The Elements of Euclid, Libros 1-6;Libro 11 |
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Página 96
THEOREM , Similar segments of circles on equal straight lines are equal to one another . Let AEB , CFD be similar segments of circles on the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD .
THEOREM , Similar segments of circles on equal straight lines are equal to one another . Let AEB , CFD be similar segments of circles on the equal straight lines AB , CD : the segment AEB shall be equal to the segment CFD .
Página 97
From the centre D , at the distance of any of the three DA , DB , DC , describe a circle ; this will pass through the other points , and the circle of which ABC is a segment is described . And because the centre D is in AC , the segment ...
From the centre D , at the distance of any of the three DA , DB , DC , describe a circle ; this will pass through the other points , and the circle of which ABC is a segment is described . And because the centre D is in AC , the segment ...
Página 98
And because the angleat A is equal to the angle at D , [ Hyp . the segment BAСis similar to the segment EDF ; [ III . Def.11 . and they are on equal straight lines BC , EF . But similar segments of circles on equal straight lines are ...
And because the angleat A is equal to the angle at D , [ Hyp . the segment BAСis similar to the segment EDF ; [ III . Def.11 . and they are on equal straight lines BC , EF . But similar segments of circles on equal straight lines are ...
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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