 | George Clinton Whitlock - 1848 - 340 σελίδες
...(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 - 1868 - 172 σελίδες
...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 σελίδες
...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 - 1872 - 382 σελίδες
...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 - 1872 - 382 σελίδες
...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 σελίδες
...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 - 1875 - 390 σελίδες
...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 - 1875 - 466 σελίδες
...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 σελίδες
...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 - 1877 - 262 σελίδες
...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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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. 
