The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 7
... triangles a fc , agb ; there- fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each ...
... triangles a fc , agb ; there- fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each ...
Σελίδα 8
... triangles is without the other triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is greater than the angle bcd ; therefore the angle adc is greater also than then is the ...
... triangles is without the other triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is greater than the angle bcd ; therefore the angle adc is greater also than then is the ...
Σελίδα 9
... triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and af is common to the two triangles da f , eaf ; the two sides da , af , are equal to the two sides ea , af , each to each ; and the ...
... triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and af is common to the two triangles da f , eaf ; the two sides da , af , are equal to the two sides ea , af , each to each ; and the ...
Σελίδα 10
... triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two sides dc , cf ...
... triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two sides dc , cf ...
Σελίδα 11
... triangles fhc , ghc , the two sides fh , hc are equal to the two gh , hc , each to each ; and the base c f is equal ( 15 def . ) to the base c g ; therefore the angle chf is equal ( i . 8 ) to the angle chg ; and they are adjacent ...
... triangles fhc , ghc , the two sides fh , hc are equal to the two gh , hc , each to each ; and the base c f is equal ( 15 def . ) to the base c g ; therefore the angle chf is equal ( i . 8 ) to the angle chg ; and they are adjacent ...
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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