The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 22.
Σελίδα 95
Íf two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimultiples of them . LET the two magnitudes a b , cd be equimultiples ...
Íf two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimultiples of them . LET the two magnitudes a b , cd be equimultiples ...
Σελίδα 96
Take of b and d any equimultiples whatever e and f ; and of a and c any equimultiples whatever g and h . First , let e be greater than g then & is less than e ; and because a is to b as c is to d , and of a and c , the first and third ...
Take of b and d any equimultiples whatever e and f ; and of a and c any equimultiples whatever g and h . First , let e be greater than g then & is less than e ; and because a is to b as c is to d , and of a and c , the first and third ...
Σελίδα 97
But e , f are equimultiples , any whatever , of a , c , and h any equimultiples whatever of b , d . Therefore a is to b , as c is to d ( v . def . 5 ) . Next , let the first a be the same part of the second b , that the third c is of ...
But e , f are equimultiples , any whatever , of a , c , and h any equimultiples whatever of b , d . Therefore a is to b , as c is to d ( v . def . 5 ) . Next , let the first a be the same part of the second b , that the third c is of ...
Σελίδα 98
Take of a and b any equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that e is of b , and that a is equal to b ; d is ( v . ax . 1 ) equal to e . Therefore , if d be greater ...
Take of a and b any equimultiples whatever d and e , and of c any multiple whatever f . Then , because d is the same multiple of a that e is of b , and that a is equal to b ; d is ( v . ax . 1 ) equal to e . Therefore , if d be greater ...
Σελίδα 99
5 ) ; wherefore eg and fg are equimultiples of a b fand cb . And it was shewn that fg was not less than k , and , by the construction , ef is greater than d ; a therefore the whole eg is greater f than k and d together .
5 ) ; wherefore eg and fg are equimultiples of a b fand cb . And it was shewn that fg was not less than k , and , by the construction , ef is greater than d ; a therefore the whole eg is greater f than k and d together .
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a b c angle a b c angle bac base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole