The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 35
... gnomon . Thus the parallelogram hg , together with the complements af , fc , is the gnomon , which is more briefly ex- pressed by the letters a gk , or eh c , which h are at the opposite angles of the parallelo- grams which make the ...
... gnomon . Thus the parallelogram hg , together with the complements af , fc , is the gnomon , which is more briefly ex- pressed by the letters a gk , or eh c , which h are at the opposite angles of the parallelo- grams which make the ...
Página 38
... 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 the square of cd ; therefore the gnomon cmg , together with 1 g , is equal to the rectangle ad ...
... 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 the square of cd ; therefore the gnomon cmg , together with 1 g , is equal to the rectangle ad ...
Página 39
... gnomon cmg . and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ... gnomon a k f , together with the square ck ; therefore the gnomon a kf , together with the square ck , is double of ...
... gnomon cmg . and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ... gnomon a k f , together with the square ck ; therefore the gnomon a kf , together with the square ck , is double of ...
Página 40
... gnomon a oh was demonstrated to be quadruple of ak ; therefore four times the rectangle ab , bc , is equal to the gnomon a oh . To each of these add xh , which is equal ( ii . 4. cor . ) to the square of a c : therefore four times ...
... gnomon a oh was demonstrated to be quadruple of ak ; therefore four times the rectangle ab , bc , is equal to the gnomon a oh . To each of these add xh , which is equal ( ii . 4. cor . ) to the square of a c : therefore four times ...
Página 138
... gnomon chl , there- fore ce , or the parallelogram a d , is greater than the parallelogram a f . Next , let ak the base of af be less than ac , and the same construction being made , the parallelogram dh is equal to dg ( i . 36 ) , for ...
... gnomon chl , there- fore ce , or the parallelogram a d , is greater than the parallelogram a f . Next , let ak the base of af be less than ac , and the same construction being made , the parallelogram dh is equal to dg ( i . 36 ) , for ...
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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