The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 95
... equimultiples of them . k LET the two magnitudes ab , cd be equimultiples of the two e , f , and ag , ch taken from the first two be equimultiples of the same e , f ; the remainders gb , hd are either equal to e , f , or equimultiples ...
... equimultiples of them . k LET the two magnitudes ab , cd be equimultiples of the two e , f , and ag , ch taken from the first two be equimultiples of the same e , f ; the remainders gb , hd are either equal to e , f , or equimultiples ...
Σελίδα 96
... equimultiples whatever e and f ; and of a and c any equimultiples whatever g and h . First , let e be greater than g then g is less than e ; and because a is to b as c is to d , and of a and c , the first and third , g and h are ...
... equimultiples whatever e and f ; and of a and c any equimultiples whatever g and h . First , let e be greater than g then g is less than e ; and because a is to b as c is to d , and of a and c , the first and third , g and h are ...
Σελίδα 97
Euclides. than h . In like manner , if e be equal to g , or less , f is equal to h , or less than it . But e , f are equimultiples , any whatever , of a , c , and g , h any equimultiples whatever of b , d Therefore a is to b , as c is to ...
Euclides. than h . In like manner , if e be equal to g , or less , f is equal to h , or less than it . But e , f are equimultiples , any whatever , of a , c , and g , h any equimultiples whatever of b , d Therefore a is to b , as c is to ...
Σελίδα 98
... equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that ... equimultiples of a , b , and f is any multiple of c . Therefore ( v . def . 5 ) , as a is to c , so is b to c ...
... equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that ... equimultiples of a , b , and f is any multiple of c . Therefore ( v . def . 5 ) , as a is to c , so is b to c ...
Σελίδα 99
... equimultiples of a b f and cb . And it was shewn that fg was not less than k , and , by the construction , ef is greater than d ; therefore the whole eg is greater than k and d together . But k , together with d , is equal to 1 ...
... equimultiples of a b f and cb . And it was shewn that fg was not less than k , and , by the construction , ef is greater than d ; therefore the whole eg is greater than k and d together . But k , together with d , is equal to 1 ...
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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