The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 7
Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . 9 PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall ...
Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . 9 PROPOSITION VI . - THEOREM . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to , the equal angles , shall ...
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 likeurise their bases equal ; the angle which is contained by the two sides of the one shall ...
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 likeurise their bases equal ; the angle which is contained by the two sides of the one shall ...
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 a c 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 a c 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 the ... made by any number of lines meeting in one point , are together equal to four right angles . a PROPOSITION XVI .
Q. E. D. CoR . 1. From this it is manifest , that , if two straight lines cut one another , the angles they make at the ... made by any number of lines meeting in one point , are together equal to four right angles . a PROPOSITION XVI .
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angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole