The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 4
... given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab , describe ( 3 post . ) the circle bcd , and from the centre b , at the ...
... given finite straight line . LET ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at the distance ab , describe ( 3 post . ) the circle bcd , and from the centre b , at the ...
Página 5
... given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight ... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc ...
... given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight ... circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to bc ...
Página 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 ...
Página 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 ... given straight lines a , b , c . Which was to be done . PROPOSITION XXIII . - PROBLEM . At a given point in a ...
... circle dkl ; f 63 g 1 a b C and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ... given straight lines a , b , c . Which was to be done . PROPOSITION XXIII . - PROBLEM . At a given point in a ...
Página 48
... circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET abc be the given circle ; it is required to find its centre . Draw ...
... circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET abc be the given circle ; it is required to find its centre . Draw ...
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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