. Memoirs and proceedings of the Manchester Literary & Philosophical Society. 5 and is obtained by using the radius AB as the constantlength. Let ABC (or /3) be the angle to be trisected. Pro-duce CB to meet the trisectrix at D. Join DA, cuttingthe circle at E. Then, since DE equals AB, the angleADB, denoted by a, is one-third of the angle ABC. On comparing Fig. 3 with Fig. 1 it will be apparentthat this solves the vevans of Archimedes. III. Use of the Conchoid of Nicomedes? This curve is such that the straight line joining anypoint on the curve with a given point is cut by a givenstraight lin
. Memoirs and proceedings of the Manchester Literary & Philosophical Society. 5 and is obtained by using the radius AB as the constantlength. Let ABC (or /3) be the angle to be trisected. Pro-duce CB to meet the trisectrix at D. Join DA, cuttingthe circle at E. Then, since DE equals AB, the angleADB, denoted by a, is one-third of the angle ABC. On comparing Fig. 3 with Fig. 1 it will be apparentthat this solves the vevans of Archimedes. III. Use of the Conchoid of Nicomedes? This curve is such that the straight line joining anypoint on the curve with a given point is cut by a givenstraight line so that the segment between the curve andthe straight line is constant. The conchoid has been used in several ways to solvethe trisection problem. Proclus states that Nicomedes, the inventor of thecurve, applied it to trisect an angle, but Pappus claimsthis application. It is possible, however, that Archimedeshimself used a curve of the nature of the conchoid, inorder to solve the vevcris problem already mentioned. The simplest application of the conchoid is as follows :. />;r. 4. Use of Conchoid,0 Circa 1 So 6 Gee AND Adamson, Trisecting an Angle. Let ABC {Fig. 4) be the angle /3 to be trisected. WithB as centre and any radius BA describe a circle. ThroughA draw any straight line cutting CB at R. Join AR mark off RS equal to BA. -Then the locus ofvS is the conchoid required, and E, its intersection withthe circle, is the point through which A ED must bedrawn in order that the angle ADB, or a, shall be one-third of the angle ABC. Pappus showed that any angle ABC {Figs. 5 and 6)
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectscience, bookyear1888
