. Memoirs and proceedings of the Manchester Literary & Philosophical Society. Fig. 16. Lowentlmrns Method (No. 1). I. Let ABC {Fig. 16) be the angle to be B as centre describe a circle cutting off BA, the chord AC. Through B place a straight lineBQR so that A Q shall be equal to the length of the chordAR. Then the angle A BR is one-third of the angle prove this, bisect RQ at T, produce RQ to meet thecircle at E, join A to F and to T. Then : 13 See CEuvres de Christian Huygens. Socictc Hollandaise des Sciences. Vol. I. (1S8S.) 24 Gee AND A DAMSON, Trisecting an Ang
. Memoirs and proceedings of the Manchester Literary & Philosophical Society. Fig. 16. Lowentlmrns Method (No. 1). I. Let ABC {Fig. 16) be the angle to be B as centre describe a circle cutting off BA, the chord AC. Through B place a straight lineBQR so that A Q shall be equal to the length of the chordAR. Then the angle A BR is one-third of the angle prove this, bisect RQ at T, produce RQ to meet thecircle at E, join A to F and to T. Then : 13 See CEuvres de Christian Huygens. Socictc Hollandaise des Sciences. Vol. I. (1S8S.) 24 Gee AND A DAMSON, Trisecting an CAR=2 L RAT= 2 L CR = 2 arc AR. ThereforeTherefore angle ABC= 3 angle ABR. The placing of the line BR may be facilitated by describinga semicircle on BA as diameter and making trials untilQR is bisected by the Fig. 17. Lowenthurns Method (No. 2). 2. Let ABC {Fig. 17) be the angle to be trisected. Asbefore, describe a circle with centre B and draw the chordAC. Draw AT perpendicular to AC. Place a tangent tothe circle so that the length PQ intercepted between ATand AC is bisected at the point of contact D. Join B to the angle BBC is one-third of the angle ABC Theproof is similar to that preceding, for it is easily seen thatthe chord DC is equal to RC Manchester Memoirs, Vol. lix. (1915), No. 13. 25 V. Another method of trisecting an angle involvingthe drawing of a tangent was suggested to one of theauthors by the fact that a limacon is a pedal curve to afixed circle with reference to a fixed point. Let ABC{Fig. 18) be the angle to be trisected. With any point A
Size: 1586px × 1575px
Photo credit: © Reading Room 2020 / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1800, bookdecade1880, booksubjectscience, bookyear1888
