The Synoptical Euclid; Being the First Four Books of Euclid's Elements of Geometry from the Edition of Dr. Robert Simson ... With Exercises. By S. A. Good ... Second Edition |
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Página 7
Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the ... AC is equal to AB ; and because the point B is the centre of the circle ACE , 2 . BC is equal to BA .
Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the ... AC is equal to AB ; and because the point B is the centre of the circle ACE , 2 . BC is equal to BA .
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Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , cach to each , viz . AB to DE , and AC to ... The point C shall coincide with the point F , because the straight line AC is equal to DF .
Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , cach to each , viz . AB to DE , and AC to ... The point C shall coincide with the point F , because the straight line AC is equal to DF .
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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 . D G А F B For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line BC upon EF ; 1 .
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 . D G А F B For if the triangle ABC be applied to DEF , so that the point B be on E , and the straight line BC upon EF ; 1 .
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upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. ) C A. B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 .
upon it an equilateral triangle ABC , and bisect ( I. 9. ) the angle ACB by the straight line CD . AB is cut into two equal parts in the point D. ) C A. B Because AC is equal to CB , and CD common to the two triangles ACD , BCD ; 1 .
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The sides CE , EB , are greater than CD , DB ; but it has been shown that BA , AC , are greater than BE , EC ; much ... To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these ...
The sides CE , EB , are greater than CD , DB ; but it has been shown that BA , AC , are greater than BE , EC ; much ... To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these ...
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AB is equal ABC is equal ABCD angle ABC angle ACB angle AGH angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line gnomon greater impossible inscribed join less Let ABC Let the straight likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take touches the circle triangle ABC twice the rectangle wherefore whole