The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 4
... triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an ... abc shall be an equilateral triangle . Because the point a is the centre of the circle bcd , ac is equal ( 15 def . ) to ...
... triangle upon a given finite straight line . LET ab be the given straight line ; it is required to describe an ... abc shall be an equilateral triangle . Because the point a is the centre of the circle bcd , ac is equal ( 15 def . ) to ...
Σελίδα 5
... 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 bc ...
... 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 bc ...
Σελίδα 6
... triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc to the angle For , if the triangle abc be applied to def , so that the point a may be on ...
... triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc to the angle For , if the triangle abc be applied to def , so that the point a may be on ...
Σελίδα 7
... 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 , which are the angles upon the other side of the base ...
... 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 , which are the angles upon the other side of the base ...
Σελίδα 8
... triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is ... abc , def be two triangles , having the two sides a b , ac , equal to the two sides de , df , each to each 8 THE ...
... triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is ... abc , def be two triangles , having the two sides a b , ac , equal to the two sides de , df , each to each 8 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