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 66
... triangle , there are six parts , three sides , and three angles . In every trigonometrical calculation , it is ... ABC , or ABC ' , or ABC " . So that it will be impossible , from knowing two of the sides of a triangle , to determine the ...
... triangle , there are six parts , three sides , and three angles . In every trigonometrical calculation , it is ... ABC , or ABC ' , or ABC " . So that it will be impossible , from knowing two of the sides of a triangle , to determine the ...
Page 69
... triangle be made radius , each of the other sides will be the sine , tangent ... ABC ( Fig . 14. ) a circle be applied , whose radius is AC , and whose ... TRIANGLES . 69.
... triangle be made radius , each of the other sides will be the sine , tangent ... ABC ( Fig . 14. ) a circle be applied , whose radius is AC , and whose ... TRIANGLES . 69.
Page 70
... triangles . If the triangle proposed be ABC , ( Fig . 17. ) another , abc , may be formed , having the same angles with the first , but differing from it in the length of its sides , so as to correspond with the numbers in the tables ...
... triangles . If the triangle proposed be ABC , ( Fig . 17. ) another , abc , may be formed , having the same angles with the first , but differing from it in the length of its sides , so as to correspond with the numbers in the tables ...
Page 73
... triangle , two of the parts , besides the right angle . ( Art . 116. ) These may be ; 1. The hypothenuse and an ... abc be a similar triangle , whose hypoth- enuse is equal to the tabular radius , be will be the tabular sine of A , and ...
... triangle , two of the parts , besides the right angle . ( Art . 116. ) These may be ; 1. The hypothenuse and an ... abc be a similar triangle , whose hypoth- enuse is equal to the tabular radius , be will be the tabular sine of A , and ...
Page 81
... triangle , AS THE SUM OF ANY TWO OF THE SIDES , TO THEIR difference ; SO IS ... ABC , to the tangent of half their difference . Demonstration . Extend CA to ... ABC , is equal to the sum of ACD and ADC ; because each of these sums is the ...
... triangle , AS THE SUM OF ANY TWO OF THE SIDES , TO THEIR difference ; SO IS ... ABC , to the tangent of half their difference . Demonstration . Extend CA to ... ABC , is equal to the sum of ACD and ADC ; because each of these sums 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.