Elementary Geometry ... |
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Página 22
James Maurice Wilson. angle A to the angle D , and the area ABC to the area DEF . Q. E. D. THEOREM 8 . If the angles ... exterior angle will be greater than either of the interior and opposite angles . Part . En . Let ABC be a triangle ...
James Maurice Wilson. angle A to the angle D , and the area ABC to the area DEF . Q. E. D. THEOREM 8 . If the angles ... exterior angle will be greater than either of the interior and opposite angles . Part . En . Let ABC be a triangle ...
Página 23
... exterior angle ACD is greater than either CAB or ABC * . Q. E. D. THEOREM IO . The greater side of every triangle has the greater angle opposite to it . * Euclid , 1. 16 . Part . En . Let ABC be a triangle having SECT . II . ] 23 TRIANGLES ...
... exterior angle ACD is greater than either CAB or ABC * . Q. E. D. THEOREM IO . The greater side of every triangle has the greater angle opposite to it . * Euclid , 1. 16 . Part . En . Let ABC be a triangle having SECT . II . ] 23 TRIANGLES ...
Página 24
... angle ABC is greater than the angle ACB . Proof . From AC cut off AD = AB ; and join DB . Because AD = AB ; therefore the angle ABD = the angle ADB . ( Constr . ) ( Th . 6. ) But because ADB is the exterior angle of the triangle BDC ...
... angle ABC is greater than the angle ACB . Proof . From AC cut off AD = AB ; and join DB . Because AD = AB ; therefore the angle ABD = the angle ADB . ( Constr . ) ( Th . 6. ) But because ADB is the exterior angle of the triangle BDC ...
Página 26
... angle . Part . En . Let ACB be a triangle , and from the ends of the side AB let two straight lines AP , BP be drawn ... exterior angle of the tri- angle PQB : therefore the angle APB is greater than the angle PQB ; ( Th . 9. ) and ...
... angle . Part . En . Let ACB be a triangle , and from the ends of the side AB let two straight lines AP , BP be drawn ... exterior angle of the tri- angle PQB : therefore the angle APB is greater than the angle PQB ; ( Th . 9. ) and ...
Página 31
... angle EFD , the exterior angle equal to the interior and opposite , which is impossible ; ( Th . 9. ) therefore the triangles would coincide and are equal in all respects , AC being equal to DF , BC to EF , and the angle BAC to the angle ...
... angle EFD , the exterior angle equal to the interior and opposite , which is impossible ; ( Th . 9. ) therefore the triangles would coincide and are equal in all respects , AC being equal to DF , BC to EF , and the angle BAC to the angle ...
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Términos y frases comunes
AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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