The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 5
... equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but ... f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance ...
... equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but ... f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance ...
Página 6
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ... f , because the straight line ac is equal to df : but the point b coincides with the point e ; wherefore the ...
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ... f , because the straight line ac is equal to df : but the point b coincides with the point e ; wherefore the ...
Página 7
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab ...
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the two sides fa , a c are equal to the two ga , ab ...
Página 8
... equal to one another , and likewise those which are terminated in the other extremity . d Ir it be possible , let ... f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the ...
... equal to one another , and likewise those which are terminated in the other extremity . d Ir it be possible , let ... f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the ...
Página 9
... equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ...
... equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ...
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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