The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 34
Straight lines which are parallel to the same straight line are parallel to each other . ... Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines AB , A EF ... Wherefore , straight lines & c .
Straight lines which are parallel to the same straight line are parallel to each other . ... Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the parallel straight lines AB , A EF ... Wherefore , straight lines & c .
Página 223
Then since the straight line AB is in the plane , it can be produced in that plane ; let it be produced to D ; and let any plane pass through the А straight line ÅD and be turned about until it pass through the point C. Then , because ...
Then since the straight line AB is in the plane , it can be produced in that plane ; let it be produced to D ; and let any plane pass through the А straight line ÅD and be turned about until it pass through the point C. Then , because ...
Página 228
Wherefore , if two straight lines & c . Q.E.D. 9 PROPOSITION 7 . THEOREM . If two straight lines be parallel , the straight line draron from any point in one to any point in the other , is in the same plane with the parallels .
Wherefore , if two straight lines & c . Q.E.D. 9 PROPOSITION 7 . THEOREM . If two straight lines be parallel , the straight line draron from any point in one to any point in the other , is in the same plane with the parallels .
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ABCD angle ABC angle ACB angle BAC Axiom base BC is equal bisected Book centre circle circle ABC circumference common Construction contained Corollary Definition demonstration described diameter divided double draw drawn edition Elements equal equal angles equiangular equilateral equimultiples Euclid exterior angle extremities fall figure four fourth given straight line greater half Hypothesis impossible join less Let ABC magnitudes manner meet multiple namely parallel parallelogram pass perpendicular plane polygon PROBLEM produced proportionals Q.E.D. PROPOSITION ratio reason rectangle rectangle contained rectilineal figure right angles segment shewn sides similar Simson solid square straight line &c suppose Take taken THEOREM third touches the circle triangle ABC Wherefore whole