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 19
... BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining ...
... BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAČ ... base AB is equal to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining ...
Página 25
... BC is also greater than the base EF . A D E G F B Of the two sides DE , DF , let DE be the side which is not greater ... base BC is equal to the base EG . And because DG is equal to DF , ( 1 , 5. ) 2 . The angle DFG is equal to the angle ...
... BC is also greater than the base EF . A D E G F B Of the two sides DE , DF , let DE be the side which is not greater ... base BC is equal to the base EG . And because DG is equal to DF , ( 1 , 5. ) 2 . The angle DFG is equal to the angle ...
Página 26
... base BC would be equal ( I. 4. ) to EF ; but it is not , therefore 1. The angle BAC is not equal to the angle EDF . Neither is it less ; because then the base BC would be less ( I. 24. ) than the base EF ; but it is not , therefore 2 ...
... base BC would be equal ( I. 4. ) to EF ; but it is not , therefore 1. The angle BAC is not equal to the angle EDF . Neither is it less ; because then the base BC would be less ( I. 24. ) than the base EF ; but it is not , therefore 2 ...
Página 27
... BC , are equal to the two DE , EF , each 6 . to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Next , let the ...
... BC , are equal to the two DE , EF , each 6 . to each ; and the angle ABC is equal ( Hyp . ) to the angle DEF ; therefore ( I. 4. ) 7. The base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Next , let the ...
Página 33
... BC ; and because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC , BCD , are equal ... base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
... BC ; and because AB is parallel to CD , and BC meets them , ( I. 29. ) 1. The alternate angles ABC , BCD , are equal ... base AC is equal to the base BD , and the triangle ABC to the triangle BCD , and the other angles to the other ...
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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