## Elements of Trigonometry, Plane and Spherical |

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added applied base becomes bottom calculations called characteristic circle circumference Co-tangent column common complement consequently consider contains correction corresponding cos˛ cosc cosec decimal deduce Degrees designated determine difference distance divided equal equation evident example expressed figure formula four fraction given gives greater half hence increase known latitude less limits lines logarithm logarithmic sine manner means measured middle minutes multiplying natural necessary negative observed obtain opposite perpendicular plane positive proportional quadrant radius ratio readily reduce relations remains represented right angle rule secant seconds sides signs similar sin b sin sin˛ sine and cosine solution spherical triangle substitute subtracting suppose tabular taken tang Tangent tions triangle trigonometrical lines unity values yards

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Page 126 - Required the logarithm of 234567. The logarithm of 234500 is 5.370143 Correction for the fifth figure 6, 111 " " sixth figure 7, 13 Therefore the logarithm of 234567 is 5.370267. To find the Logarithm of a Decimal Fraction.

Page 123 - All numbers are regarded as powers of some one number, which is called the base of the system ; and the exponent of that power of the base which is equal to a given number, is called the logarithm of that number. The base of the common system of logarithms (called, from their inventor, Briggs' logarithms) is the number 10.

Page 124 - To find the Logarithm of any Number between 1 and 100. Look on the first page of the table, along the column of numbers under N, for the given number, and against it, in the next column, will be found the logarithm, with its characteristic. Thus, opposite 13 is 1.113943, which is the logarithm of 13; " 65 is 1.812913, " " 65. To find thct Logarithm of any Number consisting of three Figures.

Page 51 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.

Page 108 - A ladder 40 feet long may be so placed that it will reach a window 33 feet high on one side of the street, and by turning it over without moving its foot it will reach a window 21 feet high on the other side. Find the breadth of the street.

Page 128 - The logarithmic tangent 73° 35' 40" is 10.531031 Proportional part for 3" is 23 Logarithmic tangent of 73° 35' 43" is 10.531054. When a cosine is required, the degrees and seconds must be sought at the bottom of the page, and the minutes on the right, and the correction for the odd seconds must be subtracted from the number in the table. Required the logarithmic cosine of 59° 33

Page 123 - The logarithm of every number between 10 and 100 is some number between 1 and 2, ie, is 1 plus a fraction. The logarithm of every number between 100 and 1000 is some number between 2 and 3, ie, is 2 plus a fraction, and so on.

Page 109 - What is the perpendicular height of a hill ; its angle of elevation, taken at the bottom of it, being 46°, and 200 yards farther off, on a level with the bottom, the angle was 31°?