The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 2
2 these two is somewhere upon one of those straight lines , and the other upon the other line . 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 ...
2 these two is somewhere upon one of those straight lines , and the other upon the other line . 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 ...
Σελίδα 4
POSTULATES . a I. Let it be granted that a straight line may be drawn from any one point to any other point . II . ... LET ab be the given straight line ; it is required to describe an equilateral ; triangle upon it .
POSTULATES . a I. Let it be granted that a straight line may be drawn from any one point to any other point . II . ... LET ab be the given straight line ; it is required to describe an equilateral ; triangle upon it .
Σελίδα 5
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the triangle a bc is therefore equilateral , and it is described upon the given straight line ab . Which was to be done . d a PROPOSITION II .
therefore ca is equal to cb ; wherefore ca , ab , bc are equal to one another ; and the triangle a bc is therefore equilateral , and it is described upon the given straight line ab . Which was to be done . d a PROPOSITION II .
Σελίδα 6
line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part a e has been cut off equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If two triangles have two sides of the one ...
line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part a e has been cut off equal to c the less . Which was to be done . PROPOSITION IV . — THEOREM . If two triangles have two sides of the one ...
Σελίδα 9
... viz . ab to d e , and a c to df ; and le also the base b c equal to the base e f . The angle bac is a d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so that the point b be on e , and the straight line ...
... viz . ab to d e , and a c to df ; and le also the base b c equal to the base e f . The angle bac is a d 8 equal to the angle ed f . For , if the triangle a b c be applied to def , so that the point b be on e , and the straight line ...
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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