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" Assuming that the areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles... "
Elements of Plane Geometry - Page 202
by William Herschel Bruce, Claude Carr Cody (Jr.) - 1910 - 263 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in tlie one equal to an angle in the other, are to each other as the rectangles of tlie sides fig. l28.ru/ucA contain the equal angles ; thus, the triangle ABC (fig. 128)...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus, the triangle ABC (fig. 128)...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 276 pages
...been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides i;ig. 123. which contain the equal angles; thus, the triangle ABC (fig. 128)...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...shall be similar to each other. PROPOSITION XVI. THEOREM. Triangles having an angle in the one equal to an angle in the other, are to each other as the rectangles of their containing sides. Let the triangles ABC, DEF have the angle B in the one equal...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...been given in articles 189, 190. THEOREM. 216. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides Fig. 128. which contain the equal angles; thus the triangle ABC (fig. 128)...
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Arithmetical Spyglass and Teacher's Assistant: Intended as a Key and ...

Charles Waterhouse - Arithmetic - 1842 - 178 pages
...mean proportional between the two segments. 20. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides, which contain the equal angles. 21. Two similar triangles are to each other...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 108 pages
...into which it divides the hypotenuse. PROP. XIX. THEOREM. Triangles, having an angle in the one equal to an angle in the other, are to each other as the rectangle of the sides which contain the equal angle. Let the triangles ABC, CDE,have the equal angle...
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Elementary and Practical Arithmetic: On the Inductive System, by Analysis ...

Charles Waterhouse - Arithmetic - 1844 - 232 pages
...double the diameter of the circumscribed circle. 10. Two triangles, which have an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides, which contain the equal angles. 11. Two similar triangles are to each other...
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...with (148).] Of PROPOSITION III. Two triangles, having an angle of the one equal to an (159) angle of the other, are to each other as the products of the sides about the equal angles. Let the equal apgles of the triangles A, B, be made vertical, and join the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...diameter; that is, AD'=BDxDC. PROPOSITION XXIII. THEOREM. Two triangles, having an angle in the one equal to an angle in the other, are to each other as the rectangles of the sides which contain the equal angles. Let the two triangles ABC, ADE have the angle...
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