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 31
... observed , that each arithmetical complement increases the index of the logarithm by 10. If the arithmetical complement be introduced into two of the terms , the index of the sum of the logarithms will be 20 too great ; if it be in ...
... observed , that each arithmetical complement increases the index of the logarithm by 10. If the arithmetical complement be introduced into two of the terms , the index of the sum of the logarithms will be 20 too great ; if it be in ...
Page 53
... observed , however , that the sine of an acute angle is op- posite to it ; while the sine of an obtuse angle falls without the angle , and is opposite to its supplement . Thus BG , the sine of the angle MCG , is not opposite to MCG ...
... observed , however , that the sine of an acute angle is op- posite to it ; while the sine of an obtuse angle falls without the angle , and is opposite to its supplement . Thus BG , the sine of the angle MCG , is not opposite to MCG ...
Page 54
... observed , that the line BC , between the sine and the center of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and center , is par- allel and equal to the sine ; ( Euc . 34. 1. ) so that one may be ...
... observed , that the line BC , between the sine and the center of the circle , is parallel and equal to the cosine ; and that LC , between the cosine and center , is par- allel and equal to the sine ; ( Euc . 34. 1. ) so that one may be ...
Page 64
... observed here , as in all other cases , that of the two angles , the less has the greater cosine . The angle belonging to the sin 9.20621 is 9 ° 15 ' 6 " the tan 10.43434 is 69 ° 48 ′ 16 ′′ the cos 9.98157 16 ° 34 ' 30 " the cot ...
... observed here , as in all other cases , that of the two angles , the less has the greater cosine . The angle belonging to the sin 9.20621 is 9 ° 15 ' 6 " the tan 10.43434 is 69 ° 48 ′ 16 ′′ the cos 9.98157 16 ° 34 ' 30 " the cot ...
Page 67
... observed , that , if one of the acute angles is given , the other is known of course . For one is the complement of the other . ( Art . 76 , 77. ) So that , in a right angled triangle , subtracting one of the acute angles from 90 ...
... observed , that , if one of the acute angles is given , the other is known of course . For one is the complement of the other . ( Art . 76 , 77. ) So that , in a right angled triangle , subtracting one of the acute angles from 90 ...
Other editions - View all
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.