The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 29
... passes , and bk , kd , the other parallelograms which make up the whole figure abcd , which are therefore called the complements . The complement bk is equal to the complement k d . Because abcd is a parallelogram , and ac its diameter ...
... passes , and bk , kd , the other parallelograms which make up the whole figure abcd , which are therefore called the complements . The complement bk is equal to the complement k d . Because abcd is a parallelogram , and ac its diameter ...
Σελίδα 50
... pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it . LET abc be a circle ; and let cd , a straight line drawn through the centre , bisect any straight line a b , which does ...
... pass through the centre , it shall cut it at right angles ; and if it cuts it at right angles , it shall bisect it . LET abc be a circle ; and let cd , a straight line drawn through the centre , bisect any straight line a b , which does ...
Σελίδα 51
... pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was ... passes through the centre is always greater than one more BOOK III . 51 PROPS . V. , VI . , VII .
... pass through the centre , it shall cut it at right angles ( iii . 3 ) : wherefore feb is a right angle : and fea was ... passes through the centre is always greater than one more BOOK III . 51 PROPS . V. , VI . , VII .
Σελίδα 52
... passes through the centre , is equal to one which is more remote ; which is impossible . There- fore , if any point ... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes ...
... passes through the centre , is equal to one which is more remote ; which is impossible . There- fore , if any point ... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes ...
Σελίδα 53
... passes through the centre . Of those which fall upon the concave part of the circumference ae fc , the greatest is ad which passes through the centre ; and the nearer to it is always greater than the more remote , viz . , de than df ...
... passes through the centre . Of those which fall upon the concave part of the circumference ae fc , the greatest is ad which passes through the centre ; and the nearer to it is always greater than the more remote , viz . , de than df ...
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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