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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... "
The Elements of Solid Geometry - Page 48
by William C. Bartol - 1893 - 95 pages
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - Mathematics - 1848 - 340 pages
...(147) 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...
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Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 174 pages
...A'B'C'. Relation of Areas of Figures. THEOREM VI. Triangles which have one angle of the one equal to one angle of the other, are to each other as the products of the sides containing the equal angle. Let the triangles ABC, A'BC' have equal angles at B. Then shall ABC...
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Catalogue of the Officers and Students

Trinity College (Hartford, Conn.) - 1870 - 1010 pages
...similar when they are mutually equiangular. 4. Two triangles having 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. 5. What is the length of the side of a regular decagon inscribed...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1871 - 380 pages
...vertex will be the point taken within it. PROPOSITION XX.— THEOREM. 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle...the other, are to each other as the products of the three edges of the equal triedral angles. Let ABCD, AB'C'D', be the given tetraedrons, placed with...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...vertex will be the point taken within, it. PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of the one equal to a triedral angle...the other, are to each other as the products of the three edges of the equal triedral angles. Let AB CD, AB'C'D', be the given tetraedrons, placed with...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1872 - 382 pages
...BOOK IV. THEOREMS. 219. Two triangles which have an angle of the one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles. (IV. 22. ) 220. Prove, geometrically, that the square described...
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Mensuration of lines, surfaces, and volumes

David Munn - 1873 - 160 pages
...area of any polygon 43 EXERCISES (4) 44 VIII. 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 47 IX. The areas of similar triangles are to each other as the squares...
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Annual Statement, Volumes 11-20

1876 - 646 pages
...similar when they are mutually equiangular. 2. Two triangles having 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. 3. To inscribe A circle in a given triangle. 4. The side of a regular...
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An Elementary Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...angle of the other, and the faces including these angles are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral...other are to each other as the products of the edges of the equal triedral angles. (70 ; II. 116, 55.) 113. State and prove the converse of Theorem XXIII....
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - Geometry - 1877 - 396 pages
...taken within it. \\ PROPOSITION XX.— THEOREM. 57. Two tetraedrons which have a triedral angle of tlie one equal to a triedral angle of the other, are to each other as the products of the three edges of the equal triedral angles. Let ABCD, AB'C'D', be the given tetraedrons, placed with...
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