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 σελίδες |
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Σελίδα 19
... angles . COR . 2. - And consequently that all the angles made by any number of lines meeting in one point are together equal to four right angles . PROP . XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is ...
... angles . COR . 2. - And consequently that all the angles made by any number of lines meeting in one point are together equal to four right angles . PROP . XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is ...
Σελίδα 20
... angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these add the angle ...
... angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these add the angle ...
Σελίδα 23
... exterior angle of a triangle is greater than the inte- rior and opposite angle ( I. 16. ) 1 . than CED . The exterior angle BDC of the triangle CDE is greater For the same reason , 2 . The exterior angle CEB of the triangle ABE is ...
... exterior angle of a triangle is greater than the inte- rior and opposite angle ( I. 16. ) 1 . than CED . The exterior angle BDC of the triangle CDE is greater For the same reason , 2 . The exterior angle CEB of the triangle ABE is ...
Σελίδα 27
... angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ...
... angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the ... exterior angle BHA of the triangle AHC is equal to its interior and opposite angle BCA , which is impossible ...
Σελίδα 28
... exterior angle AEF is greater ( I. 16. ) than the interior and opposite angle EFG ; but it is also equal to it , which is impossible ; therefore 2 . AB and CD being produced do not meet towards B , D. In like manner it may be ...
... exterior angle AEF is greater ( I. 16. ) than the interior and opposite angle EFG ; but it is also equal to it , which is impossible ; therefore 2 . AB and CD being produced do not meet towards B , D. In like manner it may be ...
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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