The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Side 273
... note on III . 10 . III . 9. The point E might be supposed to fall within the angle ADC . It cannot then be shewn that DC is greater than DB , and DB greater than DA , but only that either DC or DA is less than DB ; this however is ...
... note on III . 10 . III . 9. The point E might be supposed to fall within the angle ADC . It cannot then be shewn that DC is greater than DB , and DB greater than DA , but only that either DC or DA is less than DB ; this however is ...
Side 274
... note which figure Simson himself supplied , because it is uncertain what he means by the same side " and " opposite sides . " It is the left - hand figure in the first part of the demonstration . Euclid , however , seems to be quite ...
... note which figure Simson himself supplied , because it is uncertain what he means by the same side " and " opposite sides . " It is the left - hand figure in the first part of the demonstration . Euclid , however , seems to be quite ...
Side 276
... note on I. 32 ) . If this extension be used some of the demonstrations in the third book may be abbreviated . Thus III . 21 may be demonstrated without making two cases ; III . 22 will follow immediately from the fact that the sum of ...
... note on I. 32 ) . If this extension be used some of the demonstrations in the third book may be abbreviated . Thus III . 21 may be demonstrated without making two cases ; III . 22 will follow immediately from the fact that the sum of ...
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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