The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 24
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . A parallelogram is a four - sided figure , of which the opposite sides are parallel ...
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . A parallelogram is a four - sided figure , of which the opposite sides are parallel ...
Σελίδα 25
that is , the parallelogram a b c d is equal to the parallelogram e bcf . Therefore parallelograms upon the same base , & c . Q. E. D. PROPOSITION XXXVI . — THEOREM . Parallelograms upon equal bases , and between the same parallels ...
that is , the parallelogram a b c d is equal to the parallelogram e bcf . Therefore parallelograms upon the same base , & c . Q. E. D. PROPOSITION XXXVI . — THEOREM . Parallelograms upon equal bases , and between the same parallels ...
Σελίδα 26
31 ) e , be parallel to ca ; and through c draw с cf parallel to bd ; therefore each of b the figures ebca , dbcf is a parallelogram ; and ebca is equal ( i . 35 ) to dbcf , because they are upon the same base bc , and between the same ...
31 ) e , be parallel to ca ; and through c draw с cf parallel to bd ; therefore each of b the figures ebca , dbcf is a parallelogram ; and ebca is equal ( i . 35 ) to dbcf , because they are upon the same base bc , and between the same ...
Σελίδα 27
If a parallelogram and triangle be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram a b c d and the triangle e bc be upon the same base b c , and between the ...
If a parallelogram and triangle be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram a b c d and the triangle e bc be upon the same base b c , and between the ...
Σελίδα 28
base b c , and between the same parallels b c , a e ; a d e the parallelogram abcd is double of the triangle e b c Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle e bc , because they are upon the same base b c ...
base b c , and between the same parallels b c , a e ; a d e the parallelogram abcd is double of the triangle e b c Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle e bc , because they are upon the same base b c ...
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angle a b c angle bac applied 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 interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole