The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry, from the Edition of Dr. Robert Simson ... With ExercisesCharles Henry Law, 1854 - 120 páginas |
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Página 12
... greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB is equal to DB , ( I. 5. ) 4. The angle BDC is equal to the angle BCD ; but it has been demonstrated to be greater than it , which is ...
... greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB is equal to DB , ( I. 5. ) 4. The angle BDC is equal to the angle BCD ; but it has been demonstrated to be greater than it , which is ...
Página 15
... . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Two straight lines cannot have a common segment . PROP . XII . - PROBLEM . To draw a BOOK I. - PROP . XI . 15.
... . 1. ) 3. The angle DBE is equal to the angle CBE , the less to the greater , which is impossible ; therefore 4 . Two straight lines cannot have a common segment . PROP . XII . - PROBLEM . To draw a BOOK I. - PROP . XI . 15.
Página 18
... greater , which is impossible ; therefore 4. BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the same straight ...
... greater , which is impossible ; therefore 4. BE is not in the same straight line with BC . And in like manner it may be demonstrated that no other can be in the same straight line with it but BD , therefore 5. BD is in the same straight ...
Página 19
... greater than either of the interior opposite angles CBA , BAČ . B F E Bisect ( I. 10. ) AC in E , join BE and ... greater than the angle ECF ; therefore 5 . The angle ACD is greater than BAE . In the same manner , if the side BC be ...
... greater than either of the interior opposite angles CBA , BAČ . B F E Bisect ( I. 10. ) AC in E , join BE and ... greater than the angle ECF ; therefore 5 . The angle ACD is greater than BAE . In the same manner , if the side BC be ...
Página 20
... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC ' is also greater than the angle BCA . B Because AC is greater than AB , make ( I ...
... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC ' is also greater than the angle BCA . B Because AC is greater than AB , make ( I ...
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Términos y frases comunes
AB is equal AC is equal adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal base BC bisected circle ABC circumference diameter double draw equal angles equal Constr equal Hyp equal straight lines equal to BC equilateral and equiangular EUCLID'S ELEMENTS exterior angle given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite less Let ABC Let the straight likewise opposite angles parallel to CD parallelogram pentagon perpendicular point F produced Q.E.D. PROP rectangle AE rectangle contained remaining angle required to describe right angles semicircle side BC square of AC straight line AB straight line AC straight line drawn touches the circle triangle ABC twice the rectangle