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" If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. "
Elements of Geometry, Briefly, Yet Plainly Demonstrated by Edmund Stone - Page 31
by Euclid - 1728
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Handbook to government situations: or, The queen's Civil service considered ...

Civil service - 1871
...drawn at right angles to the diameter of a circle from the extremity of it, touches the circle. 3. 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,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...by Euclid) of another case in which two triangles are equal in all respects. PROPOSITION E. THEOEEM. 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, if the third angles in...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...two sides produced, prove that the points B and C lie upon the circle of which PQ is the diameter. 9. 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...
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...ratio of FB to GB\ and .-. cuts FG in B; ie iBPF= LAPP; .-. AP : PB as AF : FB; (vi. 2) THEOREM (</). If two triangles have one angle of the one equal to one angle of the other and the sides about two other angles proportional, then shall the triangles be equiangular...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...ABC is equiangular 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,...
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The elements of geometry, in eight books; or, First step in applied logic

L J V. Gerard - 1874
...each other. Scholium. Equilateral triangles are similar to one another. THEOREM 26. (Eucl. VI. 7.) If two triangles have one angle of the one equal to one angle of the other, if the sides forming another angle be proportional, and if the third angle be acute...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...is equiangular to the triangle DEF. \Vherefore, if two triangles, &c. QED PROPOSITION VII. THEOREM. If two triangles have one angle of the one equal to one angle of the other, and the tides abnut two other angles proportionals; then, if each of the remaining...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876
...D : F . ,(and D :E = A :B j 5- {andB = mF } then A - В = m (D _ F) EUCLID.-BOOK VI. Prop. Page 7. If two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, then if each of the remaining...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Plane - 1876 - 58 pages
...they are similar, and 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...
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First B.A. Examination, University of London: A Hand-book to the Study of ...

J. G - 1878 - 408 pages
...on the one are to one another in the same ratio as the corresponding intercepts on the other. " 7." If two triangles have one angle of the one equal to one angle of the other, and the sides about one other angle in each proportional, so that the sides opposite...
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