The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 76
If in a circle two straight lines cut one another , which do not pass through the centre , they do not bisect one another . Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another at the point E , and do not ...
If in a circle two straight lines cut one another , which do not pass through the centre , they do not bisect one another . Let ABCD be a circle , and AC , BD two straight lines in it , which cut one another at the point E , and do not ...
Página 83
If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one another interDally at the point A ; and let F ...
If two circles touch one another internally , the straight line which joins their centres , being produced , shall pass through the point of contact . Let the two circles ABC , ADE touch one another interDally at the point A ; and let F ...
Página 108
If AÇand BD both pass through the centre , so that E is the centre , it is evident , since EA , EB , EC , ED are all equal , that the rectangle AE , EC is equal to the rectangle BE , ED . But let one of them , BD , pass through the ...
If AÇand BD both pass through the centre , so that E is the centre , it is evident , since EA , EB , EC , ED are all equal , that the rectangle AE , EC is equal to the rectangle BE , ED . But let one of them , BD , pass through the ...
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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