The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 10
... equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two ...
... equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b . a d e b Because dc is equal to ce , and fc common to the two triangles d cf , ecf ; the two ...
Σελίδα 31
... equilateral ; it is therefore a square , and it is described upon the given straight line a b . the given straight line a b . Which was to be done . COR . Hence every parallelogram that has one right angle has all its angles right ...
... equilateral ; it is therefore a square , and it is described upon the given straight line a b . the given straight line a b . Which was to be done . COR . Hence every parallelogram that has one right angle has all its angles right ...
Σελίδα 37
... equilateral . It is likewise rectangular ; for cg is parallel to bk , and cb meets them ; the angles d ' kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also ...
... equilateral . It is likewise rectangular ; for cg is parallel to bk , and cb meets them ; the angles d ' kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also ...
Σελίδα 74
... equilateral triangle be inscribed in a circle , and from a point in the circumference straight lines be drawn to the three angles of the tri- angle , the greatest of these lines is equal to the sum of the other two . 16. If a ...
... equilateral triangle be inscribed in a circle , and from a point in the circumference straight lines be drawn to the three angles of the tri- angle , the greatest of these lines is equal to the sum of the other two . 16. If a ...
Σελίδα 79
... equilateral . It is also rectan- gular ; for the straight line bd , being the dia- b meter of the circle a b c d , bad is a semicircle ; wherefore the angle bad is a right ( iii . 31 ) angle ; for the same reason , each of the angles ...
... equilateral . It is also rectan- gular ; for the straight line bd , being the dia- b meter of the circle a b c d , bad is a semicircle ; wherefore the angle bad is a right ( iii . 31 ) angle ; for the same reason , each of the angles ...
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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