The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 192
Next , let the angle FBD be equal to the angle EBG , and let the sides about the equal angles be reciprocally proportional , namely , DB to BE as ĜB is to BF : the parallelogram AB shali be equal to the parallelogram BC .
Next , let the angle FBD be equal to the angle EBG , and let the sides about the equal angles be reciprocally proportional , namely , DB to BE as ĜB is to BF : the parallelogram AB shali be equal to the parallelogram BC .
Página 206
B We 7 Let the parallelogram AC be equiangular to the parallelogram CF , having the anglo BCD equal to the angle ECG : the parallelogram AC shall have to the parallelogram CF the ratio which is compounded of the ratios of their sides .
B We 7 Let the parallelogram AC be equiangular to the parallelogram CF , having the anglo BCD equal to the angle ECG : the parallelogram AC shall have to the parallelogram CF the ratio which is compounded of the ratios of their sides .
Página 209
But as BC is to CF so is the parallelogram BE to the parallelogram CM ; ( VI . 1 . therefore the figure ABC is to the figure KGH as the parallelogram BE is to the parallelogram CM . [ V. 11 . And the figure ABC is equal to the ...
But as BC is to CF so is the parallelogram BE to the parallelogram CM ; ( VI . 1 . therefore the figure ABC is to the figure KGH as the parallelogram BE is to the parallelogram CM . [ V. 11 . And the figure ABC is equal to 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