The Elements of Euclid, Bøker 1-6;Bok 11J.M. Dent & Sons, Limited, 1933 - 298 sider |
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Resultat 1-3 av 91
Side 90
... circle from the extremity of it , touches the circle ; [ III . Def.2 . and that it touches the circle at one point only , because if it did meet the circle at two points it would fall within it . [ III . 2 . Also it is evident , that ...
... circle from the extremity of it , touches the circle ; [ III . Def.2 . and that it touches the circle at one point only , because if it did meet the circle at two points it would fall within it . [ III . 2 . Also it is evident , that ...
Side 114
... circle , when the extremities of it are in the circumference of the circle . PROPOSITION 1. PROBLEM . In a given circle , to place a straight line , equal to a given straight line , which is not greater than the diameter of the circle ...
... circle , when the extremities of it are in the circumference of the circle . PROPOSITION 1. PROBLEM . In a given circle , to place a straight line , equal to a given straight line , which is not greater than the diameter of the circle ...
Side 248
... circle EFGH above the space S , by the preceding Lemma . Let then the segments EK , KF , FL , LG , GM , MH , HN , NE be those which remain , and which are together less than the excess of the circle above S ; therefore the rest of the ...
... circle EFGH above the space S , by the preceding Lemma . Let then the segments EK , KF , FL , LG , GM , MH , HN , NE be those which remain , and which are together less than the excess of the circle above S ; therefore the rest of the ...
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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