The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 45
... remaining rectangle be , ef is equal to the square of eh : but the rect- angle contained by be , ef is the parallelogram bd , because ef is equal to ed ; therefore bd is equal to the square of eh ; but bd is equal to the rectilineal ...
... remaining rectangle be , ef is equal to the square of eh : but the rect- angle contained by be , ef is the parallelogram bd , because ef is equal to ed ; therefore bd is equal to the square of eh ; but bd is equal to the rectilineal ...
Σελίδα 46
... remaining side of the triangle . 4. Given the sum of the squares of any ... angle of a right - angled triangle to the hypotenuse , the square of the ... angle . 10. If the middle points of the opposite sides of a quadrilateral figure be ...
... remaining side of the triangle . 4. Given the sum of the squares of any ... angle of a right - angled triangle to the hypotenuse , the square of the ... angle . 10. If the middle points of the opposite sides of a quadrilateral figure be ...
Σελίδα 57
... angle a fe is a right angle ; and , for the like reason , the squares of eg , gc , are equal to the square of ec ... remaining square of fe is equal to the remaining square of eg , and the straight line ef is therefore equal to eg . But ...
... angle a fe is a right angle ; and , for the like reason , the squares of eg , gc , are equal to the square of ec ... remaining square of fe is equal to the remaining square of eg , and the straight line ef is therefore equal to eg . But ...
Σελίδα 59
... angle of the semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . Q. E. D. COR . From this it is manifest , that the straight line which is drawn at right angles ...
... angle of the semicircle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . Q. E. D. COR . From this it is manifest , that the straight line which is drawn at right angles ...
Σελίδα 61
... angle at the circumference , upon the same base , that is , upon the same part of the circumference . LET abc be a ... remaining angle bec is double of the remaining angle.bd c . Therefore the g angle at the centre , & c . Q. E. D. ...
... angle at the circumference , upon the same base , that is , upon the same part of the circumference . LET abc be a ... remaining angle bec is double of the remaining angle.bd c . Therefore the g angle at the centre , & c . Q. E. D. ...
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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