Key to Robinson's New Geometry and trigonometry, and conic sections and analytical geometry; With some additional astronomical problems. Designed for teachers and students

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1875 Excerpt: ... Latitude, South polar dis. A Geographical Problem, (page 377, Text-book.) Bequired, the number of degrees on a great circle between New Orleans and Bome, also the number of miles taking 69.16 miles to each degree. Let P, be the north pole on the earth, N, the position of New Orleans, and B the position of Eome, which positions are Latitude. Longitude. New Orleans, 29 57' 30" N. 90 W. Eome, 41 53' 54" N. 12 28' 40" K The co. latitude of N. 0. is AT=60 2' 30". co. latitude of Eome is PS=48 & 6". And the sum of longitudes is 102 28' 40", which is the angle NPB. The supplement of the angle NPB, is BPD, 77 31' 20". BD, is the perpendicular let fall on NP produced. Now, in the triangle PBD, we have B.: sin. PB, 48 6' 6":: sin. 77 31' 20": sin. RD. Sin. PB 9.871767 Sin. P 9.989619 Sin. RD, 46 36' 53" 9.861386 B.cos. PB=cos. PZ.cos. BD. „ nn B.cob.pb 19.824654 Cos. PD--,, r.. cos. BD 9.836894 Cos. PD=coa. 13 32' 21" 9.987760 Add AT, 60 2'30" Sum, or ND, 73 34' 51" In the right angled triangle NDB, we have.fl.cos. NB=cos. ND.cos. DB. Cos. ND, 73 34' 51" 9.451268 Cos. DB, 46 36' 53" 9.836894 Cos. NB, 78. 48' 15" 9.288162 That is, the distance in degrees is 78.8041, and at the rate of 69.16 miles to each degree, gives 5450.1 English miles. We can compute this side more concisely by using the formula Cos. c=cos. (a + b) +2cos.2iC.sin. a.sin. b. Let the angle NPB--C= 102 28' 40", a=60 2' 30", and 6=48 6' 6", c=the arc NB. Nat. Cos. (a + 6)=Nat. cos. 108 8' 36"=-.31139. Log. 2 0.301030 Cos. C, B=l-1.796627-1.796627 Sin. a-1.937712 Sin. b-1.871767 Nat. number, 0.50555--L703763. Sum. Add,-0.31139 Nat. cos. 78 48' 15".19416. Ans. same as before. 'Ncte.--There ...