The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 10
4 ) d b , and the straight line a b is divided into two equal parts in the point d . Which was to be done . d b PROPOSITION XI . — PROBLEM . a To draw a straight line at right angles to a given straight line , from a given point in the ...
4 ) d b , and the straight line a b is divided into two equal parts in the point d . Which was to be done . d b PROPOSITION XI . — PROBLEM . a To draw a straight line at right angles to a given straight line , from a given point in the ...
Σελίδα 23
e a : four right angles , are equal to twice as many right angles as the figure has sides . d For any rectilineal figure a bcde , can be divided into as many triangles as the figure has sides , by drawing straight lines from a point f ...
e a : four right angles , are equal to twice as many right angles as the figure has sides . d For any rectilineal figure a bcde , can be divided into as many triangles as the figure has sides , by drawing straight lines from a point f ...
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 35
If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line ...
If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line , and the several parts of the divided line ...
Σελίδα 36
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole lihe . LET the straight line a b be divided into any two parts in the point c ...
If a straight line be divided into any two parts , the rectangles contained by the whole and each of the parts are together equal to the square of the whole lihe . LET the straight line a b be divided into any two parts in the point 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