 | Edward Albert Bowser - Geometry - 1890 - 414 pages
...respectively, BOOK V1I.—POLTEDSONS. Proposition 2 1 . Theorem.* 637. Two tetraedrons which have a triedrul angle of the one equal to a triedral angle of the...to each other as the products of the three edges of these triedral angles. Hyp. Let S-ABC, S-DEF be the two given tetraedrons, having the common triedral... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...A'B'C'-E' = \h(R + b + 4/BT). (635) . - . V = J7>(B + b + VBb). QED Proposition 2 1 . Theorem.* 637. Two tetraedrons which have a triedral angle of the...triedral angle of the other, are to each other as th e products of the three edges of these triedral angles. C Hyp. Let S-ABC, S-DEF be the two given... | |
 | Edward Albert Bowser - Geometry - 1890 - 420 pages
...Euclid). Proposition 8. Theorem. 375. The areas of 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. Hyp. Let ABC, ADE be the two AS A having the common Z A. _, AABC... | |
 | William C. Bartol - Geometry, Solid - 1893 - 106 pages
...edges AD, BE, and CF. THE ELEMENTS OF SOLID GEOMETRY. 159. THEOREM. Two triangular pyramids having a triedral angle of the one equal to a triedral angle...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.... | |
 | 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
...have ARC _ = 'AT? A'B'O' EXERCISE. Theorem. — 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. Suggestion. Let ADE and ABC be the two triangles. Draw BE, and compare... | |
 | 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
...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... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...perpendicular to AC. 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... | |
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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. 
