The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 21
In the same manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17.
In the same manner if BC be bisected , and the side AC be produced to G , it may be shewn that the angle BCG , that is the angle ACD , is greater than the angle ABC . [ I. 15 . Wherefore , if one side & c . Q.E.D. PROPOSITION 17.
Página 122
In the same manner it may be shown that the anglos ABC , BCD , CDA are severally bisected by the straight lines BD , AC Then , because the angle DAB is equal to the angle ABC , and that the angle EAB is half the angle DAB , and the ...
In the same manner it may be shown that the anglos ABC , BCD , CDA are severally bisected by the straight lines BD , AC Then , because the angle DAB is equal to the angle ABC , and that the angle EAB is half the angle DAB , and the ...
Página 273
15 ; all three parts might be demonstrated in the manner of III . 7 , and they should be demonstrated , for the third part is really required , as we shall see in the note on III . 10 . III . 9. The point E might be supposed to fall ...
15 ; all three parts might be demonstrated in the manner of III . 7 , and they should be demonstrated , for the third part is really required , as we shall see in the note on III . 10 . III . 9. The point E might be supposed to fall ...
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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