The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 61
... segment of a circle are equal to one another . LET abcd be a circle , and bad , bed angles in the same segment baed the angles bad , bed are equal to one another . Take f the centre of the circle abcd : and , first , let the segment ...
... segment of a circle are equal to one another . LET abcd be a circle , and bad , bed angles in the same segment baed the angles bad , bed are equal to one another . Take f the centre of the circle abcd : and , first , let the segment ...
Σελίδα 62
Euclides. b f d But if the segment baed be not greater than a semicircle , let bad , bed be angles in it ; these also are equal to one another draw a f to the centre , and produce it to c , and join ce : therefore the segment badc is ...
Euclides. b f d But if the segment baed be not greater than a semicircle , let bad , bed be angles in it ; these also are equal to one another draw a f to the centre , and produce it to c , and join ce : therefore the segment badc is ...
Σελίδα 63
... segment ad b , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle a cb is ... segment a eb is equal to the segment cfd . For if the segment aeb be applied to the segment cfd , so as the point a be on ...
... segment ad b , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle a cb is ... segment a eb is equal to the segment cfd . For if the segment aeb be applied to the segment cfd , so as the point a be on ...
Σελίδα 64
... segment abc , which is there- fore greater than a semicircle . Wherefore , a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . PROPOSITION XXVI . - THEOREM . In equal circles ...
... segment abc , which is there- fore greater than a semicircle . Wherefore , a segment of a circle being given , the circle is described of which it is a segment . Which was to be done . PROPOSITION XXVI . - THEOREM . In equal circles ...
Σελίδα 67
... segment abc , which is greater than a semicircle , is less than a right angle ; and the angle in the segment a dc , which is less than a semicircle , is greater than a right angle . f Join a e , and produce ba to f . And because be is ...
... segment abc , which is greater than a semicircle , is less than a right angle ; and the angle in the segment a dc , which is less than a semicircle , is greater than a right angle . f Join a e , and produce ba to f . And because be is ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle