The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 5
... wherefore al and bc are each of them equal to bg ; and things that are equal to the same are equal to one another ; therefore the straight line al is equal to bc . Wherefore from the given point a a straight line al has been drawn equal ...
... wherefore al and bc are each of them equal to bg ; and things that are equal to the same are equal to one another ; therefore the straight line al is equal to bc . Wherefore from the given point a a straight line al has been drawn equal ...
Σελίδα 6
... wherefore also the point c shall coincide with the point f , because the straight line ac is equal to df : but the point b coincides with the point e ; wherefore the base b c shall coincide with the base ef , because the point b ...
... wherefore also the point c shall coincide with the point f , because the straight line ac is equal to df : but the point b coincides with the point e ; wherefore the base b c shall coincide with the base ef , because the point b ...
Σελίδα 7
... wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle g cb , and the angle bcf to the angle cbg : and since it ...
... wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle g cb , and the angle bcf to the angle cbg : and since it ...
Σελίδα 8
... wherefore the angle fdc is like- wise greater than b cd ; much greater then is the angle bd c than the angle bed . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to the angle bcd ; but bdc has been proved to be ...
... wherefore the angle fdc is like- wise greater than b cd ; much greater then is the angle bd c than the angle bed . Again , because cb is equal to db , the angle bdc is equal ( i . 5 ) to the angle bcd ; but bdc has been proved to be ...
Σελίδα 9
... wherefore likewise the angle bac coincides with the angle e df , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two ...
... wherefore likewise the angle bac coincides with the angle e df , and is equal ( Sax . ) to it . Therefore if two triangles , & c . Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two ...
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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