 Assuming that 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 - Page 309by George Washington Hull - 1897 - 398 pagesFull view - About this book
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...GEOMETRY. 159. THEOREM. Two triangular pyramids having a triedral angle of the one equal to a triedral angle of the other, are to each other as the products of the edges including the equal triedral angles. C' Place the equal triedral angles in coincidence at 0. CP and CT' perpendicular to... | |
 | Examinations - 1893 - 408 pages
...intercepted arc. 1 2 5 Prove that 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. 16 6 Prove that the area of a regular polygon is equal to half the... | |
 | William Chauvenet - 1893 - 340 pages
...(v. V., Exercise 16.) 4. 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, (v. IV., 19, Exercise.) Suggestion. The intersections of... | |
 | Webster Wells - Geometry - 1894 - 400 pages
...altitudes. PROPOSITION XX. THEOREM. 531. Two tetraedrons having a triedral of one equal to a triedral of the other, are to each other as the products of the edges Including the equal triedrals. OA' x OB' X OC'' Draw CP and C'P' perpendicular to the face OA'B'. Let their plane intersect... | |
 | Electronic journals - 1917 - 528 pages
...a# their bases. THEOREM 4. Pentahedroids which have a hyperspace angle of one equal to a hyperspace angle of the other are to each other as the products of the edges of 1he equal hyperspace angles. From theorems 3 and 4 we get at once, THEOREM 5. Similar pentaJiedroids... | |
 | George Albert Wentworth, George Anthony Hill - Geometry - 1894 - 150 pages
...third side from the vertex of the opposite angle. 7. Two triangles having an angle of one equal to an angle of the other, are to each other as the products of the sides including the equal angles. MASSACHUSETTS INSTITUTE OF TECHNOLOGY, September, 1891. 1. The perpendicular... | |
 | John Macnie - Geometry - 1895 - 390 pages
...proportionals between them. 285 PROPOSITION XVII. THEOREM. 561. Tetrahedrons with a trihedral angle of the one equal to a trihedral angle of the other, are to each other as the products of the edges of these trihedral angles. Given : V and F*, the volumes of two tetrahedrons having trihedral angle... | |
 | George Albert Wentworth - Mathematics - 1896 - 68 pages
...equal altitudes are equivalent. 607. The volumes of 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. 608. The frustum of a triangular pyramid is equivalent to the... | |
 | Joe Garner Estill - Geometry - 1896 - 168 pages
...perpendicular to A C. 4. Assuming that 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, prove that the bisector of an angle of a triangle divides the opposite... | |
 | Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 570 pages
...method. PROPOSITION VIII. THEOREM 308. The areas of two triangles which have an angle of one equal to an angle of the other are to each other as the products of the sides including those angles. GIVEN — the triangles ADR and ABC placed so that their equal an- •... | |
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