The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 86.
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 8
Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are ... Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because a c is ...
Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are ... Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because a c is ...
Σελίδα 9
For , if the triangle a b c be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coincide with the point f , beb се f cause bc is equal to ef . Therefore bc coinciding with ef ...
For , if the triangle a b c be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coincide with the point f , beb се f cause bc is equal to ef . Therefore bc coinciding with ef ...
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
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 ...
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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