The first six books of the Elements of Euclid, with numerous exercises |
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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
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
... and the / d angle bfc is equal to the angle cgb , and the base bc is common to the two triangles bfc , cgb ; wherefore the triangles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are ...
... and the / d angle bfc is equal to the angle cgb , and the base bc is common to the two triangles bfc , cgb ; wherefore the triangles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are ...
Σελίδα 8
5 ) to one f another : but the angle ecd is greater than the angle bed : wherefore the angle fdc is likewise greater than b c d ; much greater then is the angle bd c than the angle bed . Again , because cb is equal to db , the angle bdc ...
5 ) to one f another : but the angle ecd is greater than the angle bed : wherefore the angle fdc is likewise greater than b c d ; much greater then is the angle bd c than the angle bed . Again , because cb is equal to db , the angle bdc ...
Σελίδα 9
8 ) to the angle e af ; wherefore the given rectilineal angle ba c is bisected b f by the straight line af . Which was to be done . PROPOSITION X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two ...
8 ) to the angle e af ; wherefore the given rectilineal angle ba c is bisected b f by the straight line af . Which was to be done . PROPOSITION X. - PROBLEM . To bisect a given finite straight line , that is , to divide it into two ...
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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