The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 7
... ab is not unequal to a c , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. b d COR . Hence every equiangular triangle is also equilateral . a PROPOSITION VII . — THEOREM . Upon the same base BOOK I. PROP . VI . 7.
... ab is not unequal to a c , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. b d COR . Hence every equiangular triangle is also equilateral . a PROPOSITION VII . — THEOREM . Upon the same base BOOK I. PROP . VI . 7.
Σελίδα 8
... Q. E. D. PROPOSITION VIII . — THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be ...
... Q. E. D. PROPOSITION VIII . — THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is contained by the two sides of the one shall be ...
Σελίδα 9
... Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ...
... Q.E.D. PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ...
Σελίδα 12
... Q. E. D. PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in ...
... Q. E. D. PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in ...
Σελίδα 13
... Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at ... PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of ...
... Q. E. D. COR . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at ... PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of ...
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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