The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 2
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
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 26
35 ) to dbcf , because they are upon the same base bc , and between the same parallels bc , ef ; and the triangle a b c is the half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the ...
35 ) to dbcf , because they are upon the same base bc , and between the same parallels bc , ef ; and the triangle a b c is the half of the parallelogram ebca , because the diameter a b bisects it ( i . 34 ) ; and the triangle dbc is the ...
Σελίδα 28
34 ) of the triangle a b c , because the diameter ac divides it into two equal parts ; wherefore a bed b is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . PROBLEM .
34 ) of the triangle a b c , because the diameter ac divides it into two equal parts ; wherefore a bed b is also double of the triangle e bc . Therefore , if a parallelogram , & c . Q. E. D. PROPOSITION XLII . PROBLEM .
Σελίδα 29
The complements of the parallelograms , which are about the diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pah d . rallelograms about a c ...
The complements of the parallelograms , which are about the diameter of any parallelogram , are equal to one another . LET abcd be a parallelogram , of which the diameter is a c , and eh , fg , the pah d . rallelograms about a 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