The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 18.
Σελίδα 50
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it .
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it .
Σελίδα 51
Again , because the straight line fe bisects the straight line b d , which does not pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was shewn to be a right angle ...
Again , because the straight line fe bisects the straight line b d , which does not pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was shewn to be a right angle ...
Σελίδα 55
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . Let the two circles a b c , ade touch each other internally in the point a , and let f be ...
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . Let the two circles a b c , ade touch each other internally in the point a , and let f be ...
Σελίδα 56
11 ) ; but it does not pass through it , because the points b , d are without the straight line which is absurd . Therefore one circle cannot touch another on the inside in more points than one . Nor can two circles touch one another on ...
11 ) ; but it does not pass through it , because the points b , d are without the straight line which is absurd . Therefore one circle cannot touch another on the inside in more points than one . Nor can two circles touch one another on ...
Σελίδα 57
Then , because the straight line e f , passing through the centre , cuts the straight line a b , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore a f is equal to fb , and a b double ...
Then , because the straight line e f , passing through the centre , cuts the straight line a b , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore a f is equal to fb , and a b double ...
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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