The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 89
V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
Σελίδα 91
I. Equimultiples of the same or of equal magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater ...
I. Equimultiples of the same or of equal magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater ...
Σελίδα 92
If the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth .
If the first be the same multiple of the second , which the third is of the fourth ; and if of the first and third there be taken equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth .
Σελίδα 93
... taken any equimultiples what. ever e , f ; and of b and d any equimultiples whatever g , h : then e has the same ratio to g , which f has to h . 1 f d h . k k a b 8 m : . Take of e and f any equimultiples whatever BOOK V. 93 PROP .
... taken any equimultiples what. ever e , f ; and of b and d any equimultiples whatever g , h : then e has the same ratio to g , which f has to h . 1 f d h . k k a b 8 m : . Take of e and f any equimultiples whatever BOOK V. 93 PROP .
Σελίδα 94
Take of e and f any equimultiples whatever k , l , and of g , h , any equimultiples whatever m , n : then , because e is the same multiple of a that f is of c : and of e and f have been taken equimultiples k , l , therefore k is the ...
Take of e and f any equimultiples whatever k , l , and of g , h , any equimultiples whatever m , n : then , because e is the same multiple of a that f is of c : and of e and f have been taken equimultiples k , l , therefore k is the ...
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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