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 16
... join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . C E II G B D Join CF , CG ; and because FH is equal to HG , and HC common to the two triangles FHC , GHC , 1 . The two ...
... join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line AB . C E II G B D Join CF , CG ; and because FH is equal to HG , and HC common to the two triangles FHC , GHC , 1 . The two ...
Página 19
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; 1 . and ( I. 15. ) 2 . AE , EB , are equal to CE , EF , each to each ; The angle AEB is equal to the ...
... join BE and produce it to F , and make EF equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; 1 . and ( I. 15. ) 2 . AE , EB , are equal to CE , EF , each to each ; The angle AEB is equal to the ...
Página 20
... . 3. ) AD equal to AB , and join BD ; and because ADB is the exterior angle of the triangle BDC , ( I. 16. ) 1. ADB is greater than the interior and opposite angle ᎠᏟᏴ ; but ( I. 5. ) 2. ADB is equal to 20 EUCLID'S ELEMENTS .
... . 3. ) AD equal to AB , and join BD ; and because ADB is the exterior angle of the triangle BDC , ( I. 16. ) 1. ADB is greater than the interior and opposite angle ᎠᏟᏴ ; but ( I. 5. ) 2. ADB is equal to 20 EUCLID'S ELEMENTS .
Página 22
... join DC . Because DA is equal to AC , likewise ( I. 5. ) 1 . The angle ADC is equal to ACD ; but the angle BCD is greater than the angle ACD ; therefore 2 . The angle BCD is greater than the angle ADC ; and because the angle BCD of the ...
... join DC . Because DA is equal to AC , likewise ( I. 5. ) 1 . The angle ADC is equal to ACD ; but the angle BCD is greater than the angle ACD ; therefore 2 . The angle BCD is greater than the angle ADC ; and because the angle BCD of the ...
Página 23
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines A , B , C. K D G H LA B C Because the 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 ...
... join KF , KG ; the triangle KFG has its sides equal to the three straight lines A , B , C. K D G H LA B C Because the 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 ...
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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