Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 2
... 3 ; that is , 2 plus a frac- tion ; and so on . 4. By means of negative exponents the application of loga- rithms may be extended , in the common system , to numbers less than 1. Thus , since 10-1 10-2 = 0.1 , 1 is the logarithm of BOOK.
... 3 ; that is , 2 plus a frac- tion ; and so on . 4. By means of negative exponents the application of loga- rithms may be extended , in the common system , to numbers less than 1. Thus , since 10-1 10-2 = 0.1 , 1 is the logarithm of BOOK.
Page 3
... less than the number of integral figures in the given number . For it has been shown ( Art . 3 ) that the logarithm of 1 is 0 , of 10 is 1 , of 100 is 2 , of 1000 is 3 , and so on . 8. The characteristic of the logarithm of ANY DECIMAL ...
... less than the number of integral figures in the given number . For it has been shown ( Art . 3 ) that the logarithm of 1 is 0 , of 10 is 1 , of 100 is 2 , of 1000 is 3 , and so on . 8. The characteristic of the logarithm of ANY DECIMAL ...
Page 8
... less ; annex to their difference two or more ciphers , and divide by the number , in the column headed D , opposite the decimal part taken from the table . Annex the result to the number corresponding to the lesser logarithm , and point ...
... less ; annex to their difference two or more ciphers , and divide by the number , in the column headed D , opposite the decimal part taken from the table . Annex the result to the number corresponding to the lesser logarithm , and point ...
Page 9
... less is .633266 , correspon . num . , 4298 Their difference is Difference from column D is 90.00 101 89 Logarithm 2.633356 has for its corresponding number 429.889 The number corresponding to the logarithm 3.441049 is 2760.89 66 66 66 ...
... less is .633266 , correspon . num . , 4298 Their difference is Difference from column D is 90.00 101 89 Logarithm 2.633356 has for its corresponding number 429.889 The number corresponding to the logarithm 3.441049 is 2760.89 66 66 66 ...
Page 10
... , and the sum , less 10 , will be the logarithm of the quotient ( Art . 31 ) . The term difference , here used , is to be understood in its algebraic signification . Therefore , the sign of the characteristic 10 TRIGONOMETRY .
... , and the sum , less 10 , will be the logarithm of the quotient ( Art . 31 ) . The term difference , here used , is to be understood in its algebraic signification . Therefore , the sign of the characteristic 10 TRIGONOMETRY .
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Common terms and phrases
A B C A+ log acute angle adjacent sides Algebra angle equal angle of elevation angle opposite angle or arc ar.co.log Arithme column headed cos² cosec Cotang decimal denoted divided Elementary Algebra equation Equations Art EXAMPLES feet find the SINE formulæ Geom Geometry given number Given the hypothenuse Greenleaf's New Series half the sum Hence included angle log cos log cot log sin logarithmic cosine logarithmic sine logarithmic tangent M.
M. Sine minus the logarithmic Napier's rules negative oblique oblique-angled spherical triangle Parker's Exercises perpendicular plane triangle Prop right-angled spherical triangle right-angled triangle equal rods School secant side b equal side opposite sin A cos sin A sin sin a+b sin² sine and cosine Solution solve the triangle spherical triangle ABC SPHERICAL TRIGONOMETRY subtract sun's declination suvers suversed sine Tang tangent of half trigonometric functions values whence yards
Popular passages
Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 7 - This process, like its converse (Art. 23), is based upon the supposition that the differences of logarithms are proportional to the differences of their corresponding numbers.
Page 4 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art. 9) M=a*, then, raising both sides to the wth power, we have Mm = (a")m = a"" . Therefore, log (M m) = xm = (log M) X »»12.
Page 74 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...
Page 43 - In every plane triangle, the sum of two sides is to their difference as the tangent of half the sum of the angles opposite those sides is to the tangent of half their difference.
Page 39 - ... be at the head of the column, take the degrees at the top of the table, and the minutes on the left ; but if the name be at the foot of the column, take the degrees at the bottom, and the minutes on the right.
Page 46 - The cosine of half of any angle of a plane triangle is equal to the square root of half the sum of the three sides, into half the sum less the side opposite the angle, divided by the rectangle of the two adjacent sides.