. Transactions and proceedings of the New Zealand Institute . accuracy of the construction increases rapidly asthe angle diminishes, the error being approximately proportional to thecube of the angle. If the given angle be a right angle the error is 0067 of a degree, foran angle of 45° it is 0 008 of a degree, and for one of 30° it is only 0002of a degree. In conclusion, we shall indicate briefly how the trisection of any anglebetween 0° and 180° can be derived from that of an angle not greater Segae.—Insanity: Some Cotn/parative tStatistics. 221 than 45°, and therefore be effected by the cons
. Transactions and proceedings of the New Zealand Institute . accuracy of the construction increases rapidly asthe angle diminishes, the error being approximately proportional to thecube of the angle. If the given angle be a right angle the error is 0067 of a degree, foran angle of 45° it is 0 008 of a degree, and for one of 30° it is only 0002of a degree. In conclusion, we shall indicate briefly how the trisection of any anglebetween 0° and 180° can be derived from that of an angle not greater Segae.—Insanity: Some Cotn/parative tStatistics. 221 than 45°, and therefore be effected by the construction of this articlewith an error less than one-hundredth of a degree. Let the angle AOB lie between 45° and 90° (fig. 2). Draw OCperpendicular to OA, and on the same side as OB. The angle BOG willhe less than 45°. Let OD, OE, be the trisectors, OD being the nearer to00. The trisectors OK, OL, of AOB will make angles of 60° and 30°with OB, OE, respectively; and the angles 60° and 30° are easily con-structed with straight-edge and Fig. 2. Fig. 3. Let the angle AOB he between 90° and 135° (fig. 3). Draw 00 asbefore. The angle BOO will again be less than 45°. Let OD, OE, be thetrisectors, OD being nearer to OC. The trisectors OK, OL, of AOB willmake angles of 60° and 30° with OD, OE, respectively. Lastly, let the angle AOB lie between 135° and 180° (fig. 4). ProduceAO to C. The angle BOO will be less than 45°. Let OD, OE, be thetrisectors, OD being nearer to OC. The trisectors OK, OL, of AOB willmake angles of 120° and 60° with OD, OE, respectively. IluIlibrar
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