| 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 - 1871 - 380 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... | |
| William Chauvenet - Geometry - 1872 - 382 pages
...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... | |
| 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... | |
| 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... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...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...the other are 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,... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...GEOMETRY. — BOOK VII. PROPOSITION XIX. THEOREM. 577. Two tetrahedrons having a trihedral angle ofth **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 vol-аmes of the two tetrahedrons D ABC,... | |
| George Albert Wentworth - Geometry - 1877 - 416 pages
...VII. PROPOSITION XIX. THEOREM. 577. Tioo tetrahedrons having a trihedral angle of the one equal io **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 of the two tetrahedrons DA BC,... | |
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