The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 35
... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . LET a and be be two straight lines ; and let bc be divided into any parts in the ...
... rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line . LET a and be be two straight lines ; and let bc be divided into any parts in the ...
Σελίδα 36
Euclides. by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , e c ... rectangle contained by a b , bc , together with the rectangle * a b , bac , shall be equal to the square of a b a d C f ...
Euclides. by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , e c ... rectangle contained by a b , bc , together with the rectangle * a b , bac , shall be equal to the square of a b a d C f ...
Σελίδα 37
... rectangle contained by ac , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle ac , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
... rectangle contained by ac , cb , for gc is equal to cb ; therefore ge is also equal to the rectangle ac , cb ; wherefore ag , ge are equal to twice the rectangle ac , cb . And hf , ck are the squares of ac , cb ; wherefore the four ...
Σελίδα 38
... contained by a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the gnomon cm8 is equal to the rectangle ad , db : to each of these add 1g , which is equal ( ii . 4. cor . ) to ...
... contained by a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the gnomon cm8 is equal to the rectangle ad , db : to each of these add 1g , which is equal ( ii . 4. cor . ) to ...
Σελίδα 39
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b , bc ...
... rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b , bc ...
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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