The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 89
... 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 of four magnitudes is said to have the same ratio to the second which the third has to the ...
... 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 of four magnitudes is said to have the same ratio to the second which the third has to the ...
Seite 90
... magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first a is said to have to the last d the 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 ...
... magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first a is said to have to the last d the 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 ...
Seite 93
... IV . - THEOREM . If the first of four magnitudes has the same 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 ...
... IV . - THEOREM . If the first of four magnitudes has the same 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 ...
Seite 95
... magnitudes , & c . Q. E. D. a h b a f PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
... magnitudes , & c . Q. E. D. a h b a f PROPOSITION A. - THEOREM . If the first of four magnitudes has to the second the same ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also ...
Seite 96
Euclides. PROPOSITION B. - THEOREM . If four magnitudes are proportionals , they are proportionals also when taken g a C inversely . IF the magnitude a be to b as c is to d , then also inversely b is to a as d to C. Take of b and d any ...
Euclides. PROPOSITION B. - THEOREM . If four magnitudes are proportionals , they are proportionals also when taken g a C inversely . IF the magnitude a be to b as c is to d , then also inversely b is to a as d to C. Take of b and d any ...
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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