Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 22
... triangle . D A B E Because the point A is the centre of the circle BCD , AC is equal ( 11. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that C A is equal to AB ...
... triangle . D A B E Because the point A is the centre of the circle BCD , AC is equal ( 11. Definition ) to AB ; and because the point B is the centre of the circle ACE , BC is equal to AB : But it has been proved that C A is equal to AB ...
Σελίδα 23
... triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each ...
... triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which the equal sides are opposite * Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each ...
Σελίδα 24
... DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ...
... DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D , and the straight line AB upon DE ; the point B shall coincide with the point E , because AB is equal to DE ...
Σελίδα 26
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
... triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to AD in the triangle ACD , the angles ECD ... DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each , viz . AB to DE ...
Σελίδα 27
... triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC ...
... triangle ABC be applied to the triangle DEF , so that the point B be on E , and the straight line BC upon EF ; the point C shall also coincide with the point F , because BC is equal to EF : therefore BC coinciding with EF , BA and AC ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore