Show I TRISECTING AN ANGLE J I h r t rf i i L 4 f 1 L I J t- t A I rr Tt J J- J 1 h t 1 s J s t L LI IM i i iJ tj p 1 J J L t y 4 t t tJ a a I I j. j I l Ii lil r I t t fit r t l. l J 1 1 I o 1 l i W I d dS S r J. J t- t J. J t I r S t e J J 4 1 t TT i 4 r- r r j. j t f I C t r. r t. t i 1 f L p it 1 rf N j r q 1 f l C. t oj to I 1 V h 5 J J 4 fl 1 r I iff 1 t tI 7 A AI 1 I i 4 LI r. r J I. I u i s II k l t A I i. 1 I I iI i So I J t t i 1 Jt 1 r I i t. t f 1 1 Jo v 0 By By ALFRED H. H THIESSEN The problem of bisecting a an angle anele Isan is isan I an old one oue i in and md is is' 5 quite simple Most after alter having ing learned how to bisect l n angle are given cn the tho problem of trisecting an angle n lc which I J think has never nevor been becu done b. b by tho the method of ot pure pnra The Tho following is a d description of a ama ma bj n by bi t the be writer niter which ac- ac tho the purpose This machine ls l's is 15 shown diagrammatical lla in the fi figure lr I anti and ma may bb ho constructed as follows Draw an nn angle Jo JorON MON rON a right richt rightangle an angle le or or quarter one of a no eli circle This an angle IB may be ba readily trisected by constructing con con- a it t- t tho apex 0 O an angles lc MOl MOg arid anti NOP NOE equal to oO 30 O degrees thou then angle anide anle an an- gle ide le FOE equals angle anglo MOE and NOi NO Take OA OB OC OD aD AE and BF equal in len length then EC EO and FD will wiIl b be equal to each other and equal to OA Consider all the circles hinges but out construct the machine so that rods rode OE and OF will wilI slide through h rin rings 8 E I and F respectively 1 From yom construction it will be read ily ny seen SeOn n that no bO matter how much or how bow little tho ancle MON is is' increased or diminished the tho lines OE and OF will always bo lo lines Jines of trisection ft rt It is practicable to use uee thi this machine with all angles up to SOO de degrees Tees Angles An An- glee larger er thau than 80 de degrees rC I may mar bo be faceted bisected and then the tho two parts tr trisected tri trL 8 with the tho machine Two of ot tho the smaller parts will b bo be third ono of ot tho the oril original an angle le |