The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying |
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Page 15
... diff . between the sine and tangent is only .00000000001 And the difference between the sine and the arc is still less . * In this manner , the Supplement to Playfair's Euclid is referred to in this work . Taking then .000255663465 for ...
... diff . between the sine and tangent is only .00000000001 And the difference between the sine and the arc is still less . * In this manner , the Supplement to Playfair's Euclid is referred to in this work . Taking then .000255663465 for ...
Page 20
... . Cos . Course : Diff . Lat . Example 1 . A ship sails from A ( Fig . 20. ) SW . by S. , 38 miles to C. Required her departure and difference of latitude ? * See Note B. 4 : 413 dep PLANE SAILING . The course is 20 NAVIGATION .
... . Cos . Course : Diff . Lat . Example 1 . A ship sails from A ( Fig . 20. ) SW . by S. , 38 miles to C. Required her departure and difference of latitude ? * See Note B. 4 : 413 dep PLANE SAILING . The course is 20 NAVIGATION .
Page 21
... Diff . Lat . R : 38 :: Example 2 . 21 A ship sails S. 29 ° E. , 34 leagues . Her departure and dif- ference of latitude are required . Ans . 16.5 and 29.7 leagues . The proportions in this and the following cases may be va- ried , by ...
... Diff . Lat . R : 38 :: Example 2 . 21 A ship sails S. 29 ° E. , 34 leagues . Her departure and dif- ference of latitude are required . Ans . 16.5 and 29.7 leagues . The proportions in this and the following cases may be va- ried , by ...
Page 22
... Diff . of latitude ; Dist . Rad . Making the distance radius , Rad.::Diff . Lat . : Cos . Course , Dist . :: Sin . Course : Departure . Example . A vessel sails between N. and E. 66 miles , from Lat . 34 ° 50 ' to Lat . 35 ° 40 ...
... Diff . of latitude ; Dist . Rad . Making the distance radius , Rad.::Diff . Lat . : Cos . Course , Dist . :: Sin . Course : Departure . Example . A vessel sails between N. and E. 66 miles , from Lat . 34 ° 50 ' to Lat . 35 ° 40 ...
Page 24
... diff . of lat . for 100 are 83.87 and 54.46 for 63 52.84 34.31 for 163 136.71 88.77 3. Given the course 39 ° , and the distance 18.23 . The departure and diff . of lat . for 18. are 11.33 and 13.99 for .23 0.14 0.18 for 18.23 11.47 ...
... diff . of lat . for 100 are 83.87 and 54.46 for 63 52.84 34.31 for 163 136.71 88.77 3. Given the course 39 ° , and the distance 18.23 . The departure and diff . of lat . for 18. are 11.33 and 13.99 for .23 0.14 0.18 for 18.23 11.47 ...
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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ... Jeremiah Day No preview available - 2016 |
Common terms and phrases
ABCD altitude axis base breadth calculation circle circular segment circumference column cone cosecant cosine cotangent course cube cylinder decimal departure diameter Diff difference of latitude difference of longitude divided earth equator feet figure find the SOLIDITY frustum given sides gles greater horizon hypothenuse inches inscribed ISOPERIMETRY JEREMIAH DAY lateral surface length line of chords loga logarithm measured Mercator's Merid meridional difference miles multiplied negative number of degrees number of sides object oblique opposite parallel of latitude parallelogram parallelopiped perimeter perpendicular perpendicular height plane sailing prism PROBLEM proportion pyramid quadrant quantity quotient radius regular polygon right angled triangle right cylinder rods secant segment sine sines and cosines slant-height sphere spherical subtracting tables tangent term theorem trapezium triangle ABC Trig trigonometry whole 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 61 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
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 29 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...