The Elements of Euclid |
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Page 17
... equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to the B angle DEF , and the angle ACB to DFE . CE D Book ...
... equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC to the B angle DEF , and the angle ACB to DFE . CE D Book ...
Page 18
... equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . 1 . In BD take any point F , and from AE the ... angles of the one s are equal to the remaining an in97 % gles of the other , each to each , -to which the equal sides ...
... equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . 1 . In BD take any point F , and from AE the ... angles of the one s are equal to the remaining an in97 % gles of the other , each to each , -to which the equal sides ...
Page 19
... equal to AC , the less , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
... equal to AC , the less , and join DC ; there- fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to the ...
Page 21
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
Page 22
... angles to a given straight line , from a given point in the same . Let AB be , a given straight line , and C a point given in it : See Note . it is required to draw a straight line from the ... angle CBE is equal to the angle 22 THE ELEMENTS.
... angles to a given straight line , from a given point in the same . Let AB be , a given straight line , and C a point given in it : See Note . it is required to draw a straight line from the ... angle CBE is equal to the angle 22 THE ELEMENTS.
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore