The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 5
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II ...
... Parallel straight lines , are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight line may be drawn from any one point to any other point . II ...
Page 24
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . 1 For , if it be not parallel , AB and CD being pro- * duced ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another : AB shall be parallel to CD . 1 For , if it be not parallel , AB and CD being pro- * duced ...
Page 25
... parallel to one an- * 35 Def . other ; therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines make the exterior angle equal to ...
... parallel to one an- * 35 Def . other ; therefore AB is parallel to CD . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVIII . THEOR . If a straight line falling upon two other straight lines make the exterior angle equal to ...
Page 26
... parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two ...
... parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two ...
Page 27
... parallel straight lines AB , EF , the angle AGH is equal to the angle GHF . Again , Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle E- GHF is equal to the angle GKD : and it was shewn that the ...
... parallel straight lines AB , EF , the angle AGH is equal to the angle GHF . Again , Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle E- GHF is equal to the angle GKD : and it was shewn that the ...
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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