A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges, Volumes 1-3 |
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Page 66
... problems in the mensuration of heights and dis- tances , in surveying , navigation , and astronomy , are solved by rectangular trigonometry . Any triangle whatever may be divided into two right angled triangles , by drawing a perpen ...
... problems in the mensuration of heights and dis- tances , in surveying , navigation , and astronomy , are solved by rectangular trigonometry . Any triangle whatever may be divided into two right angled triangles , by drawing a perpen ...
Page 85
... problem . Let the side b , ( Fig . 28. ) the angle A , and the length of the side opposite this angle , be given . With the latter for radius , ( if it be shorter than b , ) describe an arc , cutting the line AH in the points B and B ...
... problem . Let the side b , ( Fig . 28. ) the angle A , and the length of the side opposite this angle , be given . With the latter for radius , ( if it be shorter than b , ) describe an arc , cutting the line AH in the points B and B ...
Page 94
... 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 of a triangle being given ; to find , by construction ...
... 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 of a triangle being given ; to find , by construction ...
Page 95
... problem . 3. Given the angle A 116 ° , the opposite side a 38 , and the side b 26 ; to construct the triangle . 171. PROB . III . Two sides and the included angle being given ; to find the other side and angles . Draw one of the given ...
... problem . 3. Given the angle A 116 ° , the opposite side a 38 , and the side b 26 ; to construct the triangle . 171. PROB . III . Two sides and the included angle being given ; to find the other side and angles . Draw one of the given ...
Page 97
... problems in trigonometry , and making other logarithmic calculations , in a mechanical way , has been contrived by Mr. Edmund Gunter . The logarithms of numbers , of sines , tangents , & c . , are represented by lines . By means of ...
... problems in trigonometry , and making other logarithmic calculations , in a mechanical way , has been contrived by Mr. Edmund Gunter . The logarithms of numbers , of sines , tangents , & c . , are represented by lines . By means of ...
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Common terms and phrases
ABCD altitude arithmetical complement axis base calculation circle circular segment circumference column cone cosecant cosine cotangent course cylinder decimal diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the area find the SOLIDITY frustum given side greater horizon hypothenuse inches JEREMIAH DAY length less line of chords logarithm measured Mercator's Merid meridional difference miles minutes multiplied negative number of degrees number of sides object oblique parallel of latitude parallelogram parallelopiped perimeter perpendicular plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right ascension right cylinder rods root scale secant segment sine sines and cosines slant-height sphere spherical square subtract tables tangent term theorem trapezium triangle ABC Trig trigonometry whole
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 55 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 71 - 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 21 - AND ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 14 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 98 - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.
Page 79 - T8T of the axis, and the product by .7854. Ex. If the axis of a parabolic spindle be 30, and the middle diameter 17, what is the solidity ? Ans.
Page 56 - CoR. 9. From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.