The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... bc , or cba ; that which is contained by a b , db , is named the angle abd , or dba ; and that which is con- tained ... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference ...
... bc , or cba ; that which is contained by a b , db , is named the angle abd , or dba ; and that which is con- tained ... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference ...
Σελίδα 49
... bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the ... circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle ...
... bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the ... circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle ...
Σελίδα 51
... bc , c d g cut one another in the points b , c ; they have not the same centre . For , if it be possible , let e be ... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
... bc , c d g cut one another in the points b , c ; they have not the same centre . For , if it be possible , let e be ... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and ...
Σελίδα 53
... circumference h1kg , the least is dg between the point d and the dia- meter a g ; and the nearer to it is always less than the more remote , viz . dk than dl , and dl than dh . d Take ( i . 3 ) m the centre of the circle a bc , and join ...
... circumference h1kg , the least is dg between the point d and the dia- meter a g ; and the nearer to it is always less than the more remote , viz . dk than dl , and dl than dh . d Take ( i . 3 ) m the centre of the circle a bc , and join ...
Σελίδα 54
... circumference , and dc greater de ( iii . 7 ) than db , and db than da . But they are likewise equal , which is impossible ; there- fore e is not the centre of the circle a bc . In like manner it may be demonstrated that no other point ...
... circumference , and dc greater de ( iii . 7 ) than db , and db than da . But they are likewise equal , which is impossible ; there- fore e is not the centre of the circle a bc . In like manner it may be demonstrated that no other point ...
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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