The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 5
bg ; but it has been shewn that bc is equal to bg ; wherefore al and bč 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 .
bg ; but it has been shewn that bc is equal to bg ; wherefore al and bč 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 .
Σελίδα 14
18 ) ; but it is not ; b therefore the side a c is not less than a b ; and it has been shewn that it is not equal to a b ; therefore a c is greater than a b . Wherefore the greater angle , & c . Q. E. D. PROPOSITION XX .
18 ) ; but it is not ; b therefore the side a c is not less than a b ; and it has been shewn that it is not equal to a b ; therefore a c is greater than a b . Wherefore the greater angle , & c . Q. E. D. PROPOSITION XX .
Σελίδα 15
... the triangle ced are greater than cd , add db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has been shewn that ba , a c , are greater than be , ec , much greater then are b ba , a c than bd , dc .
... the triangle ced are greater than cd , add db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has been shewn that ba , a c , are greater than be , ec , much greater then are b ba , a c than bd , dc .
Σελίδα 18
24 ) than the base e f ; but it is not ; therefore the angle bac is not less than the angle edf ; b sf and it was shewn that it is not equal to it ; therefore the angle bac is greater than the angle ed f . than the angle edf .
24 ) than the base e f ; but it is not ; therefore the angle bac is not less than the angle edf ; b sf and it was shewn that it is not equal to it ; therefore the angle bac is greater than the angle ed f . than the angle edf .
Σελίδα 21
29 ) to the angle gkd ; and it was shewn that the angle agk is equal to the angle k d ghf ; therefore also a gk is equal to gk d ; and they are alternate angles ; therefore a b is parallel ( i . 27 ) to cd ; Wherefore , straight lines ...
29 ) to the angle gkd ; and it was shewn that the angle agk is equal to the angle k d ghf ; therefore also a gk is equal to gk d ; and they are alternate angles ; therefore a b is parallel ( i . 27 ) to cd ; Wherefore , straight lines ...
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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