Plane and spherical trigonometry. [With] Solutions of problems. [Followed by] Appendix: being the solutions of problems

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Page 46 - EULE VIII. — SECOND METHOD, WITHOUT HAVERSINES. Three sides of a spherical triangle being given, to find an angle. Put down the two sides containing the required angle, * A spherical triangle is that part of the surface of a sphere which is bounded by arcs of three great circles, that is, three circles whose planes pass through the centre of the sphere. The three arcs are the sides of the triangles ; and any one of its angles is the same as the inclination of the planes of the r.ides containing...
Page 88 - May-pole, whose top was broken off" by a blast of wind, struck the ground at the distance of 15 feet from the foot of the pole ; what was the height of the whole May-pole, supposing the length of the broken piece to be 39 feet ?
Page 164 - AB describe a segment of a circle containing an angle equal to the given angle, (in.
Page 10 - Hence, if we find the logarithm of the dividend, and from it subtract the logarithm of the divisor, the remainder will be the logarithm of the quotient. This additional caution may be added. The difference of the logarithms, as here used, means the algebraic difference ; so that, if the logarithm of the divisor...
Page 44 - RULE. from half the sum of the three sides, subtract each side separately; multiply the half sum and the three remainders together, and the square root of the product will be the area required.
Page 109 - The hour angle of a heavenly body, is the angle at the pole between the celestial meridian and the circle of declination passing through the place of the body ; thus, zpx is the hour angle of x.
Page 158 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 43 - Heath,* believe that he probably discovered the theorem that bears his name, to the effect that, in a right-angled triangle, the square on the side opposite the right angle is equal to the sum of the squares on the other two sides.
Page 16 - The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 89 - A ladder 70 feet long is so planted as to reach a window 40 feet from the ground, on one side of the street, and without moving it at the foot, will reach a window 30 feet high on the other side ; what is the breadth of the street ? Ans.

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