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 12
... angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2. The angle ADC is greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB ...
... angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2. The angle ADC is greater than BCD ; much more then 3. The angle BDC is greater than the angle BCD . Again , because CB ...
Σελίδα 13
... equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line BC upon EF ; 1 . The point C shall coincide with the point F ...
... equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line BC upon EF ; 1 . The point C shall coincide with the point F ...
Σελίδα 14
... angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be ...
... angle DAF is equal to the angle EAF ; 4. The angle BAC is bisected by the straight line AF . Which was to be done . PROP . X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be ...
Σελίδα 15
... equal to the two EC , CF , each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) 3 . The base DF is equal to the base EF ; The angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one ...
... equal to the two EC , CF , each to each ; and ( Constr . ) 2 . therefore ( I. 8. ) 3 . The base DF is equal to the base EF ; The angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one ...
Σελίδα 16
... angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ...
... angle CHG ; and they are adjacent angles ; but when a straight line standing on another straight line makes the adjacent angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ...
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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