The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 13
... join be and produce it to f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e , eb are equal to ce , ef , each to each ; and the angle a e b is equal ( i . 15 ) to the ...
... join be and produce it to f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e , eb are equal to ce , ef , each to each ; and the angle a e b is equal ( i . 15 ) to the ...
Σελίδα 14
... join bd ; and because adb is the exterior angle of the triangle bd c , it is greater ( i . 16 ) than the interior and opposite angle dcb ; but ad bis equal ( i . 5 ) to a bd , because the side a b is equal to the side ad ; therefore the ...
... join bd ; and because adb is the exterior angle of the triangle bd c , it is greater ( i . 16 ) than the interior and opposite angle dcb ; but ad bis equal ( i . 5 ) to a bd , because the side a b is equal to the side ad ; therefore the ...
Σελίδα 16
... join kf , kg ; the triangle kfg has its sides equal to the three straight lines a , b , c . Because the point fis the centre of the circle d k 1 , fd is equal ( 15 def . ) to fk ; but fd is equal to the straight line a ; therefore fk is ...
... join kf , kg ; the triangle kfg has its sides equal to the three straight lines a , b , c . Because the point fis the centre of the circle d k 1 , fd is equal ( 15 def . ) to fk ; but fd is equal to the straight line a ; therefore fk is ...
Σελίδα 17
... join eg , gf . Because a b is equal to de , and ac to dg , the two sides ba , ac are equal to the two , ed , dg , each to each , and the angle bac is equal to the angle edg ; there- fore the base bc is equal ( i . 4 ) to the base eg ...
... join eg , gf . Because a b is equal to de , and ac to dg , the two sides ba , ac are equal to the two , ed , dg , each to each , and the angle bac is equal to the angle edg ; there- fore the base bc is equal ( i . 4 ) to the base eg ...
Σελίδα 18
... join gc ; therefore , because bg is equal to de , and bc to ef , the two sides gb , bc are equal to the two de , ef , each to each ; and the angle gbc is equal to the angle def ; therefore the base gc is equal ( i . 4 ) to the base df ...
... join gc ; therefore , because bg is equal to de , and bc to ef , the two sides gb , bc are equal to the two de , ef , each to each ; and the angle gbc is equal to the angle def ; therefore the base gc is equal ( i . 4 ) to the base df ...
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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