The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 32
... common to the two triangles dac , bac , the two da , ac are equal to the two ba , a c ; and the base dc is equal to the base bc ; therefore the angle dac is equal ( i . 8 ) to the angle bac ; but dac is a right angle ; therefore also ...
... common to the two triangles dac , bac , the two da , ac are equal to the two ba , a c ; and the base dc is equal to the base bc ; therefore the angle dac is equal ( i . 8 ) to the angle bac ; but dac is a right angle ; therefore also ...
Σελίδα 43
... common to both , therefore the remain- ing rectangle cf , fa , is equal to the square of ab ; and the figure fk is the rectangle contained by cf fa , for af is equal to fg ; and ad is the square of of a ab ; therefore fk is equal to ad ...
... common to both , therefore the remain- ing rectangle cf , fa , is equal to the square of ab ; and the figure fk is the rectangle contained by cf fa , for af is equal to fg ; and ad is the square of of a ab ; therefore fk is equal to ad ...
Σελίδα 45
... common to both ; and the remaining rectangle be , ef is equal to the square of eh : but the rect- angle contained by be , ef is the parallelogram bd , because ef is equal to ed ; therefore bd is equal to the square of eh ; but bd is ...
... common to both ; and the remaining rectangle be , ef is equal to the square of eh : but the rect- angle contained by be , ef is the parallelogram bd , because ef is equal to ed ; therefore bd is equal to the square of eh ; but bd is ...
Σελίδα 49
... common to the two triangles a dg , bdg , the two sides a d , dg , are equal to the two b d d g , each to each ; and the base ga is equal to the base g b , because they are drawn from the centre g * : therefore the angle ad g is equal ...
... common to the two triangles a dg , bdg , the two sides a d , dg , are equal to the two b d d g , each to each ; and the base ga is equal to the base g b , because they are drawn from the centre g * : therefore the angle ad g is equal ...
Σελίδα 50
... common to the two tri- angles afe , bfe , there are two sides in the one equal to two sides in the other , and the base e a is equal to the base e b ; therefore the angle a fe is equal ( i . 8 ) to the angle bfe : but when a straight ...
... common to the two tri- angles afe , bfe , there are two sides in the one equal to two sides in the other , and the base e a is equal to the base e b ; therefore the angle a fe is equal ( i . 8 ) to the angle bfe : but when a straight ...
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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