The Elements of Euclid |
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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 the ...
... 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 the ...
Page 22
... 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 point C at ... angle CBE is equal to the angle 22 THE ELEMENTS.
... 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 point C at ... angle CBE is equal to the angle 22 THE ELEMENTS.
Page 23
Euclid Robert Simson. line , the angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight ... given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given straight line ...
Euclid Robert Simson. line , the angle CBE is equal to the angle EBA ; in the same manner , because ABD is a straight ... given straight line of an unlimited length , from a given ) point without it . zi Let AB be the given straight line ...
Page 30
... given straight lines A , B , C. Which was to be done . a 22. 1 . PROP . XXIII . PROB . AT a given point to a given straight line , to make a rectilineal angle equal to a given rectilineal angle . C A Let AB be the given straight line , and ...
... given straight lines A , B , C. Which was to be done . a 22. 1 . PROP . XXIII . PROB . AT a given point to a given straight line , to make a rectilineal angle equal to a given rectilineal angle . C A Let AB be the given straight line , and ...
Page 36
... angle BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal to two right ... given point pa- rallel to a given straight line . Let A be the given point , and BC the given straight line ; it is ...
... angle BGH ; therefore the angles EGB , BGH are equal to the angles BGH , GHD ; but EGB , BGH are equal to two right ... given point pa- rallel to a given straight line . Let A be the given point , and BC the given straight line ; it is ...
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Common terms and phrases
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