The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 6
... side ab is equal to a C , and let the straight lines a b , ac be produced to d and e , the angle a bc shall be equal to the angle a c b , and the angle cbd to the angle bce . а . 09 In bd take any point f , 6 THE ELEMENTS OF EUCLID .
... side ab is equal to a C , and let the straight lines a b , ac be produced to d and e , the angle a bc shall be equal to the angle a c b , and the angle cbd to the angle bce . а . 09 In bd take any point f , 6 THE ELEMENTS OF EUCLID .
Σελίδα 7
09 In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
09 In bd take any point f , and from a e the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , g b . Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ...
Σελίδα 9
Take any point d in a b , and from a c cut ( i . 3 ) off a e equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af a bisects the angle bac . Because a d is equal to a e ...
Take any point d in a b , and from a c cut ( i . 3 ) off a e equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af a bisects the angle bac . Because a d is equal to a e ...
Σελίδα 10
LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line from the point c at right angles to a b . Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de describe ( i .
LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line from the point c at right angles to a b . Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon de describe ( i .
Σελίδα 11
Take any point d upon the other side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle egf meeting a b in f , g ; and bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ...
Take any point d upon the other side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle egf meeting a b in f , g ; and bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ...
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a b c angle a b c angle bac base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole