. Memoirs and proceedings of the Manchester Literary & Philosophical Society. opens up a little-studied fieldof Geometry abounding in interesting applications. TJie Method of Archimedes: One of the ways ofsolving geometrical problems adopted by the Greek 1 See J. (low, A Short History of Greek Squaring the Circle : a History of the Problem. 1913. -1 Circa 2S7-212 October ylli, n)i5- 2 Gee and Adamson, Trisecting an Angle. geometers is expressed by the word veixris, which presentsdifficulties of exact translation. It has been rendered byinclinalio in Latin, and by einschiebu
. Memoirs and proceedings of the Manchester Literary & Philosophical Society. opens up a little-studied fieldof Geometry abounding in interesting applications. TJie Method of Archimedes: One of the ways ofsolving geometrical problems adopted by the Greek 1 See J. (low, A Short History of Greek Squaring the Circle : a History of the Problem. 1913. -1 Circa 2S7-212 October ylli, n)i5- 2 Gee and Adamson, Trisecting an Angle. geometers is expressed by the word veixris, which presentsdifficulties of exact translation. It has been rendered byinclinalio in Latin, and by einschiebung in German. Thislatter word signifies putting in, intercalation, orinterpolation, meanings only partly expressing what isimplied by a vevcri^ which requires the interpolation of aline in a diagram under special conditions, as is evidentin the following construction that Archimedes used tosolve the trisection problem. Let ABC (Fig. i) be the angle to be trisected. WithB as centre and any radius BA, describe a circle. ProduceCB to F. then from A draw a line AED so that the. D F Fig. I. Method of Archir^edes. intercept ED is equal to the radius of the circle. Herethe i>eu(ris requires the interpolation of a line passingthrough a given point A and drawn so as to cut thecircle in a point E that must satisfy the condition thatED is of the specified length. This can only be doneby certain indirect methods as stated below. If wesuppose the operation be accomplished, then— The angle EBF= - the angle ABC, or a = - \d3 for y = 2« and (3 = a + BG drawn parallel to AD will be a trisector ofthe angle ABC. Manchester Memoirs, Vol. lix. (1915), No. \%. 3 The indirect methods referred to above may beclassed as follows :— Methods involving the use of loci other than the circle and straight methods, with or without the use of special measuring methods involving the use of a linkwork application of these method
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