Elements of Surveying and Navigation: With Descriptions of the Instruments and the Necessary Tables |
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Page 39
... cosine of an arc is the part of the diameter in- tercepted between the foot of the sine and centre . OD is the cosine of the arc AB . Thus , 9. The tangent of an arc is the line which touches it at one extremity , and is limited by a ...
... cosine of an arc is the part of the diameter in- tercepted between the foot of the sine and centre . OD is the cosine of the arc AB . Thus , 9. The tangent of an arc is the line which touches it at one extremity , and is limited by a ...
Page 40
... 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 ; and the cosine of an G are is ...
... 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 ; and the cosine of an G are is ...
Page 41
... cosines , & c . , are expressed on the page . The vertical columns on the left and right , are columns of minutes . CASE I. To find , in the table , the logarithmic sine , cosine , tangent , or cotangent of any given arc or angle . 16 ...
... cosines , & c . , are expressed on the page . The vertical columns on the left and right , are columns of minutes . CASE I. To find , in the table , the logarithmic sine , cosine , tangent , or cotangent of any given arc or angle . 16 ...
Page 42
... 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 it from 180 ° , and take the sine , cosine , tangent ...
... 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 it from 180 ° , and take the sine , cosine , tangent ...
Page 43
... cosine of 3 ° 40 ′ 40 ′′ . The cosine of 3 ° 40 ' Tabular difference .13 . Number of seconds 40 • 9.999110 Product , 5.20 to be subtracted 5.20 Gives for the cosine of 3 ° 40 ' 40 " 9.999105 . 2. Find the tangent of 37 ° 28 ′ 31 ′′ . 3 ...
... cosine of 3 ° 40 ′ 40 ′′ . The cosine of 3 ° 40 ' Tabular difference .13 . Number of seconds 40 • 9.999110 Product , 5.20 to be subtracted 5.20 Gives for the cosine of 3 ° 40 ' 40 " 9.999105 . 2. Find the tangent of 37 ° 28 ′ 31 ′′ . 3 ...
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Common terms and phrases
Awwwwwwwww axis azimuth back-sight base line bearing called centre chords column comp compass Cosine Cosine D 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 LatDegDegDegDeg latitude and departure length limb line of collimation logarithm longitude 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 rods sailing scale of equal screws sides sights Sine Cotang Sine D spherical excess spider's lines square chains staff stakes station subtract surface survey Tang tangent telescope theodolite TRAVERSE TABLE trigonometrical variation vernier plate vertical yards
Popular passages
Page 22 - 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 21 - ... 20. An EQUILATERAL polygon is one which has all its sides equal ; an equiangular polygon, is one which has all . its angles equal. 21. Two polygons are mutually equilateral, when they have their sides equal each to each, and placed in the same order : that is to say, when following their...
Page 45 - In any triangle, the sum of the two sides containing either angle, is to their difference, as the tangent of half the sum of the two other angles, to the tangent of half their difference.
Page 9 - 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 138 - ... the intersection of the vertical plane passing through it and ,the place, with the surface of the earth, would be the true meridian. But, the star being at a distance from the pole, equal to 1° 30...
Page 44 - CB : CA : : sin A : sin B. For, with A as a centre, and AD equal to the less side...
Page 61 - 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 38 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 39 - 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.
Page 21 - If the lines are straight, the space they enclose is called a rectilineal figure, or polygon, and the lines themselves, taken together, form the contour, or perimeter of the polygon. 14. The polygon of three sides, the simplest of all, is called a triangle ; that of four sides, a quadrilateral; that of five, a pentagon; that of six, a hexagon; that of seven, a heptagon; that of eight, an octagon ; that of nine, a nonagon; that of ten, a decagon ; and that of twelve, a dodecagon.