The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 4
... circle bcd , and from the centre b , at the distance ba , describe the circle ace ; and from the point c , in which the circles cut one another , draw the straight lines ( 1 post . ) ca , cb , to the points a , b ; abc shall be an ...
... circle bcd , and from the centre b , at the distance ba , describe the circle ace ; and from the point c , in which the circles cut one another , draw the straight lines ( 1 post . ) ca , cb , to the points a , b ; abc shall be an ...
Σελίδα 5
... abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done ... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc . Because the ...
... abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done ... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc . Because the ...
Σελίδα 48
... circle . LET abc be the given circle ; it is required to find its centre . Draw within it any straight line a b , and bisect ( i . 10 ) it in d ; from the point d draw ( i . 11 ) dc at right angles to a b , and produce it to e , and ...
... circle . LET abc be the given circle ; it is required to find its centre . Draw within it any straight line a b , and bisect ( i . 10 ) it in d ; from the point d draw ( i . 11 ) dc at right angles to a b , and produce it to e , and ...
Σελίδα 49
... circle is in the line which bisects the other . e d PROPOSITION II . - THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and ...
... circle is in the line which bisects the other . e d PROPOSITION II . - THEOREM . If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and ...
Σελίδα 50
... 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 . LET abc be a circle ; and let cd , a straight line drawn through the ...
... 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 . LET abc be a circle ; and let cd , a straight line drawn through the ...
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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