The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first ...
... Ratio is a mutual relation of two magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first ...
Σελίδα 90
... ratio compounded of the ratio of a to b , and the ratio of b to c , and the ratio of c to d ; or , the ratio of a to d is said to be compounded of the ratios of a to b , b to c , and c to d : And if a has to b the same ratio which e has ...
... ratio compounded of the ratio of a to b , and the ratio of b to c , and the ratio of c to d ; or , the ratio of a to d is said to be compounded of the ratios of a to b , b to c , and c to d : And if a has to b the same ratio which e has ...
Σελίδα 93
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
Σελίδα 94
... 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 . Let a the first have to b the second , the same ration which the third c has to ...
... 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 . Let a the first have to b the second , the same ration which the third c has to ...
Σελίδα 95
... ratio which the third has to the 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 ...
... ratio which the third has to the 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 ...
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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