The Elements of Euclid |
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Page 13
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . Book I. POSTULATES . I : Let it be granted that a straight line may be drawn from any one point to any other ...
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . Book I. POSTULATES . I : Let it be granted that a straight line may be drawn from any one point to any other ...
Page 34
... parallel . Let the straight line EF , which falls upon the two straight Fines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . 1 . E B pro- For , if it be not parallel , AB and CD being produced ...
... parallel . Let the straight line EF , which falls upon the two straight Fines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . 1 . E B pro- For , if it be not parallel , AB and CD being produced ...
Page 35
... parallel to CD . Wherefore , if a straight line , & c . Q , ED . PROP . XXIX . THEOR . 11 d 13. 1 . notes on this IF a straight line fall upon two parallel straight See the lines , it makes the alternate angles equal to one ano ...
... parallel to CD . Wherefore , if a straight line , & c . Q , ED . PROP . XXIX . THEOR . 11 d 13. 1 . notes on this IF a straight line fall upon two parallel straight See the lines , it makes the alternate angles equal to one ano ...
Page 36
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF ; AB is also parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight a lines ...
... parallel to the same straight line are parallel to one another . Let AB , CD , be each of them parallel to EF ; AB is also parallel to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the parallel straight a lines ...
Page 37
... parallel to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the alternate angles BAC , ACE are equalb . Again ; because AB is parallel to CE , and BD falls upon them , the ex- terior angle ECD is equal to ...
... parallel to the straight line AB ; and be- cause AB is parallel to CE and AC meets them , the alternate angles BAC , ACE are equalb . Again ; because AB is parallel to CE , and BD falls upon them , the ex- terior angle ECD is equal to ...
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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