Elements of Surveying, and Navigation: With Descriptions of the Instruments and the Necessary Tables |
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Page 28
... REMARK I. If a line is so long that the whole of it cannot be taken from the scale , it must be divided , and the parts of it taken from the scale in succession . REMARK II . If a line be given upon the paper , its length can be found ...
... REMARK I. If a line is so long that the whole of it cannot be taken from the scale , it must be divided , and the parts of it taken from the scale in succession . REMARK II . If a line be given upon the paper , its length can be found ...
Page 34
... REMARK I. This problem explains the manner of repre enting a line upon paper , so that a given number of its parts shall correspond to the unit of the scale , whether that unit be an inch or any part of an inch . When the length of the ...
... REMARK I. This problem explains the manner of repre enting a line upon paper , so that a given number of its parts shall correspond to the unit of the scale , whether that unit be an inch or any part of an inch . When the length of the ...
Page 35
... REMARK II . When the length of a line on the paper is given , and it is required to find the true length of the line which it represents , take the line in the dividers and apply it to the scale , and note the number of units , and ...
... REMARK II . When the length of a line on the paper is given , and it is required to find the true length of the line which it represents , take the line in the dividers and apply it to the scale , and note the number of units , and ...
Page 42
... remarks are applicable in respect of the column D , after the column cosine , and of the column D between the tangents and cotangents . The column D , be- tween the columns tangents and cotangents , answers to both of these columns ...
... remarks are applicable in respect of the column D , after the column cosine , and of the column D between the tangents and cotangents . The column D , be- tween the columns tangents and cotangents , answers to both of these columns ...
Page 47
... : Ꭱ : COS A :: AC : AB . REMARK . The relations between the sides and angles sufficient to solve all the cases of Plane Trigonometry . of plane triangles , demonstrated in these five theorems , are SEC . III ] PLANE TRIGONOMETRY .
... : Ꭱ : COS A :: AC : AB . REMARK . The relations between the sides and angles sufficient to solve all the cases of Plane Trigonometry . of plane triangles , demonstrated in these five theorems , are SEC . III ] PLANE TRIGONOMETRY .
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Common terms and phrases
axis azimuth back-sight base line bearing called centre chords column comp compass Cosine Cosine D Cotang course decimal degrees determined diff difference of latitude difference of level difference of longitude direction dist divided double meridian distance draw east error example feet figure fore-sight ground half hence horizontal distance horizontal line horizontal plane inches instrument intersection latitude and departure length limb line of collimation logarithm M.
M. Sine marked measure method middle latitude miles multiplied needle parallel PARALLEL SAILING perpendicular plane of reference plane sailing plot protractor radius right angles right-angled triangle rods sailing scale of equal screws sides sights Sine D spherical excess spider's lines square chains staff stakes station subtract surface survey Tang tangent telescope theodolite trigonometrical variation vernier plate vertical wwwwwwwwww yards
Popular passages
Page 44 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 67 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 119 - Longitude of the preceding course^ plus the Departure of that course, plus the Departure of the course itself* The Double Longitude of the last course (as well as of the first) is equal to its Departure. Its "coming out" so, when obtained by the above rule, proves the accuracy of the calculation of all the preceding Double Longitudes.
Page 15 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number.
Page 148 - Now, if the elongation, at the time of observation, was west, and the north end of the needle is on the west side of the line, the azimuth, plus the angle shown by the needle, is the true variation. But should the north end of the needle be found on the east side of the line, the elongation being west, the difference between the azimuth and the angle would show the variation, and the reverse when the elongation is east. 1. Elongation west, azimuth 2° 04' North end of the needle on the west, angle...
Page 98 - What must be the nominal value of 4% bonds that will yield to their owner an annual income of $720 ? 7. A owns $6000 of 5% bonds; B owns $8000 of 4£% bonds. How much greater is the annual income from B's bonds than from A's ? 8. Find the area of a piece of land in the form of a rhomboid, whose base is 32 rods and whose altitude is 15 rods.
Page 148 - Then if the star depart from the plumb-line, move the compass-sight, east or west, along the timber, as the case may be, until the star shall attain its greatest elongation, when it will continue behind the plumb-line for several minutes ; and will then recede from it in the direction contrary to its motion before it became stationary. Let the compass-sight be now fastened to'the horizontal plank.
Page 28 - In a Right-angled Triangle, the side opposite the right angle is called the Hypothenuse ; and the other two sides are called the Legs, and sometimes the Base and Perpendicular.
Page 51 - 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 45 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, . 00 is the secant of the arc AB.