Elements of Surveying, and Navigation: With a Description of the Instruments and the Necessary Tables |
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Page 35
... cosine of an arc is the part of the diameter inter- cepted between the foot of the sine and centre . Thus , OD is the cosine of the arc AB . 46. 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 inter- cepted between the foot of the sine and centre . Thus , OD is the cosine of the arc AB . 46. The tangent of an arc is the line which touches it at one extremity , and is limited by a ...
Page 36
... cosine of AB ; OT , the secant of EB , is called the cosecant of AB . In general , if A is any arc or angle , we ... 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 ...
... cosine of AB ; OT , the secant of EB , is called the cosecant of AB . In general , if A is any arc or angle , we ... 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 ...
Page 37
... 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 . 52. If ...
... 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 . 52. If ...
Page 38
... cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 49 ) . If the angle is greater than 90 ° , we have only to subtract it from 180 ° , and take the sine , cosine , tangent or ...
... cosine , at the bottom ; cosine with sine , tang with cotang , and cotang with tang , as in the tables ( Art . 49 ) . If the angle is greater than 90 ° , we have only to subtract it from 180 ° , and take the sine , cosine , tangent or ...
Page 39
... cosine and cotangent , it must be remembered , that they increase while the arcs decrease , and decrease as the arcs ... cosine of 3 ° 40 ′ 40 ′′ The cosine of 3 ° 40 ' Tabular difference Number of seconds 13 40 9.999110 Product 5.20 to ...
... cosine and cotangent , it must be remembered , that they increase while the arcs decrease , and decrease as the arcs ... cosine of 3 ° 40 ′ 40 ′′ The cosine of 3 ° 40 ' Tabular difference Number of seconds 13 40 9.999110 Product 5.20 to ...
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Elements of Surveying, and Navigation: With a Description of the Instruments ... Charles Davies No preview available - 2016 |
Elements of Surveying, and Navigation: With a Description of the Instruments ... Charles Davies No preview available - 2016 |
Popular passages
Page 12 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant Jigure.
Page 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 41 - 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 34 - 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, fourths, &c.
Page 73 - 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 Cway 33° 45' ; required the height of the tower.
Page 40 - THEOREM I. The sides of a plane triangle are proportional to the sines of their opposite angles.
Page 19 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Page 85 - 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 35 - 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, OC is the secant of the arc AB.
Page 130 - Take a board, of about one foot square, paste white paper upon it, and perforate it through the center; the diameter of the hole being somewhat larger than the diameter of the telescope of the theodolite. Let this board be so fixed to a vertical staff" as to slide up and down freely ; and let a small piece of board, about three inches square, be nailed to the lower edge of it, for the purpose of holding a candle. About twenty-five minutes before the time of the greatest eastern or western elongation...