Elements of Plane and Spherical Trigonometry: With Practical Applications |
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Page 2
... Hence , since 10 ° = 1 , 0 is the logarithm of 1 ; 101 = 10 , 1 66 16 10 ; 102 = 100 , 2 66 66 100 ; 103 = 1,000 , 3 66 66 1,000 ; 10 * = 10,000 , 4 66 66 10,000 ; & C . , & c . It thus appears that , in the common system , the ...
... Hence , since 10 ° = 1 , 0 is the logarithm of 1 ; 101 = 10 , 1 66 16 10 ; 102 = 100 , 2 66 66 100 ; 103 = 1,000 , 3 66 66 1,000 ; 10 * = 10,000 , 4 66 66 10,000 ; & C . , & c . It thus appears that , in the common system , the ...
Page 5
... Hence , by means of logarithms , we can perform multipli- cation by addition , and division by subtraction ; also , we can raise a number to any power by a single multiplication , and extract any root of a number by a single division ...
... Hence , by means of logarithms , we can perform multipli- cation by addition , and division by subtraction ; also , we can raise a number to any power by a single multiplication , and extract any root of a number by a single division ...
Page 10
... Hence , since an arithmetical complement added makes the result 10 too great , a corresponding allowance must be made in any operation in which arithmetical complements of loga- rithms are used . MULTIPLICATION BY LOGARITHMS . 32. Add ...
... Hence , since an arithmetical complement added makes the result 10 too great , a corresponding allowance must be made in any operation in which arithmetical complements of loga- rithms are used . MULTIPLICATION BY LOGARITHMS . 32. Add ...
Page 14
... Hence , as r is taken as unity , any number of degrees may be expressed as a multiple or fractional part of л . Thus 360 ° 2л , 180 ° and 30 ° = = π , 90 ° π = 2 ' П 44. The COMPLEMENT OF AN ANGLE , or arc , is the remain- der obtained ...
... Hence , as r is taken as unity , any number of degrees may be expressed as a multiple or fractional part of л . Thus 360 ° 2л , 180 ° and 30 ° = = π , 90 ° π = 2 ' П 44. The COMPLEMENT OF AN ANGLE , or arc , is the remain- der obtained ...
Page 15
... Hence , since the acute angles of a right - angled triangle are complements one of the other ( Art . 44 ) , we have , according to the definitions , cos Asin B : 2/2 prove b - cos B : sin A = h b cot Atan B = cot B tan A = p ( 4 ) p ...
... Hence , since the acute angles of a right - angled triangle are complements one of the other ( Art . 44 ) , we have , according to the definitions , cos Asin B : 2/2 prove b - cos B : sin A = h b cot Atan B = cot B tan A = p ( 4 ) p ...
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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.