 | George Clinton Whitlock - 1848 - 340 lapas
...(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 lapas
...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 lapas
...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 lapas
...THEOREM. , -•. ,." 57. Two tetraedrons which have a triedral angle of the 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 their equal triedral angles... | |
 | William Chauvenet - 1871 - 380 lapas
...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... | |
 | William Chauvenet - 1872 - 382 lapas
...PROPOSITION XX.—THEOREM. 57. Two tetraedrons which have a triedral angle of the 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 AB CD, AB'C'D', be the given tetraedrons, placed with their equal triedral angles... | |
 | William Chauvenet - 1872 - 382 lapas
...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 lapas
...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 lapas
...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... | |
 | George Albert Wentworth - 1877 - 416 lapas
...as the products of their bases and altitudes. PROPOSITION XIX. THEOREM. 677. Two tetrahedrons having a trihedral angle of the one equal to a trihedral...to each other as the products of the three edges of these trihedral angles. Let V and V denote the volumes of the two tetrahedrons D-ABС, jy-AB'C1, having... | |
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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. 
