The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 34
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines ...
... parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines ...
Side 42
... parallels . Let the equal triangles ABC , DBC be on the same base BC , and on the same side of it : they shall be be- tween the same parallels . Join AD . AD shall be parallel to BC . For if it is not , through A draw AE parallel to BC ...
... parallels . Let the equal triangles ABC , DBC be on the same base BC , and on the same side of it : they shall be be- tween the same parallels . Join AD . AD shall be parallel to BC . For if it is not , through A draw AE parallel to BC ...
Side 231
... parallel to CD . Wherefore , if two straight lines & c . Q.E.D. [ XI . 6 . PROPOSITION 10 . THEOREM . If two straight lines meeting one another be parallel to two others that meet one another , and are not in the same plane with the ...
... parallel to CD . Wherefore , if two straight lines & c . Q.E.D. [ XI . 6 . PROPOSITION 10 . THEOREM . If two straight lines meeting one another be parallel to two others that meet one another , and are not in the same plane with the ...
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ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC bisected centre circle ABC circumference Constr Construction Corollary Definition 15 demonstration diameter double draw equal angles equal to F equiangular equimultiples Euclid Euclid's Elements exterior angle fourth given circle given straight line gnomon greater ratio greater than F Hypothesis less Let ABC Let the straight meet multiple opposite angle parallel to BC parallelogram perpendicular polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION rectangle contained remaining angle right angles segment shewn sides similar and similarly Simson square described square on AC straight line &c straight line AB THEOREM tiples touches the circle triangle ABC triangle DEF twice the rectangle Wherefore