The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 9
To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle ... 8 ) to the angle e af ; wherefore the given rectilineal angle ba c is bisected b f by the straight line af .
To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle ... 8 ) to the angle e af ; wherefore the given rectilineal angle ba c is bisected b f by the straight line af .
Σελίδα 10
1 ) upon a b an equilateral triangle a b c , and bisect ( i . 9 ) the angle ac b by the straight line cd . ab is cut into two equal parts in the point d . Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the ...
1 ) upon a b an equilateral triangle a b c , and bisect ( i . 9 ) the angle ac b by the straight line cd . ab is cut into two equal parts in the point d . Because a c is equal to cb , and cd common to the two triangles a cd , bcd ; the ...
Σελίδα 11
the circle egf meeting a b in f , g ; and bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b .
the circle egf meeting a b in f , g ; and bisect ( i . 10 ) fg in h , and join h cf , ch , cg ; the straight a f g b line ch , drawn from the d given point c , is perpendicular to the given straight line a b .
Σελίδα 13
LET a b c be a triangle , and let its side bc be produced to d , the exterior с angle a cd is greater than either of the interior opposite angles c ba , bac Bisect ( i . 10 ) a c in e , join be and produce it to f , and make ef equal to ...
LET a b c be a triangle , and let its side bc be produced to d , the exterior с angle a cd is greater than either of the interior opposite angles c ba , bac Bisect ( i . 10 ) a c in e , join be and produce it to f , and make ef equal to ...
Σελίδα 28
It is required to describe a parallelogram that shall be equal to the given triangle a b c , and have one of its angles equal to d . Bisect ( i . 10 ) bc in e , join a e , and at the point e in the straight line ec make ( i .
It is required to describe a parallelogram that shall be equal to the given triangle a b c , and have one of its angles equal to d . Bisect ( i . 10 ) bc in e , join a e , and at the point e in the straight line ec make ( i .
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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