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 AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the ...
Straight lines which are parallel to the same straight line are parallel to each other . Let AB , CD be each of them parallel to EF : AB shall be parallel to CD . Let the straight line GHK cut AB , EF , CD . Then , because GHK cuts the ...
Página 42
Equal triangles on the same base , and on the sano side of it , are between the same parallels . Let the equal triangles ABC , DBC be on ... For if it is not , through A draw AE parallel to BC , meeting BD at E. [ I. 31 . and join EC .
Equal triangles on the same base , and on the sano side of it , are between the same parallels . Let the equal triangles ABC , DBC be on ... For if it is not , through A draw AE parallel to BC , meeting BD at E. [ I. 31 . and join EC .
Página 231
And EF is parallel to AB ; [ Hypothesis . therefore AB is at right angles to the plane HGK . [ XI . 8 . For the same reason CD is at right angles to the plane HGK . Therefore AB and CD are both at right angles to the plane HGK .
And EF is parallel to AB ; [ Hypothesis . therefore AB is at right angles to the plane HGK . [ XI . 8 . For the same reason CD is at right angles to the plane HGK . Therefore AB and CD are both at right angles to the plane HGK .
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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