The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 46
... perpendicular be drawn from the right angle of a right - angled triangle to the hypotenuse , the square of the perpendicular is equal to the rectangle contained by the segments of the hypotenuse 9. If the base of a triangle be bisected ...
... perpendicular be drawn from the right angle of a right - angled triangle to the hypotenuse , the square of the perpendicular is equal to the rectangle contained by the segments of the hypotenuse 9. If the base of a triangle be bisected ...
Σελίδα 47
... perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . Definition VI . VII . The angle of a segment ...
... perpendicular falls is said to be farther from the centre . Definitions IV . and V. VI . A segment of a circle is the figure contained by a straight line and the circumference it cuts off . Definition VI . VII . The angle of a segment ...
Σελίδα 58
... perpendicular to fa , and let it meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is greater ( i . 19 ) than dg . But da is equal to dh ; therefore dh is greater than dg ...
... perpendicular to fa , and let it meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is greater ( i . 19 ) than dg . But da is equal to dh ; therefore dh is greater than dg ...
Σελίδα 60
... perpendicular to the line touching the circle . LET the straight line de touch the circle abc in the point c ; take the centre f , and draw the straight line fc ; fc is perpendicular to de . a For , if it be not , from the point f draw ...
... perpendicular to the line touching the circle . LET the straight line de touch the circle abc in the point c ; take the centre f , and draw the straight line fc ; fc is perpendicular to de . a For , if it be not , from the point f draw ...
Σελίδα 70
... perpendicular to ac ; therefore ag is equal ( iii . 3 ) to gc ; wherefore the rectangle a e , ec , together with the square of eg , is equal ( ii . 5 ) to the square of a g : to each of these equals add the square of gf ; therefore the ...
... perpendicular to ac ; therefore ag is equal ( iii . 3 ) to gc ; wherefore the rectangle a e , ec , together with the square of eg , is equal ( ii . 5 ) to the square of a g : to each of these equals add the square of gf ; therefore the ...
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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