The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 72
... circumference it cuts off . 7. The angle of a segment is that which is contained by the straight line and the circumference . 8. An angle in a segment is the angle contained by two straight lines drawn from any point in the ...
... circumference it cuts off . 7. The angle of a segment is that which is contained by the straight line and the circumference . 8. An angle in a segment is the angle contained by two straight lines drawn from any point in the ...
Side 79
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . For , at the point E , in the straight ...
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . For , at the point E , in the straight ...
Side 82
... circumference there fall more than two equal straight lines , namely DA , DB , DC : the point D shall be the centre of the circle . For , if not , let E be the centre ; join DE and produce it both ways to meet the circumference at F and ...
... circumference there fall more than two equal straight lines , namely DA , DB , DC : the point D shall be the centre of the circle . For , if not , let E be the centre ; join DE and produce it both ways to meet the circumference at F and ...
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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