The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 24
... abcd , ebcf ( see the second figure ) be upon the same base bc , and between the same parallels af , bc ; the parallelogram abcd shall be equal to the parallelogram ebc f If the sides a d , df of the parallelograms abcd , dbcf ...
... abcd , ebcf ( see the second figure ) be upon the same base bc , and between the same parallels af , bc ; the parallelogram abcd shall be equal to the parallelogram ebc f If the sides a d , df of the parallelograms abcd , dbcf ...
Página 25
... abcd , efgh , be paral- lelograms upon equal bases bc , fg , and between the same paral- lels ah , bg ; the parallelogram abcd is equal to efgh . b d e h f g Join be , ch ; and because bc is equal to fg , and fg to eh ( i . 34 ) , bc is ...
... abcd , efgh , be paral- lelograms upon equal bases bc , fg , and between the same paral- lels ah , bg ; the parallelogram abcd is equal to efgh . b d e h f g Join be , ch ; and because bc is equal to fg , and fg to eh ( i . 34 ) , bc is ...
Página 27
... same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a b d base bc , and between the same BOOK I. PROPS . XL . , XLI . 27.
... same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a b d base bc , and between the same BOOK I. PROPS . XL . , XLI . 27.
Página 28
... abcd is double of the tri- angle e bc . Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle ebc , because they are upon the same base bc , and between the same parallels bc , ae . But the parallelogram abcd is double ( i ...
... abcd is double of the tri- angle e bc . Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle ebc , because they are upon the same base bc , and between the same parallels bc , ae . But the parallelogram abcd is double ( i ...
Página 29
... abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa- rallelograms about a c , that is , through which ac passes , and bk , kd , the other parallelograms which make up the whole figure abcd , which are therefore ...
... abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pa- rallelograms about a c , that is , through which ac passes , and bk , kd , the other parallelograms which make up the whole figure abcd , which are therefore ...
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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