Plane and spherical trigonometry. [With] Solutions of problems

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Page 57 - 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 12 - 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 56 - 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 54 - 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 22 - The logarithm of a quotient is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 22 - In any system, the logarithm of any power of a quantity is equal to the logarithm of the quantity multiplied by the exponent of the power. Assume the equation a
Page 13 - Multiply the logarithm of the number given by the proposed index of the power, and the product will be the logarithm of the power sought Note. In multiplying a logarithm with a negative index by any affirmative number, the product will be negative. — But what is to be carried from the...
Page 63 - AB'C, each corresponding with the conditions of the problem. 3. Given the angle A 116░, the opposite side a 38, and the side b 26 ; to construct the triangle. 171. PROB. III. Two sides and the included angle being given ; to find the other side and angles. Draw one of the given sides. From one end of it lay off the given angle, and draw the other given side. Then connect the extremities of this and the first line. Ex. 1. Given the angle A (Fig. 30.) 26░ 14', the side b 78, and the side c 106 ;...
Page 11 - .... -6945 7-875061 „ .... -00000075 3-602060 „ .... -004 2-394452 „ .... -0248 EULE V. Multiplication by logarithms. (14). Take out the logarithms of the given numbers from the tables ; add them together : their sum will be the logarithm of the product of the given numbers ; the natural number corresponding to which is therefore the product required.* * In Part II. it is shown that log.
Page 55 - A=56░ 29' 15" c=1177 C=33 30 45 B=90░ 6=2132-1 EULE VI. Two sides and the included angle of a plane triangle being given, to find the area. Add together the logarithms of the two given sides, and log. sine of the given angle; the sum, rejecting 10 in the index, will be the logarithm of twice the required area.* EXAMPLE. Given a=798, 6=460, and C=55░ 2

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