The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 2
Thus the angle which is contained by the straight lines ab , cb , is named the angle a b c , or cba ; that which is contained by a b , db , is named the angle a bd ... Trilateral figures , or triangles , by three straight lines . XXII .
Thus the angle which is contained by the straight lines ab , cb , is named the angle a b c , or cba ; that which is contained by a b , db , is named the angle a bd ... Trilateral figures , or triangles , by three straight lines . XXII .
Σελίδα 4
LET ab be the given straight line ; it is required to describe an equilateral ; triangle upon it . From the centre a , at the distance ... ca , cb , to the points a , b ; abc shall be an equilateral triangle . Because the point a is the ...
LET ab be the given straight line ; it is required to describe an equilateral ; triangle upon it . From the centre a , at the distance ... ca , cb , to the points a , b ; abc shall be an equilateral triangle . Because the point a is the ...
Σελίδα 6
If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles ... Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the ...
If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles ... Wherefore the whole triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the ...
Σελίδα 7
THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET a b c be a triangle having the angle a b c equal to the angle acb ...
THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall also be equal to one another . LET a b c be a triangle having the angle a b c equal to the angle acb ...
Σελίδα 8
Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are ... LET a b c , d ef be two triangles , having the two sides a b , a c , equal to the two sides de , d f , each to 8 THE ...
Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are ... LET a b c , d ef be two triangles , having the two sides a b , a c , equal to the two sides de , d f , each to 8 THE ...
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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