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 ...
... 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 ...
Página 6
... equal to 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 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 af , the less , and join fc , gb . Because af is equal to ag , and ab to ac , the two sides fa , ac are equal to the two ga , ab , each to each ...
Euclides. In bd take any point f , and from ae the greater , cut off ag equal ( i . 3 ) to a af , the less , and join fc , gb . Because af is equal to ag , and ab to ac , the two sides fa , ac are equal to the two ga , ab , each to each ...
Página 8
... equal to one another , and likewise those which are terminated in the other extremity . c d IF it be possible , let ... f ; therefore , because ac 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 . c d IF it be possible , let ... f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the ...
Página 9
... equal to the angle edf . dg Ce f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with the point f , be- b cause bc is equal to ef ...
... equal to the angle edf . dg Ce f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with the point f , be- b cause bc is equal to ef ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle