The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 36
... rectangles af , ce ; and ae is the square of a b ; and af is the rectangle con- tained by ba , 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 to ab ; therefore the ...
... rectangles af , ce ; and ae is the square of a b ; and af is the rectangle con- tained by ba , 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 to ab ; therefore the ...
Σελίδα 37
... rectangle con- tained by a c , cb . C a g c b k f Upon ab describe ( i . 46 ) the square a deb , and join bd , and through e draw ( i . 31 ) cgf parallel to ad ... a d , and b'd falls upon them , the exterior angle bgc is equal ( i . 29 ) to ...
... rectangle con- tained by a c , cb . C a g c b k f Upon ab describe ( i . 46 ) the square a deb , and join bd , and through e draw ( i . 31 ) cgf parallel to ad ... a d , and b'd falls upon them , the exterior angle bgc is equal ( i . 29 ) to ...
Σελίδα 38
Euclides. and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is ... a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the ...
Euclides. and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is ... a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the ...
Σελίδα 39
Euclides. angle a d , db , together with the square of c b , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg . and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ...
Euclides. angle a d , db , together with the square of c b , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg . and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db ...
Σελίδα 40
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... a d : therefore four times the rectangle ab , bc , together with the square of a c , is equal to the square of a d , that ...
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... a d : therefore four times the rectangle ab , bc , together with the square of a c , is equal to the square of a d , that ...
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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