The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Resultat 1-3 av 15
Side 259
... demonstrated directly and which indirectly , it may be observed that the order is similar to that in I. 5 and I. 6 . I. 20. " " Proclus , in his commentary , relates , that the Epi- cureans derided Prop . 20 , as being manifest even to ...
... demonstrated directly and which indirectly , it may be observed that the order is similar to that in I. 5 and I. 6 . I. 20. " " Proclus , in his commentary , relates , that the Epi- cureans derided Prop . 20 , as being manifest even to ...
Side 273
... demonstrated in the manner of III . 7 , and they should be demonstrated , for the third part is really required , as we shall see in the note on III . 10 . III . 9. The point E might be supposed to fall within the angle ADC . It cannot ...
... demonstrated in the manner of III . 7 , and they should be demonstrated , for the third part is really required , as we shall see in the note on III . 10 . III . 9. The point E might be supposed to fall within the angle ADC . It cannot ...
Side 277
... demonstrated indirectly . For , if possible , sup- pose that the straight line which meets the circle does not touch it . Draw through the point of meeting a straight line to touch the circle . Then , by III . 32 and the hypothesis , it ...
... demonstrated indirectly . For , if possible , sup- pose that the straight line which meets the circle does not touch it . Draw through the point of meeting a straight line to touch the circle . Then , by III . 32 and the hypothesis , it ...
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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