The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 39
... square of cd ; therefore the rectangle ad , db , together with the square of cb , is equal to the square of cd ... a c . a h bo C b k Upon a b describe ( i . 46 ) the square a deb , and construct the figure as in the preceding ...
... square of cd ; therefore the rectangle ad , db , together with the square of cb , is equal to the square of cd ... a c . a h bo C b k Upon a b describe ( i . 46 ) the square a deb , and construct the figure as in the preceding ...
Σελίδα 40
... square of a c : therefore four times the rectangle a b , bc , together with the square of a c , is equal to the gnomon aoh and the square xh but the gnomon a oh and xh make up the figure a efd , which is the square of a d : therefore ...
... square of a c : therefore four times the rectangle a b , bc , together with the square of a c , is equal to the gnomon aoh and the square xh but the gnomon a oh and xh make up the figure a efd , which is the square of a d : therefore ...
Σελίδα 41
... ac is equal to ce , the square of a c is equal to the square of ce ; therefore the squares of a c , ce , are double of the square of a c : but the square of e a is equal ( i . 47 ) to the squares of ac , ce , because ace is a right angle ; ...
... ac is equal to ce , the square of a c is equal to the square of ce ; therefore the squares of a c , ce , are double of the square of a c : but the square of e a is equal ( i . 47 ) to the squares of ac , ce , because ace is a right angle ; ...
Σελίδα 42
... square of ec is equal to the square of ca ; therefore the squares of e c , ca are double of the square of ca. But the square of ea is equal ( i . 47 ) to the squares of ec , ca ; therefore the square of ea is double of the square of a c ...
... square of ec is equal to the square of ca ; therefore the squares of e c , ca are double of the square of ca. But the square of ea is equal ( i . 47 ) to the squares of ec , ca ; therefore the square of ea is double of the square of a c ...
Σελίδα 43
... square of a e , is equal to the squares of ba , ae : take away the square of a e , which is common to both ... ac , cb , by twice the rectangle bc , cd . Because the straight line bd is divided into two parts in the point c , the square ...
... square of a e , is equal to the squares of ba , ae : take away the square of a e , which is common to both ... ac , cb , by twice the rectangle bc , cd . Because the straight line bd is divided into two parts in the point c , the square ...
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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