The Elements of Euclid, Libros 1-6;Libro 11 |
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But , because the polygons are similar , [ Hypothesis . therefore the whole angle ABC is equal to the whole angle FGH ; ( VI . Definition 1 . therefore the remaining angle EBC is equal to the remaining angle LGH . [ Axiom 3 .
But , because the polygons are similar , [ Hypothesis . therefore the whole angle ABC is equal to the whole angle FGH ; ( VI . Definition 1 . therefore the remaining angle EBC is equal to the remaining angle LGH . [ Axiom 3 .
Página 203
But any rectilineal figure described on AB is to the similar and similarly described rectilineal figure on FG in the duplicate ratio of AB to FG , ( Corollary 1 . Therefore as AB is to M , so is the figure on AB to the figure on FG ...
But any rectilineal figure described on AB is to the similar and similarly described rectilineal figure on FG in the duplicate ratio of AB to FG , ( Corollary 1 . Therefore as AB is to M , so is the figure on AB to the figure on FG ...
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grammic figure similar to a given one : thus the given rectilineal figure must not be greater than the parallelogram described on the half of the straight line and similar to the defect . Let AB be the given straight line , Ç the given ...
grammic figure similar to a given one : thus the given rectilineal figure must not be greater than the parallelogram described on the half of the straight line and similar to the defect . Let AB be the given straight line , Ç the given ...
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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