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On an instrument for trisecting any angle

1901
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Proceedings of the Edinburgh Mathematical Society
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FIGURE 5. 2. Antiparallel to sides, (a) Let O and O' be two points, and let the intercepts cut off be by lines drawn antiparallel to the sides. AODE is isosceles. .-. ~ = cotODE = cot A. 2x .: a = 2a;cotA, (3 = 2ycotB, etc. a' = 2a;'cot A, etc. .-. ax' = 2xx'cotA = a'x or AO'DE = AOD'E', / V = 2y2/'cotB=£'// or AO'FG = AOFG', yz = 2«s'cotO = y'z or AO'HI * AOH'I'; and the six triangles will be equal if the conditions a;a:'cotA = yy'cotH = zz'cotC are fulfilled, or if xx':yy :zz : : tanA: tanB :

doi:10.1017/s0013091500032740
fatcat:jirk3za4ibatvbfi2gujwmbz5m