. Memoirs and proceedings of the Manchester Literary & Philosophical Society. curve is defined as the locus of a point P{Fig. 2), such that the angle PAC is three times the anglePBC, where A and B are fixed points and C lies on BA f ^^ P F< t _,*•** 1^ *&* ~^^^ • /B D A C Fig. 2. Trisectrix of Maclaurin. produced. The curve can easily be constructed as follows:Bisect AB at D. Draw DE perpendicular to B draw any straight line intersecting DE at !■. Gomes Teixcira, Proc. Edinburgh Math. Soc, Vol. 30, p. 96, 1911-12. 4 Gee AND ADAMSON, Trisecting an Angle. Join AF. With A as cen
. Memoirs and proceedings of the Manchester Literary & Philosophical Society. curve is defined as the locus of a point P{Fig. 2), such that the angle PAC is three times the anglePBC, where A and B are fixed points and C lies on BA f ^^ P F< t _,*•** 1^ *&* ~^^^ • /B D A C Fig. 2. Trisectrix of Maclaurin. produced. The curve can easily be constructed as follows:Bisect AB at D. Draw DE perpendicular to B draw any straight line intersecting DE at !■. Gomes Teixcira, Proc. Edinburgh Math. Soc, Vol. 30, p. 96, 1911-12. 4 Gee AND ADAMSON, Trisecting an Angle. Join AF. With A as centre and AF as radius, describea circle cutting BF at P. The locus of P is the curverequired, since obviously the angle PA C is equal to threetimes the angle PBA. If KAC, denoted by /3, be the angle to be trisected,find //, the point where AK cuts the trisectrix. Join the angle HBA (or a) is one-third of the angleKAC. II. Use of the Lima con of Pascals Let A (Fig. 3) be a point on the circumference of acircle of which B is the centre. Through A draw any D. Fig. 3. Use of Limacon. straight line cutting the circle at Pt and on this line markoff a length PQ equal to a constant length. The locusof Q is a limacon curve. The special form of limaconused for the trisection of angles is called the trisectrix, 6 1623-1662. Manchester Memoirs, Vol. lix, (1915), No. 1*5. 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
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Keywords: ., bookcentury1800, bookdecade1880, booksubjectscience, bookyear1888
