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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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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 12 pages
...perpendicular to the line touching the circle. Voluntary Portion. 1. To inscribe a square in a given circle. 2. 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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Liber Cantabrigiensis: An Account of the Aids Afforded to Poor ..., Volume 2

Robert Potts - 1863 - 482 pages
...and the other two sides produced. Also describe a circle touching three sides of a parallelogram. 6. 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, triangle shall be equiangular,...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 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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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...triangle ABC iB equiangular to the triangle DEF. Wherefore, if two angles, &c. QED PROP. VII.— THEOREM. 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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Report on Education in the Parochial Schools of the Counties of Aberdeen ...

Simon Somerville Laurie - Dick bequest for elevating the character and position of the parochial schools and schoolmasters in the counties of Aberdeen, Banff and Moray - 1865 - 401 pages
...to two right angles." ft. To inscribe an equilateral and equiangular pentagon in a given circle. 0. If two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proper tionals, the triangles shall be equiangular....
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 404 pages
...of a quadrilateral described about a circle are together equal to the other two opposite sides. 5. 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 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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Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868
...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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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 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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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 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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