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 σελίδες |
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Σελίδα 7
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from ...
... triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equi- lateral triangle upon it . From the centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from ...
Σελίδα 8
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP ... triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles ...
... given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . PROP ... triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles ...
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c . Q.E.D. PROP . IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
... angle BAC coincides with the angle EDF , and is equal ( Ax . 8. ) to it . Therefore if two triangles , & c . Q.E.D. PROP . IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the ...
Σελίδα 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 ...
Σελίδα 15
... triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr . ) 2 ... given point C , in the given straight line AB , 5. FC has been drawn at right angles to AB . Which was to be done ...
... triangles DCF , ECF ; 1 . The two sides DC , CF , are equal to the two EC , CF , each to each ; and ( Constr . ) 2 ... given point C , in the given straight line AB , 5. FC has been drawn at right angles to AB . Which was to be done ...
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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