The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 6
... angle a cb to dfe . LET abc , def be two triangles , which have the two sides a b , ac equal to the two sides de , df , each to each , viz . ab to de , and a c to df ; and the angle bac equal to the angle edf , the base bc shall be ...
... angle a cb to dfe . LET abc , def be two triangles , which have the two sides a b , ac equal to the two sides de , df , each to each , viz . ab to de , and a c to df ; and the angle bac equal to the angle edf , the base bc shall be ...
Página 17
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line a b ... edf ; the base bc is also greater than the base ef . Of the two sides de , df , let de be the side which is not greater than ...
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line a b ... edf ; the base bc is also greater than the base ef . Of the two sides de , df , let de be the side which is not greater than ...
Página 18
... angle bac is not equal to the angle edf ; neither is it less : because then the base bc would be less ( i . 24 ) than the base ef ; but it is not ; therefore the angle bac is not less than the angle edf ; f and it was shewn that it is ...
... angle bac is not equal to the angle edf ; neither is it less : because then the base bc would be less ( i . 24 ) than the base ef ; but it is not ; therefore the angle bac is not less than the angle edf ; f and it was shewn that it is ...
Página 19
... angles , gbc each to each , to which the equal sides are opposite ; therefore the angle gcb is equal to the angle ... edf . Therefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . - THEOREM . If a straight line falling ...
... angles , gbc each to each , to which the equal sides are opposite ; therefore the angle gcb is equal to the angle ... edf . Therefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . - THEOREM . If a straight line falling ...
Página 59
... angle a straight line makes with the diameter at the point a , or however small an angle it makes with a e , the ... edf : g c is a right angle , wherefore eba is a right angle ; and eb is drawn from the centre but a straight line ...
... angle a straight line makes with the diameter at the point a , or however small an angle it makes with a e , the ... edf : g c is a right angle , wherefore eba is a right angle ; and eb is drawn from the centre but a straight line ...
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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