The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 13
... base DF is equal to the base EF ; therefore + Constr . the angle DAF is equal to the angle EAF : wherefore 8.1 . the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . * PROP . X. PROB . To bisect a ...
... base DF is equal to the base EF ; therefore + Constr . the angle DAF is equal to the angle EAF : wherefore 8.1 . the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . * PROP . X. PROB . To bisect a ...
Page 21
... base DE to the base FG ; the angle DCE is equal to the angle FAG . Therefore at the * 8 . 1 . given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . * PROP ...
... base DE to the base FG ; the angle DCE is equal to the angle FAG . Therefore at the * 8 . 1 . given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . * PROP ...
Page 22
... base BC shall be greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make * the angle EDG equal to the angle BAC ; and make DG ...
... base BC shall be greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line DE , make * the angle EDG equal to the angle BAC ; and make DG ...
Page 23
... base BC would be less than the base EF ; but it is + not ; therefore the angle BAC is not less than the angle EDF : and * B D it was shewn that it is not equal to it ; therefore the an- gle BAC is greater than the angle EDF . Wherefore ...
... base BC would be less than the base EF ; but it is + not ; therefore the angle BAC is not less than the angle EDF : and * B D it was shewn that it is not equal to it ; therefore the an- gle BAC is greater than the angle EDF . Wherefore ...
Page 24
... base AC is equal to the base DF , and the third angle BAC to the third angle EDF . * B D ПС Е Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . AB to DE : likewise in this case ...
... base AC is equal to the base DF , and the third angle BAC to the third angle EDF . * B D ПС Е Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . AB to DE : likewise in this case ...
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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