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
... produced to any length both ways , and let C be a point without it . It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD ...
... produced to any length both ways , and let C be a point without it . It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the other side of AB , and from the centre C , at the distance CD ...
Página 19
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA ...
... produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA ...
Página 20
... 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 ; therefore 2. The angles ACD , ACB , are greater ...
... 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 ; therefore 2. The angles ACD , ACB , are greater ...
Página 21
... third side , viz . the sides BA , AC , greater than the side BC ; and AB , BC , greater than ɅC ; and BC , CA , greater than AB . B Produce BA to the point D , and make ( BOOK I. - PROP . XIX . XX . 21 PROP. XIX.-THEOREM. ...
... third side , viz . the sides BA , AC , greater than the side BC ; and AB , BC , greater than ɅC ; and BC , CA , greater than AB . B Produce BA to the point D , and make ( BOOK I. - PROP . XIX . XX . 21 PROP. XIX.-THEOREM. ...
Página 22
... Produce BD to E ; and because two sides of a triangle are greater than the third side ( I. 20. ) 1. The two sides BA , AE , of the triangle ABE , are greater than BE ; to each of these add EC ; therefore 2. The sides BA , AC , are ...
... Produce BD to E ; and because two sides of a triangle are greater than the third side ( I. 20. ) 1. The two sides BA , AE , of the triangle ABE , are greater than BE ; to each of these add EC ; therefore 2. The sides BA , AC , are ...
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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