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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: Or, Second Lessons in Geometry,in the Order of Simson's ... - Page 90
by Dennis M'Curdy - 1846 - 138 pages
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...proportional, but not their angles equal. VI. 7. In VI. 7 the enunciation is imperfect ; it should be, "if two triangles have one angle of the one equal to one angle of the other, and the sides about two other angles proportionals, so that the sides subtending...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...triangle ABC is equiangular to the triangle DEF. Wherefore, if the sides, &c. QED PROPOSITION VI. 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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Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868 - 150 pages
...additional equality of a pair of corresponding sides involves the identity of the triangles. THEOREM 7. If two triangles have one angle of the one equal to one angle of the other; and the sides about the equal angles proportionals, then will the triangles be...
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Handbook to government situations: or, The queen's Civil service considered ...

Civil service - 1871 - 258 pages
...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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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 320 pages
...polygon on AB + the area of the polygon on AC is equal to the area of the polygon on BC. EXAMPLES. 1. If two triangles have one angle of the one equal to one angle of the other, and likewise one angle of the one supplementary to one angle of the other, the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 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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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 - 428 pages
...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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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 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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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...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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