 | George Albert Wentworth - 1879 - 196 σελίδες
...PAGE 217. Ex. i. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. Let A ABC and CDE have AACB and DCE supplements of each other.... | |
 | William Frothingham Bradbury - 1880 - 260 σελίδες
...the other, and the faces including these angles are respectively similar. 112. Two tetraedrons having a triedral angle of the one equal to a triedral angle...the other are to each other as the products of the edges of the equal triedral angles. (70 ; II. 116, 55.) 113i State and prove the converse of Theorem... | |
 | George Albert Wentworth - 1881 - 266 σελίδες
...value. Ex. 1. Show that two triangles which have an angle of the one equal to the supplement of the angle of the other are to each other as the products of the sides including the supplementary angles. 2. Show, geometrically, that the square described upon the... | |
 | Evan Wilhelm Evans - 1884 - 242 σελίδες
...equal altitudes (?). These volumes are V and V'(?). Therefore, (3) V : V = EAO : EAJ (?). Complete. 12. Two tetraedrons, which have a triedral angle of the...other as the products of the three edges of the equal diedrals. A-BCDandA'-BC'D' A are the tetraedrons having a common triedral, B. Prove that they are to... | |
 | Evan Wilhelm Evans - 1884 - 170 σελίδες
...CAO. ANC = CBA + BAN. Complete the proof. 24. 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 in- B eluding the equal angles. See Theo. VII. BAC : BAF = BC : BF(?). BAF : BEF = BA : BE (?).... | |
 | Webster Wells - 1886 - 392 σελίδες
...equivalent bases are equivalent. PROPOSITION XXI. THEOREM. 569. Two tetraedrons having a triedral angle of one equal to a triedral angle of the other, are to each other as the products of the edges including the equal triedral angles - the triangles AUU and AKU have for their common MS 'ie,... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 336 σελίδες
...perpendicular from the sides of the base, and these distances have a constant sum. (v. V., Exercise 16.) 4. Two tetraedrons which have a triedral angle of the...products of the three edges of the equal triedral angles. (v. IV., 19, Exercise.) n Suggestion. The intersections of the planes with the base are medial lines... | |
 | William Chauvenet, William Elwood Byerly - 1887 - 331 σελίδες
...and we have ABC A' B' C' 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... | |
 | William Chauvenet - 1888 - 826 σελίδες
...the polyedron, and whose common vertex will be the point taken within it. PROPOSITION XX.— THEOREM. 57. Two tetraedrons which have a triedral angle 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 in coincidence at... | |
 | Trinity College (Hartford, Conn.) - 1888 - 978 σελίδες
...other. 3. 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. 4. A sphere may be inscribed in any given tetrahedron. 5. In two polar spherical... | |
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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. 
