The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... circle . XVII . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by ...
... circle . XVII . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by ...
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
... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc . Because the point b is the centre of the circle cgh , bc is equal ( 15 def . ) to bg ; and because d is the centre of the ...
... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc . Because the point b is the centre of the circle cgh , bc is equal ( 15 def . ) to bg ; and because d is the centre of the ...
Σελίδα 11
... circle e gf meet- ing a bin 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 ...
... circle e gf meet- ing a bin 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 ...
Σελίδα 16
... 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 has its sides equal to the three straight lines a , b , c . Because the point fis ...
... 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 has its sides equal to the three straight lines a , b , c . Because the point fis ...
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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