The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 23
... parallel . LET ab , cd be equal and parallel straight lines , and joined towards the same parts by the straight lines ac , bd ; ac , bd are also equal and parallel . Join be ; and because a bis parallel to cd , and bc meets them , the ...
... parallel . LET ab , cd be equal and parallel straight lines , and joined towards the same parts by the straight lines ac , bd ; ac , bd are also equal and parallel . Join be ; and because a bis parallel to cd , and bc meets them , the ...
Σελίδα 24
... parallel ; and the diameter is the straight line joining two of its opposite angles . Let a cd b be a parallelogram ... parallel to cd , and bc meets them , the alternate angles c b abc , bcd are equal ( i . 29 ) to one another ; and ...
... parallel ; and the diameter is the straight line joining two of its opposite angles . Let a cd b be a parallelogram ... parallel to cd , and bc meets them , the alternate angles c b abc , bcd are equal ( i . 29 ) to one another ; and ...
Σελίδα 25
... parallel straight lines towards the same parts , are themselves equal and parallel ( i . 33 ) ; therefore e b , c h , are both equal and parallel , and e bch is a parallelogram ; and it is equal ( i . 35 ) to a bcd , because it is upon ...
... parallel straight lines towards the same parts , are themselves equal and parallel ( i . 33 ) ; therefore e b , c h , are both equal and parallel , and e bch is a parallelogram ; and it is equal ( i . 35 ) to a bcd , because it is upon ...
Σελίδα 26
... parallels bf , a d . The triangle abc is equal to the triangle def g a d h Produce ad both ways to the points g , h , and through b draw bg parallel ( i . 31 ) to ca , and through f draw fh parallel to ed . Then each of the figures gbca ...
... parallels bf , a d . The triangle abc is equal to the triangle def g a d h Produce ad both ways to the points g , h , and through b draw bg parallel ( i . 31 ) to ca , and through f draw fh parallel to ed . Then each of the figures gbca ...
Σελίδα 27
... parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same straight line and towards the same parts , are between the same ...
... parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same straight line and towards the same parts , are between the same ...
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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