The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 24
... third angle of the one to the third angle of the other ( i . 26 ) , viz . the side ab to the side cd , and ac to bd , and the angle bac equal to the angle bdc and because the angle abc is equal to the angle bcd , and the angle cbd to ...
... third angle of the one to the third angle of the other ( i . 26 ) , viz . the side ab to the side cd , and ac to bd , and the angle bac equal to the angle bdc and because the angle abc is equal to the angle bcd , and the angle cbd to ...
Σελίδα 34
... third side . 20. The sum of two sides of a triangle is greater than twice the line joining the vertex and the middle of the base .. 21. Each angle at the base of an isosceles triangle is equal to , or is less , or is greater than the ...
... third side . 20. The sum of two sides of a triangle is greater than twice the line joining the vertex and the middle of the base .. 21. Each angle at the base of an isosceles triangle is equal to , or is less , or is greater than the ...
Σελίδα 52
... third , be , ef , are greater than bf ; but ae is equal to a eb ; therefore a e , ef , that is af , is greater than bf . Again , because be is equal to ce , and fe common to the triangles bef , cef , the two sides be , ef are equal to ...
... third , be , ef , are greater than bf ; but ae is equal to a eb ; therefore a e , ef , that is af , is greater than bf . Again , because be is equal to ce , and fe common to the triangles bef , cef , the two sides be , ef are equal to ...
Σελίδα 81
... third angle . TAKE any straight line a b , and divide ( ii . 11 ) it in the point c , so that the rectangle a b , bc be equal to the square of ca ; and from the centre a , at the distance a b , describe the circle bd e , in which place ...
... third angle . TAKE any straight line a b , and divide ( ii . 11 ) it in the point c , so that the rectangle a b , bc be equal to the square of ca ; and from the centre a , at the distance a b , describe the circle bd e , in which place ...
Σελίδα 82
... third angle . Which was to be done . PROPOSITION XI . - PROBLEM . To inscribe an equilateral and equiangular pentagon in a given circle . LET abcde be the given circle ; it is required to inscribe an equilateral and equiangular pentagon ...
... third angle . Which was to be done . PROPOSITION XI . - PROBLEM . To inscribe an equilateral and equiangular pentagon in a given circle . LET abcde be the given circle ; it is required to inscribe an equilateral and equiangular pentagon ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle