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 3
... centre of the circle . XVII . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the ...
... centre of the circle . XVII . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the ...
Σελίδα 5
... centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same POSTULATES . 5 POSTULATES. ...
... centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same POSTULATES . 5 POSTULATES. ...
Σελίδα 7
... centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one another , draw ( Post . 1. ) the ...
... centre A , at the distance AB , describe ( Postulate 3. ) the circle BCD ; and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one another , draw ( Post . 1. ) the ...
Σελίδα 8
... centre A , and at the distance AD , describe ( Post . 3. ) the circle DEF : AE shall be equal to C. D E B Because A is the centre of the circle DEF , ( Def . 15. ) 1. AE is equal to AD ; but the straight line C is likewise equal to AD ...
... centre A , and at the distance AD , describe ( Post . 3. ) the circle DEF : AE shall be equal to C. D E B Because A is the centre of the circle DEF , ( Def . 15. ) 1. AE is equal to AD ; but the straight line C is likewise equal to AD ...
Σελίδα 16
... centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in H , and join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line ...
... centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( I. 10. ) FG in H , and join CH ; the straight line CH , drawn from the given point C , is perpendicular to the given straight line ...
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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