The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 3
... straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS . 3.
... straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS . 3.
Σελίδα 4
Euclides. POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be ...
Euclides. POSTULATES . I. Let it be granted that a straight line may be drawn from any one point to any other point . II . That a terminated straight line may be produced to any length in a straight line . III . And that a circle may be ...
Σελίδα 5
... straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw from ...
... straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw from ...
Σελίδα 6
... straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM ... LET abc , def be two triangles , which have the two sides a b , ac equal to the two sides de , df , each to each ...
... straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM ... LET abc , def be two triangles , which have the two sides a b , ac equal to the two sides de , df , each to each ...
Σελίδα 9
... straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ... LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ( i . 3 ) ...
... straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef ... LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ( i . 3 ) ...
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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