Elements of Surveying, and Navigation: With Descriptions of the Instruments and the Necessary Tables |
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Page 39
... sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity . Thus , BD is the sine of the arc AB . 8. The cosine of an arc is the part of the diameter in ...
... sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity . Thus , BD is the sine of the arc AB . 8. The cosine of an arc is the part of the diameter in ...
Page 40
... sine will be FH ; OH will be its cosine ; AQ its tangent , and OQ its secant . But FH is the sine of the arc GF , which is the supplement of AF , and OH is its cosine ; hence , the sine of an arc is equal to the sine of its supplement ...
... sine will be FH ; OH will be its cosine ; AQ its tangent , and OQ its secant . But FH is the sine of the arc GF , which is the supplement of AF , and OH is its cosine ; hence , the sine of an arc is equal to the sine of its supplement ...
Page 41
... sine , cosine , tangent , or cotangent , as he case may be : the number so indicated is the logarithm sought . Thus , on page 37 , for 19 ° 55 ' , we find , sine 19 ° 55 ' 9.532312 • cos 19 ° 55 ' • 9.973215 tan 19 ° 55 ' 9.559097 cot ...
... sine , cosine , tangent , or cotangent , as he case may be : the number so indicated is the logarithm sought . Thus , on page 37 , for 19 ° 55 ' , we find , sine 19 ° 55 ' 9.532312 • cos 19 ° 55 ' • 9.973215 tan 19 ° 55 ' 9.559097 cot ...
Page 42
... sine , at the top of the page , should correspond with cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 12 ) . If the angle is greater than 90 ° , we have only to sub- tract ...
... sine , at the top of the page , should correspond with cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 12 ) . If the angle is greater than 90 ° , we have only to sub- tract ...
Page 43
... sine and cotangent , it must be remembered , that they in- crease while the arcs decrease , and decrease as the arcs are increased ; consequently , the proportional numbers found for the seconds , must be subtracted , not added ...
... sine and cotangent , it must be remembered , that they in- crease while the arcs decrease , and decrease as the arcs are increased ; consequently , the proportional numbers found for the seconds , must be subtracted , not added ...
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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.