The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI . And this point is called the centre of the circle . XVII . A diameter of a circle ...
... circumference , and is such that all straight lines drawn from a certain point within the figure to the circumference , are equal to one another . XVI . And this point is called the centre of the circle . XVII . A diameter of a circle ...
Σελίδα 47
... circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ; for , if the circles ... circumference it cuts off . Definition VI . VII . The angle of a segment is that which BOOK III . DEFINITIONS ...
... circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ; for , if the circles ... circumference it cuts off . Definition VI . VII . The angle of a segment is that which BOOK III . DEFINITIONS ...
Σελίδα 48
... circumference . VIII . An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment . IX . And an ...
... circumference . VIII . An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the extremities of the straight line which is the base of the segment . IX . And an ...
Σελίδα 49
... circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the circle . d ...
... circumference of a circle , the straight line which joins them shall fall within the circle . LET a b c be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b shall fall within the circle . d ...
Σελίδα 51
... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and of any others , that which is nearer to the line which passes through the centre is always greater than one more BOOK ...
... circumference , the greatest is that in which the centre is , and the other part of that diameter is the least ; and of any others , that which is nearer to the line which passes through the centre is always greater than one more BOOK ...
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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