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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. "
Elements of Geometry: Plane and Solid - Page 283
by John Macnie - 1895 - 374 pages
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Elements of Geometry, Theoretical and Practical: Containing a Full ...

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...
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Modern Methods in Elementary Geometry

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...
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Catalogue of the Officers and Students

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

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...
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Mensuration of lines, surfaces, and volumes

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...
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Annual Statement, Volumes 11-20

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...
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Elements of Plane and Solid Geometry

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,...
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Elements of Plane and Solid Geometry

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,...
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Elements of Plane and Solid Geometry

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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