The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 6
Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to ...
Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to ...
Σελίδα 7
4 ) to the base gb , and the triangle afc to the triangle agb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle acf to ...
4 ) to the base gb , and the triangle afc to the triangle agb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ; viz . the angle acf to ...
Σελίδα 12
Again , because the angle d ba is equal to the two angles dbe , e ba , add to these equals the angle a b c , therefore ... to the remaining angle a b d , the less to the greater , which is impossible ; therefore be is not in the same ...
Again , because the angle d ba is equal to the two angles dbe , e ba , add to these equals the angle a b c , therefore ... to the remaining angle a b d , the less to the greater , which is impossible ; therefore be is not in the same ...
Σελίδα 13
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 , a ed are equal . Therefore , if two straight lines , & c .
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 , a ed are equal . Therefore , if two straight lines , & c .
Σελίδα 20
13 ) to two right angles ; the angles a g h , bgh , are equal to the angles bgh , ghd : take away the common angle bgh ; therefore the remaining angle a gh is equal to the remaining angle ghd ; and they are alternate angles ; therefore ...
13 ) to two right angles ; the angles a g h , bgh , are equal to the angles bgh , ghd : take away the common angle bgh ; therefore the remaining angle a gh is equal to the remaining angle ghd ; and they are alternate angles ; therefore ...
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a b c angle a b c angle bac 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 join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole