The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 23.
Σελίδα 95
C Make ck equal to f ; and because a g is the same multiple of e , that ch is of f , and that gb is equal ' to e , and ck to f ; therefore a b is the same multiple of e that kh is of f . But a b , by the hypo8 h thesis , is the same ...
C Make ck equal to f ; and because a g is the same multiple of e , that ch is of f , and that gb is equal ' to e , and ck to f ; therefore a b is the same multiple of e that kh is of f . But a b , by the hypo8 h thesis , is the same ...
Σελίδα 96
If the first be the same multiple of the second , or the same part of it , that the third is of the fourth , the first is to the second as the third is to the fourth . Let the first a be the same multiple of b the second , that c the ...
If the first be the same multiple of the second , or the same part of it , that the third is of the fourth , the first is to the second as the third is to the fourth . Let the first a be the same multiple of b the second , that c the ...
Σελίδα 97
Next , let the first a be the same part of the second b , that the third c is of the fourth d : a is to b as c is to d : for b is the same multiple of a that d is of c : wherefore , by the preceding case , b is to a as d is to c ...
Next , let the first a be the same part of the second b , that the third c is of the fourth d : a is to b as c is to d : for b is the same multiple of a that d is of c : wherefore , by the preceding case , b is to a as d is to c ...
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
eg first that becomes greater than fg , the next preceding multiple k is not greater than fg ; that is , fg is not less than k . And since ef is the same multiple of a c that fg is of cb ; fg is the same multiple of cb that eg is of a b ...
eg first that becomes greater than fg , the next preceding multiple k is not greater than fg ; that is , fg is not less than k . And since ef is the same multiple of a c that fg is of cb ; fg is the same multiple of cb that eg is of a b ...
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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