The Elements of Euclid, Libros 1-6;Libro 11J.M. Dent & Sons, Limited, 1933 - 298 páginas |
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Página 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 ...
Página 91
... touches the circle ; therefore AB touches the circle . [ III . 16 , Corollary . And AB is drawn from the given point A. Q.E.F. But if the given point be in the circumference of the circle , as the point D , draw DE to the centre E ...
... touches the circle ; therefore AB touches the circle . [ III . 16 , Corollary . And AB is drawn from the given point A. Q.E.F. But if the given point be in the circumference of the circle , as the point D , draw DE to the centre E ...
Página 112
... circle , the line which meets the circle shall touch it . Let any point D be taken without the circle ABC , and from it let two straight lines DCA , DB be drawn , of which DCA cuts the circle , and DB meets it ; and let the rectangle AD ...
... circle , the line which meets the circle shall touch it . Let any point D be taken without the circle ABC , and from it let two straight lines DCA , DB be drawn , of which DCA cuts the circle , and DB meets it ; and let the rectangle AD ...
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ABCD angle ABC angle ACB angle BAC angle DEF angle EDF angles equal Axiom base BC BC is equal 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 whole angle