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 9
... angle DEF , and the angle ACB to DFE . A D B E For if the triangle ABC be applied to DEF , so that the point △ may be on D , and the straight line AB upon DE ; 1 . The point B shall coincide with the point E , because AB is equal to DE ...
... angle DEF , and the angle ACB to DFE . A D B E For if the triangle ABC be applied to DEF , so that the point △ may be on D , and the straight line AB upon DE ; 1 . The point B shall coincide with the point E , because AB is equal to DE ...
Página 10
... angle ACB , and the angle CBD to the angle BCE . A B F G E D In BD take any point F , and from AE , the greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and AB ...
... angle ACB , and the angle CBD to the angle BCE . A B F G E D In BD take any point F , and from AE , the greater , cut off AG equal ( I. 3. ) to AF , the less , and join FC , GB . Because AF is equal ( Constr . ) to 4G , and AB ...
Página 11
... angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . Ꭰ B C For if AB be not equal to AC , one of them is greater than the other . Let AB ...
... angles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB is also equal to the side AC . Ꭰ B C For if AB be not equal to AC , one of them is greater than the other . Let AB ...
Página 12
... angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2 ... ACB ; produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles upon the ...
... angle ACD is equal to the angle ADC . But the angle ACD is greater than the angle BCD ( Ax . 9. ) ; therefore also 2 ... ACB ; produce AC , AD to E , F ; therefore because AC is equal to AD in the triangle ACD , ( I. 5. ) the angles upon the ...
Página 20
... angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these add the angle ACB ...
... angles together are less than two right angles . A B Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ( I. 16. ) 1. ACD is greater than the interior and opposite angle ABC ; to each of these add the angle ACB ...
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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