The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 5
... angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done ... triangle da b , and produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance ...
... angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done ... triangle da b , and produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance ...
Σελίδα 6
... triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the ...
... triangle a b c shall coincide with the whole triangle def , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle a b c to the angle def , and the ...
Σελίδα 7
... angles cbg , bcf are also equal ; the remaining augle abc is therefore equal to the remaining angle a cb , which are the angles at the base of the triangle a b c and it has also been proved that the angle fbc is equal to the angle gcb ...
... angles cbg , bcf are also equal ; the remaining augle abc is therefore equal to the remaining angle a cb , which are the angles at the base of the triangle a b c and it has also been proved that the angle fbc is equal to the angle gcb ...
Σελίδα 8
... angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is greater than the angle bcd ; therefore the angle ... abc , def be two triangles , having the two sides a b , ac , equal to the two sides de , df , each to each 8 THE ...
... angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is greater than the angle bcd ; therefore the angle ... abc , def be two triangles , having the two sides a b , ac , equal to the two sides de , df , each to each 8 THE ...
Σελίδα 9
... angle bac is equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal ...
... angle bac is equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal ...
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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