The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 26
... meet together if continually produ- ced ; therefore the straight lines AB , CD , if produced far enough , will meet : but they never meet , since they are parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle ...
... meet together if continually produ- ced ; therefore the straight lines AB , CD , if produced far enough , will meet : but they never meet , since they are parallel by the hypothesis ; therefore the angle AGH is not unequal to the angle ...
Page 27
... meets the two straight lines BC , EF , makes the alternate angles EAD , ADC equal to one another , EF is parallel to BC . * 27.1 . Therefore the straight line EAF is drawn through the given point A , parallel to the given straight line ...
... meets the two straight lines BC , EF , makes the alternate angles EAD , ADC equal to one another , EF is parallel to BC . * 27.1 . Therefore the straight line EAF is drawn through the given point A , parallel to the given straight line ...
Page 28
... meets them , the alternate angles BAC , ACE are equal * . Again , because AB is parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC : but the angle ACE was shewn to be equal ...
... meets them , the alternate angles BAC , ACE are equal * . Again , because AB is parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC : but the angle ACE was shewn to be equal ...
Page 29
... meets them , the alternate angles * ABC , BCD are 29.1 . equal : and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC , are equal to the two DC , CB , each to each : and the angle ABC ...
... meets them , the alternate angles * ABC , BCD are 29.1 . equal : and because AB is equal to CD , and BC com- mon to the two triangles ABC , DCB , the two sides AB , BC , are equal to the two DC , CB , each to each : and the angle ABC ...
Page 30
... meets them , the alternate angles ABC , BCD , are equal to one another : and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD , are equal to one another : where- fore the two triangles ABC , CBD have two ...
... meets them , the alternate angles ABC , BCD , are equal to one another : and because AC is parallel to BD , and BC meets them , the alternate angles ACB , CBD , are equal to one another : where- fore the two triangles ABC , CBD have two ...
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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