The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 31
... meet to- wards B , D. In the same manner , it may be shown that they do not meet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore ...
... meet to- wards B , D. In the same manner , it may be shown that they do not meet towards A , C. But those straight lines which being produced ever so far both ways do not meet , are parallel . Therefore AB is parallel to CD . Wherefore ...
Side 33
... meet on that side on which are the angles which are less than two right angles . [ Axiom 12 . Therefore the straight lines AB , CD , if continually pro- duced , will meet . But they never meet , since they are parallel by hypothesis ...
... meet on that side on which are the angles which are less than two right angles . [ Axiom 12 . Therefore the straight lines AB , CD , if continually pro- duced , will meet . But they never meet , since they are parallel by hypothesis ...
Side 278
... meet will be the centre of the required circle . The demonstration will be similar to that in IV . 4 . A circle which touches one side of a triangle and the other two sides produced , is called an escribed circle of the triangle . 3 We ...
... meet will be the centre of the required circle . The demonstration will be similar to that in IV . 4 . A circle which touches one side of a triangle and the other two sides produced , is called an escribed circle of the triangle . 3 We ...
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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