The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 31
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
Σελίδα 32
... al ; and the square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between the same parallels fb , gc . But the dou- bles of equals are equal ( 6 ax . ) to one another therefore the parallelogram ...
... al ; and the square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between the same parallels fb , gc . But the dou- bles of equals are equal ( 6 ax . ) to one another therefore the parallelogram ...
Σελίδα 36
... square of the whole line . LET the straight line ab be divided into any two parts in the point c ; the rectangle ... a c ; for it is contained by da , a c , of which ad is equal to a b ; and ce is contained by ab , bc , for be is equal ...
... square of the whole line . LET the straight line ab be divided into any two parts in the point c ; the rectangle ... a c ; for it is contained by da , a c , of which ad is equal to a b ; and ce is contained by ab , bc , for be is equal ...
Σελίδα 37
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of a c ...
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of a c ...
Σελίδα 38
... square of c d , is equal to the square of cb . a C 1 h k d b Upon cb ... a c is equal to cb ; therefore also al is equal to df . To each of these add ... square of cd ; therefore the gnomon cmg , together with 1 g , is equal to the ...
... square of c d , is equal to the square of cb . a C 1 h k d b Upon cb ... a c is equal to cb ; therefore also al is equal to df . To each of these add ... square of cd ; therefore the gnomon cmg , together with 1 g , is equal to the ...
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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