The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 53
... , therefore db is equal to dn ; that is , the nearer to the least equal to the more remote , which is impossible . If therefore any point , & c . Q. E. D. PROPOSITION IX . THEOREM . If a point be taken BOOK III . PROP . VIII . 53.
... , therefore db is equal to dn ; that is , the nearer to the least equal to the more remote , which is impossible . If therefore any point , & c . Q. E. D. PROPOSITION IX . THEOREM . If a point be taken BOOK III . PROP . VIII . 53.
Σελίδα 54
Euclides. PROPOSITION IX . THEOREM . If a point be taken within a circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . LET the point d be taken within the ...
Euclides. PROPOSITION IX . THEOREM . If a point be taken within a circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . LET the point d be taken within the ...
Σελίδα 72
... taken without the circle abc , and from it let two straight lines dca and db be drawn , of which dca cuts the circle , and db meets it ; if the rectangle a d , dc be equal to the square of db ; db touches the circle . Draw ( iii . 17 ) ...
... taken without the circle abc , and from it let two straight lines dca and db be drawn , of which dca cuts the circle , and db meets it ; if the rectangle a d , dc be equal to the square of db ; db touches the circle . Draw ( iii . 17 ) ...
Σελίδα 74
... taken without a circle , there cannot be drawn from that point more than two equal straight lines to touch the circumfer- ence of the circle . 15. If an equilateral triangle be inscribed in a circle , and from a point in the ...
... taken without a circle , there cannot be drawn from that point more than two equal straight lines to touch the circumfer- ence of the circle . 15. If an equilateral triangle be inscribed in a circle , and from a point in the ...
Σελίδα 89
... taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be ...
... taken , and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ; or , if the multiple of the first be ...
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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