The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 7
... ab is not unequal to ac , 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 C PROPOSITION VII . - THEOREM . Upon the same base BOOK I. PROP . VI . 7.
... ab is not unequal to ac , 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 C PROPOSITION VII . - THEOREM . Upon the same base BOOK I. PROP . VI . 7.
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... 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 ...
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... 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 ab , and from ac cut ( i ...
... 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 ab , and from ac cut ( i ...
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... 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 ...
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... Q. E. D. COR . 1. From this it is manifest , that , if two straight lines ... PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the ... Q. E. D. b PROPOSITION XVII . - THEOREM . c d 3 Any two angles of a ...
... Q. E. D. COR . 1. From this it is manifest , that , if two straight lines ... PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the ... Q. E. D. b PROPOSITION XVII . - THEOREM . c d 3 Any two angles of a ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle