The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 7
Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ; and they contain the angle fag common to the two triangles afc , ag b ; therefore the base fc is equal ( i .
Because a f is equal to ag , and a b to a c , the two sides fa , a c are equal to the two ga , a b , each to each ; and they contain the angle fag common to the two triangles afc , ag b ; therefore the base fc is equal ( i .
Σελίδα 9
Because a d is equal to a e , and a f is common to the two triangles da f , eaf ; the two sides da , d a f , are equal to the two sides ea , a f , each to each ; and the base df is equal to the base ef ; therefore the angle daf is equal ...
Because a d is equal to a e , and a f is common to the two triangles da f , eaf ; the two sides da , d a f , are equal to the two sides ea , a f , each to each ; and the base df is equal to the base ef ; therefore the angle daf is equal ...
Σελίδα 10
Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the two sides a C , cd are equal to bc , cd , each to each ; and the angle acd is equal to the angle bcd ; therefore the base a d is equal to the base ( i .
Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the two sides a C , cd are equal to bc , cd , each to each ; and the angle acd is equal to the angle bcd ; therefore the base a d is equal to the base ( i .
Σελίδα 11
Because fh is equal to hg , and hc common to the two triangles fh c , ghc , the two sides fh , h care equal to the two gh , hc , each to each ; and the base cf is equal ( 15 def . ) to the base cg ; therefore the angle chf is equal ( i ...
Because fh is equal to hg , and hc common to the two triangles fh c , ghc , the two sides fh , h care equal to the two gh , hc , each to each ; and the base cf is equal ( 15 def . ) to the base cg ; therefore the angle chf is equal ( i ...
Σελίδα 12
... but the angles a b c , a b d are likewise together equal to two right angles ; therefore the angles cba , a be are equal to the angles cba , abd : take away the common angle cba , the remaining angle a be is equal ( 3 ax . ) ...
... but the angles a b c , a b d are likewise together equal to two right angles ; therefore the angles cba , a be are equal to the angles cba , abd : take away the common angle cba , the remaining angle a be is equal ( 3 ax . ) ...
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angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole