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 49
... measuring the latter , a circle is introduced . The periphery of every circle , whether great or small , is supposed to be divided into 360 equal parts called degrees , each degree into 60 minutes , each minute into 60 seconds , each ...
... measuring the latter , a circle is introduced . The periphery of every circle , whether great or small , is supposed to be divided into 360 equal parts called degrees , each degree into 60 minutes , each minute into 60 seconds , each ...
Page 50
... measured by either of the arcs AG , ag . For ACD is to ACH , as AG to AH , or as ag to ah .. ( Euc . 33. 6. ) 75. In the circle ADGH , ( Fig . 2. ) let the two diameters AG and DH be perpendicular to each other . The angles ACD , DCG ...
... measured by either of the arcs AG , ag . For ACD is to ACH , as AG to AH , or as ag to ah .. ( Euc . 33. 6. ) 75. In the circle ADGH , ( Fig . 2. ) let the two diameters AG and DH be perpendicular to each other . The angles ACD , DCG ...
Page 55
... measured by this arc , will also 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 ...
... measured by this arc , will also 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 ...
Page 92
... measuring an angle , therefore , an arc must be drawn , with a radius which is equal to the extent from 0 to 60 on the ... measured by the same line from which the radius is taken . 161. To make an angle , then , of a given number of de ...
... measuring an angle , therefore , an arc must be drawn , with a radius which is equal to the extent from 0 to 60 on the ... measured by the same line from which the radius is taken . 161. To make an angle , then , of a given number of de ...
Page 94
... measured , ac- cording to Arts . 158 , 162. The following problems corres- pond with the four cases of oblique angled triangles ; ( Art . 148. ) but are equally adapted to right angled triangles . 169. PROB . I. The angles and one side ...
... measured , ac- cording to Arts . 158 , 162. The following problems corres- pond with the four cases of oblique angled triangles ; ( Art . 148. ) but are equally adapted to right angled triangles . 169. PROB . I. The angles and one side ...
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.