 | George Clinton Whitlock - 1848 - 340 pagina’s
...(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 pagina’s
...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 pagina’s
...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 - 1871 - 380 pagina’s
...whose common vertex will be the point taken within it. ^ VV * PROPOSITION XX.— THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of...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 pyramids D-ABC, D'-AB'C', and... | |
 | William Chauvenet - 1871 - 380 pagina’s
...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 pagina’s
...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... | |
 | 1876 - 646 pagina’s
...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 pagina’s
...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... | |
 | George Albert Wentworth - 1877 - 436 pagina’s
...PROPOSITION XIX. THEOREM. 577. Two tetrahedrons having a trihedral angle of the one equal to a trihedral angle of the other are to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes oî the two tetrahedrons D-ABC, D'-AB'C', having... | |
 | George Albert Wentworth - 1877 - 416 pagina’s
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. С \j 2. Show, geometrically, that the square described upon... | |
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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. 
