The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 74
... fall without the circle . In the same manner it may be shewn that it does not fall on the circumference . Therefore it falls within the circle . Wherefore , if any two points & c . Q.E.D. PROPOSITION 3. THEOREM . If a straight line ...
... fall without the circle . In the same manner it may be shewn that it does not fall on the circumference . Therefore it falls within the circle . Wherefore , if any two points & c . Q.E.D. PROPOSITION 3. THEOREM . If a straight line ...
Side 89
... fall within the circle . And in the same manner it may be shewn that it does not fall on the circumference . Therefore it must fall without the circle , as AE . Also between the straight line AE and the circumfer- ence , no straight ...
... fall within the circle . And in the same manner it may be shewn that it does not fall on the circumference . Therefore it must fall without the circle , as AE . Also between the straight line AE and the circumfer- ence , no straight ...
Side 260
... fall on EG , or above EG , or below EG . It may be objected that even if Simson's condition be added , it ought to be shewn that F will fall below EG . Simson accordingly says " ... it is very easy to perceive , that DG being equal to ...
... fall on EG , or above EG , or below EG . It may be objected that even if Simson's condition be added , it ought to be shewn that F will fall below EG . Simson accordingly says " ... it is very easy to perceive , that DG being equal to ...
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Vanlige uttrykk og setninger
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