The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 91
... tiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others ...
... tiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others ...
Σελίδα 95
... tiple of e that ch is of f ; and gb the same mul- tiple of e that c k is of f ; therefore ab is the same multiple of e that k h is of f ( v . 2 ) . But ab is the same multiple of e that cd is of f ; therefore kh is the same multiple of ...
... tiple of e that ch is of f ; and gb the same mul- tiple of e that c k is of f ; therefore ab is the same multiple of e that k h is of f ( v . 2 ) . But ab is the same multiple of e that cd is of f ; therefore kh is the same multiple of ...
Σελίδα 96
... tiple of b that c is of d ; and that e is the same multiple of a that f is of e g f h b c a b c d ce is the same multiple of b that f is of d ( v . 3 ) ; therefore e and f are the same multiples of b and d . But g and h are ...
... tiple of b that c is of d ; and that e is the same multiple of a that f is of e g f h b c a b c d ce is the same multiple of b that f is of d ( v . 3 ) ; therefore e and f are the same multiples of b and d . But g and h are ...
Σελίδα 99
... tiple of d ; and fg , eg are equi- f g b 1 k h d g b 1 k d fig . 2 . fig . 3 . multiples of cb , ab ; therefore d has to cb a greater ratio ( v . def . 7 ) than it has to a b . Wherefore , of unequal magnitudes , & c . Q. E. D. ...
... tiple of d ; and fg , eg are equi- f g b 1 k h d g b 1 k d fig . 2 . fig . 3 . multiples of cb , ab ; therefore d has to cb a greater ratio ( v . def . 7 ) than it has to a b . Wherefore , of unequal magnitudes , & c . Q. E. D. ...
Σελίδα 104
... tiple of a that f is of b , and that magnitudes have the same ratio to one another which their equimultiples have ( v . 15 ) ; therefore a is to b , as e e a b f g- C d h is to f ; but as a is to b , so is c to d ; wherefore as c is to ...
... tiple of a that f is of b , and that magnitudes have the same ratio to one another which their equimultiples have ( v . 15 ) ; therefore a is to b , as e e a b f g- C d h is to f ; but as a is to b , so is c to d ; wherefore as c is to ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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