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
... point where they cut , are together equal to four right angles . COR . 2. - And consequently that all the angles made by any number of lines meeting in one point ... F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE ...
... point where they cut , are together equal to four right angles . COR . 2. - And consequently that all the angles made by any number of lines meeting in one point ... F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE ...
Σελίδα 23
... point F is the centre of the circle DKL , ( Def . 15. ) 1. FD is equal to FK ; but FD is equal to the straight line 4 ; therefore 2 . FK is equal to A. Again , because G is the centre of the circle BOOK I. PROP . XXI . XXII . 23.
... point F is the centre of the circle DKL , ( Def . 15. ) 1. FD is equal to FK ; but FD is equal to the straight line 4 ; therefore 2 . FK is equal to A. Again , because G is the centre of the circle BOOK I. PROP . XXI . XXII . 23.
Σελίδα 31
... point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD , which meets the two straight lines BC , EF ...
... point 4 , in the straight line AD , make ( I. 23. ) the angle DAE equal to the angle ADC ; and produce the straight line EA to F ; EF is parallel to BC . E F B D Because the straight line AD , which meets the two straight lines BC , EF ...
Σελίδα 32
... point F within the figure to each of its angles . And by the preceding proposition , all the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there are sides of the figure ; and the ...
... point F within the figure to each of its angles . And by the preceding proposition , all the angles of these triangles are equal to twice as many right angles as there are triangles , that is , as there are sides of the figure ; and the ...
Σελίδα 37
... points G , H , and through B draw BG parallel ( I. 31. ) to CA , and through F draw FH parallel to ED . Then ( I. 34. Def . ) 1 . and ( I. 36. ) Each of the figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one ...
... points G , H , and through B draw BG parallel ( I. 31. ) to CA , and through F draw FH parallel to ED . Then ( I. 34. Def . ) 1 . and ( I. 36. ) Each of the figures GBCA , DEFH , is a parallelogram ; 2. GBCA , DEFH , are equal to one ...
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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