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 11
... containing MORE than FOUR significant figures . By turning to the tables , it will be seen , that if the differ- ences between several numbers be small , in comparison with the numbers themselves ; the differences of the logarithms will ...
... containing MORE than FOUR significant figures . By turning to the tables , it will be seen , that if the differ- ences between several numbers be small , in comparison with the numbers themselves ; the differences of the logarithms will ...
Page 50
... containing 90 degrees . As a right angle is subtended by an arc of 90 ° , the angle itself is said to contain 90 ° . Hence , in two right angles , there are 180 ° , in four right angles 360 ° ; and in any other angle , as many degrees ...
... containing 90 degrees . As a right angle is subtended by an arc of 90 ° , the angle itself is said to contain 90 ° . Hence , in two right angles , there are 180 ° , in four right angles 360 ° ; and in any other angle , as many degrees ...
Page 55
... contain 60 ° ; ( Art . 75. ) and the triangle ACS will be equilateral . For the sum of the three angles is equal to 180 ° . ( Art . 76. ) From this , taking the angle ACS , which is 60 ° , the sum of the remain- ing two is 120 ° . But ...
... contain 60 ° ; ( Art . 75. ) and the triangle ACS will be equilateral . For the sum of the three angles is equal to 180 ° . ( Art . 76. ) From this , taking the angle ACS , which is 60 ° , the sum of the remain- ing two is 120 ° . But ...
Page 56
... contain 45 ° . The angle CAD is a right angle , because the tangent is , by defi- nition , perpendicular to the radius AC . ( Art . 84. ) Subtract- ing ACD , which is 45 ° , from 90 ° , ( Art . 77. ) the other acute angle ADC will be 45 ...
... contain 45 ° . The angle CAD is a right angle , because the tangent is , by defi- nition , perpendicular to the radius AC . ( Art . 84. ) Subtract- ing ACD , which is 45 ° , from 90 ° , ( Art . 77. ) the other acute angle ADC will be 45 ...
Page 68
... contain the same number of degrees . ( Art . 74. ) The sines of these arcs are BG and bg , the tangents AD and ad , and the ... contains one right angle ; the angle at C is common to them all ; and the other acute angle in each is the ...
... contain the same number of degrees . ( Art . 74. ) The sines of these arcs are BG and bg , the tangents AD and ad , and the ... contains one right angle ; the angle at C is common to them all ; and the other acute angle in each is the ...
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.