 | Evan Wilhelm Evans - Geometry - 1884 - 242 pages
...EAJ (?). Complete. 12. 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 diedrals. A-BCDandA'-BC'D' A are the tetraedrons having a common triedral,... | |
 | Mathematical association - 1884 - 146 pages
...two adjoining: sides of the one respectively equal to two adjoining sides of the other, and likewise an ang:le of the one equal to an angle of the other ; the parallelograms are identically equal. Let ABCD, EFGH be two parallelograms having the angle ABC... | |
 | William Kingdon Clifford - Mathematics - 1885 - 310 pages
...proposition about parallel lines.1 The first of these deductions will now show us that if two triangles have an angle of the one equal to an angle of the other and the sides containing these angles respectively equal, they must be equal in all particulars. For... | |
 | Lewis Carroll - Geometry - 1885 - 318 pages
...have two adjacent sides of the one respectively equal to two adjacent sides of the other, and likewise an angle of the one equal to an angle of the other ; the Parallelograms are identically equal.' This might be a useful exercise to set ; but really it... | |
 | Webster Wells - Geometry - 1886 - 392 pages
...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 - Geometry - 1887 - 346 pages
...the similarity of ABC and A' B'C', BC _ AB . B'C' ~ A'B' ' hence AD BC and we have ABC _ Tff_ A'B'C'~ EXERCISE. Theorem. — Two triangles having an angle...products of the sides including the equal angles. A Suggestion. Let ADE and ABC be the two triangles. Draw BE, and compare the two triangles with AEB.... | |
 | University of St. Andrews - 1903 - 762 pages
...consecutive rays are given. 4. Define reciprocally proportional, and prove thai parallelograms which have an angle of the one equal to an angle of the other and their sides about the equal angles reciprocally proportional are equal in area. TP and TQ are tangents... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...THEOBEM 397. If two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. A Given the A ABC and ADF having ZA in common/ _, A ABC ABXAC T°prOVe ~K~ADF'= ADXAF Proof. Draw the... | |
 | Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...altitudes. 397. // two triangles have an angle of one equal to an angle of the other, their areas are to each other as the products of the sides including the equal angles. 398. The areas of any two similar triangles are to each other as the squares of any two homologous... | |
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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. 
