(2). The = square of a side of a pentagon inscribed in a circle square of a side of the inscribed hexagon, together with the square of the side of the inscribed decagon. (3). The area of a circle and that of a regular polygon inscribed in it being given, find the number of the sides of the polygon, and the angles they make one with another. 22. Adapt to logarithmic computation ; (1). √a+b+√a - b. In the following questions is required. (3). Sin (0+ a) = m . sin 0. (7). Sin0.√{1+ (tan A.tan B)3}+cose.√{1-(tan A.tan B)2? (3). If from an arc AB of a circle of radius r whose centre is 0, AC be cut off = r. sin AOB; сс then (2). x3-6x-4=0. [x=-2, or 1±√3.] (3). x3-147x 343 = 0. [One root is 13.1556964; given cos 20° = .9396926.] 25. LOGARITHMS. (1). From 1102, and 1103, find 11072. (2). From 1014, and 11016, find 1102, 1105, 1107, 110 (3). From 1102, and 11067, find L tan 15o. 1960 N2 == + 1.2 THE ELEMENTS OF SPHERICAL TRIGONOMETRY. BY J. C. SNOWBALL, M.A. FELLOW OF ST JOHN'S COLLEGE, CAMBRIDGE. SECOND EDITION. CAMBRIDGE: PRINTED BY JOHN W. PARKER, UNIVERSITY PRINTER. T. STEVENSON, CAMBRIDGE; A. H. BAILY & Co., LONDON. M.DCCC.XXXVII. 2, 3. Every section of a sphere made by a plane is a circle. 1 1 4. Objects of SPHERICAL TRIGONOMETRY.. 2 6. Def. POLES and AXIS of a circle................................ 3 8. The Pole of a circle is equidistant from every point in its circumference...... 3 9. The angle between a circle and a great circle through its pole is a right angle... 3 10, 11. Methods of finding the Pole of a circle............. 12. The arc joining the Poles of two great circles subtends the angle at which the circles are inclined to each other........ ........... 13. Two great circles are bisected by their intersections..... 5 6 14. Every side, and also every angle, of a spherical triangle is less than 180o... 6 Arc AB sin Pa; P being the pole of a great, and a small, circle, of arc ab which the arcs AB and ab lie between the same secondaries.......... 7 16-19. The Polar, or Supplemental, triangle 8 20. If the angles of the triangle ABC, be A, B, C and the opposite sides be a,b,c; then a+b>c, a+b+c<2π, &c............ 10 |