The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 34
... triangle have its exterior angle and one of its opposite interior angles double ... twice the line joining the vertex and the middle of the base .. 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
... triangle have its exterior angle and one of its opposite interior angles double ... twice the line joining the vertex and the middle of the base .. 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
Seite 37
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of a c , cb , and to twice the rectangle con- tained by a c , cb . C a g c b k f Upon ab ...
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of a c , cb , and to twice the rectangle con- tained by a c , cb . C a g c b k f Upon ab ...
Seite 39
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b ...
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of ab , bc are equal to twice the rectangle a b ...
Seite 43
... rectangle cf , fa , together with the square of a e , is equal to the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight line ...
... rectangle cf , fa , together with the square of a e , is equal to the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight line ...
Seite 44
... twice the rectangle cb , bd . b First , let ad fall within the triangle abc ; and because the straight a d line cb is divided into two parts in the point d , the squares of cb , bd , are equal ( ii . 7 ) to twice the rectangle contained ...
... twice the rectangle cb , bd . b First , let ad fall within the triangle abc ; and because the straight a d line cb is divided into two parts in the point d , the squares of cb , bd , are equal ( ii . 7 ) to twice the rectangle contained ...
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Häufige Begriffe und Wortgruppen
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