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 29
Euclid, Samuel A. GOOD. Because the angle EGB is equal to the angle GHD , and the angle EGB equal ( I. 15. ) to the angle AGH , 1 . The angle AGH is equal to the angle GHD , and they are alternate angles ; therefore ( I. 27. ) 2. AB is ...
Euclid, Samuel A. GOOD. Because the angle EGB is equal to the angle GHD , and the angle EGB equal ( I. 15. ) to the angle AGH , 1 . The angle AGH is equal to the angle GHD , and they are alternate angles ; therefore ( I. 27. ) 2. AB is ...
Σελίδα 30
... angle AGH is not unequal to the angle GHD , that is , it is equal to it ; but ( L. 15. ) the angle AGH is equal to the angle EGB ; therefore likewise 5. EGB is equal to GHD ; add to each of these the angle BGH ; therefore 6. The angles ...
... angle AGH is not unequal to the angle GHD , that is , it is equal to it ; but ( L. 15. ) the angle AGH is equal to the angle EGB ; therefore likewise 5. EGB is equal to GHD ; add to each of these the angle BGH ; therefore 6. The angles ...
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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