The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 26
34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax . ) ; therefore the triangle a be is equal to the triangle dbc .
34 ) ; and the triangle dbc is the half of the parallelogram dbcf , because the diameter dc bisects it : but the halves of equal things are equal ( 7 ax . ) ; therefore the triangle a be is equal to the triangle dbc .
Σελίδα 33
Given an angle divided into any number of equal angles , to divide one half of the angle into the same number of equal angles . 6. Given the base , one of the angles at the base , and the sum of the other two sides , to construct the ...
Given an angle divided into any number of equal angles , to divide one half of the angle into the same number of equal angles . 6. Given the base , one of the angles at the base , and the sum of the other two sides , to construct the ...
Σελίδα 34
Each angle at the base of an isosceles triangle is equal to , or is less , or is greater than the half of the vertical angle , according as the triangle is right , obtuse , or acute - angled . 22. If the vertical angle of an isosceles ...
Each angle at the base of an isosceles triangle is equal to , or is less , or is greater than the half of the vertical angle , according as the triangle is right , obtuse , or acute - angled . 22. If the vertical angle of an isosceles ...
Σελίδα 37
If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half ...
If a straight line be divided into two equal parts , and also into two unequal parts , the rectangle contained by the unequal parts , together with the square of the line between the points of section , is equal to the square of half ...
Σελίδα 38
If a straight line be bisected , and produced to any point , the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of the ...
If a straight line be bisected , and produced to any point , the rectangle contained by the whole line thus produced , and the part of it produced , together with the square of half the line bisected , is equal to the square of 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