The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 94
... fourth , then also any equimultiples whatever of the first and third have the same ratio to the second and fourth . And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth ...
... fourth , then also any equimultiples whatever of the first and third have the same ratio to the second and fourth . And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth ...
Σελίδα 95
... fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of each ; then , by def . 5th of this ...
... fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of each ; then , by def . 5th of this ...
Σελίδα 96
... 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 third is of the fourth d : a is to b as c is to d . Take of a and c any equimultiples whatever e and f ...
... 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 third is of the fourth d : a is to b as c is to d . Take of a and c any equimultiples whatever e and f ...
Σελίδα 97
... 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 ... fourth , and if the first be a multiple , or part , of the second ; the third is the same multiple , or the same part ...
... 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 ... fourth , and if the first be a multiple , or part , of the second ; the third is the same multiple , or the same part ...
Σελίδα 100
... fourth ( v . def . 5 ) . But f is not greater than d , which is impossible . Therefore a is equal to b . Wherefore , magnitudes , & c . Q. E. D. PROPOSITION X. - THEOREM . That magnitude which has a greater ratio than another has unto ...
... fourth ( v . def . 5 ) . But f is not greater than d , which is impossible . Therefore a is equal to b . Wherefore , magnitudes , & c . Q. E. D. PROPOSITION X. - THEOREM . That magnitude which has a greater ratio than another has unto ...
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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