The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 64
... pass through the other points ; and the circle of which abc is a segment is described . And it is evident that if the angle abd be greater than the angle bad , the centre e falls without the segment abc , which therefore is less than a ...
... pass through the other points ; and the circle of which abc is a segment is described . And it is evident that if the angle abd be greater than the angle bad , the centre e falls without the segment abc , which therefore is less than a ...
Σελίδα 66
... passes through the centre ( i . 3 . cor . ) . Wherefore the circumference a d is equal to the circumference db . Therefore the given circumference is bisected in d . Which was to be done . a b PROPOSITION XXXI . - THEOREM . In a circle ...
... passes through the centre ( i . 3 . cor . ) . Wherefore the circumference a d is equal to the circumference db . Therefore the given circumference is bisected in d . Which was to be done . a b PROPOSITION XXXI . - THEOREM . In a circle ...
Σελίδα 69
... pass through the point b ; let this be the circle ahb : and because from the point a , the extremity of the diameter a e , a d is drawn at right angles to a e , there- fore a d ( iii . 16. cor . ) touches the circle ; and because ab ...
... pass through the point b ; let this be the circle ahb : and because from the point a , the extremity of the diameter a e , a d is drawn at right angles to a e , there- fore a d ( iii . 16. cor . ) touches the circle ; and because ab ...
Σελίδα 70
... pass through the centre , and cut the other ac which does not pass through the centre , at right angles , in the point e : then , if bd be bisected in f , f is the centre of the circle abcd ; join af . And because bd , which passes ...
... pass through the centre , and cut the other ac which does not pass through the centre , at right angles , in the point e : then , if bd be bisected in f , f is the centre of the circle abcd ; join af . And because bd , which passes ...
Σελίδα 71
... passes through the centre , or it does not ; first , let it pass through the centre e , and join eb ; therefore the angle ebd is a right ( iii . 18 ) angle ; and because the straight line ac is bisected in e , and produced to the point ...
... passes through the centre , or it does not ; first , let it pass through the centre e , and join eb ; therefore the angle ebd is a right ( iii . 18 ) angle ; and because the straight line ac is bisected in e , and produced to the point ...
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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