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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. "
A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ... - Page 53
by Daniel Cresswell - 1816 - 294 pages
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A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - Mathematics - 1866 - 426 pages
...the other have their sides about the equal angles reciprocally proportional: and parallelograms that 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. CO-ORDINATE...
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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
...and shall have those angles equal about which the sides are proportionals. Let the triangles ABC, DEF have one angle of the one equal to one angle of the other, namely, the angle BA C equal to the angle EDF, and the sides about two other angles ABC, DEF, proportionals,...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...Hence the result may be extended to triangle?, and we hava the following theorem, triangles which, ham one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of their sides. Then VI. 19 is an immediate...
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Elementary Geometry, Volume 2

James Maurice Wilson - Geometry - 1868 - 150 pages
...similar, the sides which are opposite the equal angles being homologous ......... 62 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 similar . . -64 THEOREM...
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The Oxford, Cambridge, and Dublin Messenger of Mathematics, Volume 4

Mathematics - 1868 - 272 pages
...joining the point P to the points A and B cut a line in the points a, /3. The areas of triangles which have one angle of the one equal to one angle of the other, have to one another the ratio which is compounded of the ratios of the sides. Applying this to the...
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The Edinburgh university calendar

Edinburgh univ - 1868 - 334 pages
...by the segments of the other. 4. To inscribe a circle in a given triangle. 5- 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. 6. Find the continued product of...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...AB, BC, a mean proportional DB is found. QEF PEOPOSITION XIV. THEOREM. Equal parallelograms, which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional: and conversely, parallelograms that...
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The Cambridge Examiner, Volume 3

Education, Higher - 1883 - 536 pages
...proportion. When is a straight line said to be cut in extreme and mean ratio ? 14. Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angels reciprocally proportional ; and triangles which have one angle...
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Elements of Geometry

Simon Newcomb - Geometry - 1881 - 418 pages
...the other two angles each equal to its supplement. I "i 1 . Corollary 2. If two parallelograms Itave one angle of the one equal to one angle of the other, all the remaining angles of the one will be equal to the corresponding angles of the other. 125. Corollary...
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882 - 152 pages
...circle. 10. To describe a circle about a given square. 11. Define equal triangles, and prove that ifequal triangles have one angle of the one equal to one angle of the other, then the sides about the equal angles are reciprocally proportional. 12. Show that the linos which...
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