The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 89
... proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . VII . When of the equimultiples of four magnitudes ( taken as in the fifth ...
... proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . VII . When of the equimultiples of four magnitudes ( taken as in the fifth ...
Σελίδα 90
... proportionals , so as that they continue still to be proportionals . XIII . Permutando , or alternando , by permutation , or alternately . This word is used when there are four proportionals , and it is inferred that the first has the ...
... proportionals , so as that they continue still to be proportionals . XIII . Permutando , or alternando , by permutation , or alternately . This word is used when there are four proportionals , and it is inferred that the first has the ...
Σελίδα 95
... second , or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROPOSITION B. - THEOREM . If four magnitudes are proportionals -BOOK V. PROPS . VI . , A. 95.
... second , or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. PROPOSITION B. - THEOREM . If four magnitudes are proportionals -BOOK V. PROPS . VI . , A. 95.
Σελίδα 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 ...
Σελίδα 101
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number of magnitudes a , b , c , d , e , f be proportionals ; that is , as a is to b , so ...
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the con- sequents . LET any number of magnitudes a , b , c , d , e , f be proportionals ; that is , as a is to b , so ...
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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