
by John Keill - 1733 - 397 pages
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The Cambridge Examiner, Volume 3

Education, Higher - 1883
...other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another. 15. If...
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Metrical Geometry: An Elementary Treatise on Mensuration

George Bruce Halsted - Measurement - 1881 - 232 pages
...ratio m:n, and its area E. f^jj l^g = •/ ; 0=-\l — . Ans. \ n \ m 521. If two triangles have one angle of the one equal to one angle of the other, and the sides about a second angle in each equal, then the third angles will be either equal or supplemental....
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882
...nearer to the centre than the less. 7. Define equal triangles, and prove that if equal triangles have one angle of the one equal to one angle of the other, then the sides about the equal angles are reciprocally proportional. GENEEAL PAPEE. 1. Trace very briefly...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883
...those sides which are opposite to the equal angles are homologous. THEOR. 3. If two triangles have one angle of the one equal to one angle of the other and the sides about these angles proportional, they are similar, and those angles which are opposite...
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Glasgow University Calendar

University of Glasgow - 1883
...of the radins of the circle to the side of the second square ? 12. Prove that if two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportional, the triangles are similar. 14. One of the parallel...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...to the triangle DEF. Wherefore, if the sides &c. QED PROPOSITION 6. THEOREM. 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 to one another,...
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Examinations Papers

1884
...given circle. Inscribe a regular figure of ten sides in a given circle. 3. Equal triangles which have one angle of the one equal to one angle of the other have their sides about the equal angles reciprocally proportional. If one of the said sides in the one triangle be equal to one of the said...
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Cambridge University Examination Papers

University of Cambridge - 1884
...same ratio which the other sides of the triangle have to one another. 9. Equal triangles, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional. THURSDAY, December 6, 1883. 9— ARITHMETIC. (A) 1. MULTIPLY fifty thousand...
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Calendar of Dalhousie College and University

Dalhousie University - 1884
...angles of two triangles are proportional, the triangles -are equiangular. 8. Equal triangles that have one angle of the one -equal to one angle of the other, have the sides about the equal angles reciprocally proportional. Extend the enunciation, shewing why you...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884
...have their sides about the equal angles reciprocally proportional. Conversely : Triangles which have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal. (1) Let BAC, DAE be equal...
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