A Treatise of Plane Trigonometry: To which is Prefixed a Summary View of the Nature and Use of Logarithms : Being the Second Part of a Course of Mathematics, Adapted to the Method of Instruction in the American Colleges |
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Page 23
... cube of 6.296 ? Root 6.296 , its log . 0.79906 Index of the power Power 249.6 3 2.39718 2. Required the 4th power of 21.32 Root 21.32 Power 206614 log . Index 1.32879 4 5.31516 3. Required the 6th power of 1.689 Root 1.689 log . Index ...
... cube of 6.296 ? Root 6.296 , its log . 0.79906 Index of the power Power 249.6 3 2.39718 2. Required the 4th power of 21.32 Root 21.32 Power 206614 log . Index 1.32879 4 5.31516 3. Required the 6th power of 1.689 Root 1.689 log . Index ...
Page 24
... cube , 30 too great , & c . Ex . 1. Required the cube of 0.0649 Root 0.0649 • log . Index 2.81224 3 or 8.81224 3 4.43672 6.43672 Power 0.0002733 2. Required the 4th power of 0.1234 Root 0.1234 log . Index 1.09132 or 9.09132 4 4 4.36528 ...
... cube , 30 too great , & c . Ex . 1. Required the cube of 0.0649 Root 0.0649 • log . Index 2.81224 3 or 8.81224 3 4.43672 6.43672 Power 0.0002733 2. Required the 4th power of 0.1234 Root 0.1234 log . Index 1.09132 or 9.09132 4 4 4.36528 ...
Page 25
... cube root of 897.1 . Power 897.1 Root 9.645 3 ) 2.95284 0.98428 In the first of these examples , the logarithm of the given number is divided by 2 ; in the other , by 3 . 3. Required the 10th root of 6948 . Power 6948 10 ) 3.84186 Root ...
... cube root of 897.1 . Power 897.1 Root 9.645 3 ) 2.95284 0.98428 In the first of these examples , the logarithm of the given number is divided by 2 ; in the other , by 3 . 3. Required the 10th root of 6948 . Power 6948 10 ) 3.84186 Root ...
Page 26
... cube root of 0.0000892 is required . The logarithm of this is 5.95036 . If we divide the index by 3 , the quotient will be 1 , with 2 remainder . This remain- der , if it were positive , might , as in other cases of division , be ...
... cube root of 0.0000892 is required . The logarithm of this is 5.95036 . If we divide the index by 3 , the quotient will be 1 , with 2 remainder . This remain- der , if it were positive , might , as in other cases of division , be ...
Page 100
... cube of 4. The extent from 1 to 4 , re- peated three times , will reach to 64 the cube of 4 . 183. On the other hand , to perform evolution on the scale ; take half , one third , & c . of the logarithm of the quantity , ac- cording to ...
... cube of 4. The extent from 1 to 4 , re- peated three times , will reach to 64 the cube of 4 . 183. On the other hand , to perform evolution on the scale ; take half , one third , & c . of the logarithm of the quantity , ac- cording to ...
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A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2017 |
A Treatise of Plane Trigonometry: To Which Is Prefixed, a Summary View of ... Jeremiah Day No preview available - 2018 |
A Treatise of Plane Trigonometry: To Which Is Prefixed a Summary View of the ... Jeremiah Day No preview available - 2018 |
Common terms and phrases
ABC Fig ABCD altitude axis base breadth bung diameter calculation cask circle circular sector circular segment circumference column cosecant cosine cotangent course cube cubic decimal departure Diff difference of latitude difference of longitude distance divided earth equal to half equator figure find the area find the SOLIDITY frustum given sides gles greater hypothenuse inches inscribed lateral surface length less logarithm longitude measured Mercator's meridian meridional difference middle diameter miles multiply the sum number of degrees number of sides oblique parallelogram parallelopiped perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right cylinder rods rule secant sector segment ship sine sines and cosines slant-height sphere spherical subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry wine gallons zone
Popular passages
Page 81 - C' (89) (90) (91) (92) (93) 112. 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.
Page 43 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 50 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Page 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 69 - It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 89 - Divide the height of the segment by the diameter of the circle ; look for the quotient in the column of heights in the table ; take out the corresponding number in the column of areas ; and multiply it by the square of the diameter.