| 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... | |
| E. M. Reynolds - Geometry - 1868 - 172 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... | |
| Trinity College (Hartford, Conn.) - 1870 - 1008 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...the polyedron, and whose common vertex will be the point taken within, it. PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of...the three edges of the equal triedral angles. Let AB CD, AB'C'D', be the given tetraedrons, placed with their equal triedral angles in coincidence at... | |
| William Chauvenet - Mathematics - 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... | |
| 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... | |
| William Chauvenet - Geometry - 1875 - 390 pages
...bases will be the faces of the polyedron, and whose common vertex will be the point taken within it PROPOSITION XX.— THEOREM. 57. Two tetraedrons which...in coincidence at A. From D and D', let fall DO and D' O' perpendicular to the face AB C. Then, taking the faces AB C, AB'C', as the bases of the triangular... | |
| William Chauvenet - Geometry - 1875 - 466 pages
...the polyedron, and whose common vertex will be the point taken within it. PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of...in coincidence at A. From D and D', let fall DO and D' O' perpendicular to the face ABC. Then, taking the faces ABC, AB'C', as the bases of the triangular... | |
| 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... | |
| William Frothingham Bradbury - Geometry - 1877 - 262 pages
...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 angle...the 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... | |
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