The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 90
... Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance .; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and two of each rank , and it is inferred ...
... Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance .; when there is any number of magnitudes more than two , and as many others , so that they are proportionals when taken two and two of each rank , and it is inferred ...
Σελίδα 91
Euclides. XX . Ex æquali in proportione perturbata seu inordinata , from equality in perturbate or disorderly proportion . * This term is used when the first magnitude is to the second of the first rank as the last but one is to the last ...
Euclides. XX . Ex æquali in proportione perturbata seu inordinata , from equality in perturbate or disorderly proportion . * This term is used when the first magnitude is to the second of the first rank as the last but one is to the last ...
Σελίδα 109
... ex æquali , " or æquo . " + 66 ex FIRST , let there be three magnitudes a , b , c , and as many others d , e , f , gk m h 1 n abc b c d e f which , taken two and two , have the same BOOK V. 109 PROP . XXII .
... ex æquali , " or æquo . " + 66 ex FIRST , let there be three magnitudes a , b , c , and as many others d , e , f , gk m h 1 n abc b c d e f which , taken two and two , have the same BOOK V. 109 PROP . XXII .
Σελίδα 110
... ex æquali in proportione perturbata , " or " ex æquo perturbato . " FIRST , let there be three magnitudes a , b , c , and other three , d , e , f , which , taken two and two , in a cross order , have the same ratio : that is , such that ...
... ex æquali in proportione perturbata , " or " ex æquo perturbato . " FIRST , let there be three magnitudes a , b , c , and other three , d , e , f , which , taken two and two , in a cross order , have the same ratio : that is , such that ...
Σελίδα 111
... ex æquali ( v . 22 ) , a b is to bg , as de to eh and because these magnitudes are proportionals , they shall like- wise be proportionals when taken jointly ( v . 18 ) ; as therefore a g is to gb , so is dh to he : but as gb to c , so ...
... ex æquali ( v . 22 ) , a b is to bg , as de to eh and because these magnitudes are proportionals , they shall like- wise be proportionals when taken jointly ( v . 18 ) ; as therefore a g is to gb , so is dh to he : but as gb to c , 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