The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 13
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed are equal ...
Euclides. are equal to the angles aed , deb . Take away the common angle a ed , and the remaining angle cea is equal ( 3 ax . ) to the remaining angle de b . In the same manner it can be demonstrated , that the angles ceb , aed are equal ...
Σελίδα 20
... common angle bgh ; therefore the remaining angle agh is equal to the remaining angle ghd ; and they are alternate angles ; there- fore a b is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXIX . - THEOREM ...
... common angle bgh ; therefore the remaining angle agh is equal to the remaining angle ghd ; and they are alternate angles ; there- fore a b is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXIX . - THEOREM ...
Σελίδα 23
... common vertex of the triangles : that is ( i . 15 , cor . 2 ) , together with four right angles . Therefore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides ...
... common vertex of the triangles : that is ( i . 15 , cor . 2 ) , together with four right angles . Therefore all the angles of the figure , together with four right angles , are equal to twice as many right angles as the figure has sides ...
Σελίδα 24
... common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third angle of the other ( i . 26 ) , viz . the side ab to the ...
... common to the two triangles , which is adjacent to their equal angles ; therefore their other sides shall be equal , each to each , and the third angle of the one to the third angle of the other ( i . 26 ) , viz . the side ab to the ...
Σελίδα 25
... common ; there- fore the whole , or the remainder , ae is equal ( 2 or 3 ax . ) to the whole , or the remainder df ; ab also is equal to dc ; and the two ea , ab are a d e f a e d f b b therefore equal to the two fd , d c , each to each ...
... common ; there- fore the whole , or the remainder , ae is equal ( 2 or 3 ax . ) to the whole , or the remainder df ; ab also is equal to dc ; and the two ea , ab are a d e f a e d f b b therefore equal to the two fd , d c , each to each ...
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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