The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 11
... f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b a h f d g b Because fh is equal to hg , and he common to the two ...
... f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch , drawn from the given point c , is perpendicular to the given straight line a b a h f d g b Because fh is equal to hg , and he common to the two ...
Σελίδα 13
... equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed ... f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e ...
... equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed ... f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e ...
Σελίδα 16
... equal to c ; and from the centre f , at the distance fd , describe ( 3 post . ) the circle dkl ; f 63 g 1 a b C and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the triangle kfg ...
... equal to c ; and from the centre f , at the distance fd , describe ( 3 post . ) the circle dkl ; f 63 g 1 a b C and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the triangle kfg ...
Σελίδα 18
... f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would b d be equal ( i . 4 ) to ef ; but it is not ; there- fore the angle bac is not ...
... f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would b d be equal ( i . 4 ) to ef ; but it is not ; there- fore the angle bac is not ...
Σελίδα 19
... equal sides are opposite ; therefore the angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis ... f . Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . ab to de ...
... equal sides are opposite ; therefore the angle gcb is equal to the angle dfe ; but dfe is , by the hypothesis ... f . Next , let the sides which are opposite to equal angles in each triangle be equal to one another , viz . ab to de ...
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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