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 13
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to DEF , so that the ...
... equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and also the base BC equal to the base EF . The angle BAC is equal to the angle EDF . A D G B E For if the triangle ABC be applied to DEF , so that the ...
Página 14
... equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( I. 1. ) upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two ...
... equal parts . Let AB be the given straight line ; it is required to divide it into two equal parts . Describe ( I. 1. ) upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle 4CB by the straight line CD . AB is cut into two ...
Página 15
... equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC ... ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ; and ...
... equal to CE , and FC common to the two triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC ... ABC , ABD , have the seg- ment AB common to both of them . E A B Ꭰ C From the point B draw BE at right angles to AB ; and ...
Página 17
... equal to two right angles . E D B D B Ꮹ For , if the angle CBA be equal to ABD , each of them is a right angle ... ABC ; therefore ( Ax . 2. ) 3. The angles DBA , ABC , are equal to the three angles DBE , EBA , ABC ; but the angles CBE ...
... equal to two right angles . E D B D B Ꮹ For , if the angle CBA be equal to ABD , each of them is a right angle ... ABC ; therefore ( Ax . 2. ) 3. The angles DBA , ABC , are equal to the three angles DBE , EBA , ABC ; but the angles CBE ...
Página 18
... ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the ...
... ABC , ABE , are together equal to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles ( Hyp . ) ; therefore ( Ax . 1. ) 2. The angles CBA , ABE , are equal to the angles CBA , ABD . Take away the ...
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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