The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 13
... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is re- quired to bisect it . Take any point D in AB , and from AC cut off AE * 3. 1 . equal to AD ; join DE , and upon ...
... given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle ; it is re- quired to bisect it . Take any point D in AB , and from AC cut off AE * 3. 1 . equal to AD ; join DE , and upon ...
Page 14
... given point C , shall be at right angles to the given straight line AB . * A D ER Because DC is equal † to CE , and ... angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one straight ...
... given point C , shall be at right angles to the given straight line AB . * A D ER Because DC is equal † to CE , and ... angle DCF is equal to the angle ECF ; and they are adjacent angles . But when the adjacent angles which one straight ...
Page 15
... given point C , shall be perpendicular to the given straight line AB . * * * Join CF , CG : and because FH is equal ... angle CHF is equal to the angle 8. 1 . CHG ; and they are adjacent angles : but when a straight line , standing on ...
... given point C , shall be perpendicular to the given straight line AB . * * * Join CF , CG : and because FH is equal ... angle CHF is equal to the angle 8. 1 . CHG ; and they are adjacent angles : but when a straight line , standing on ...
Page 21
... given straight lines A , B , C. Which was to be done . PROP . XXIII . PROB . At a given point in a given straight line , to make a recti- lineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given ...
... given straight lines A , B , C. Which was to be done . PROP . XXIII . PROB . At a given point in a given straight line , to make a recti- lineal angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given ...
Page 27
... angles ; therefore AB is parallel to . CD . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB . To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given ...
... angles ; therefore AB is parallel to . CD . Wherefore , straight lines , & c . Q. E. D. PROP . XXXI . PROB . To draw a straight line through a given point parallel to a given straight line . Let A be the given point , and BC the given ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore