Elements of Surveying: With the Necessary TablesJ. & J. Harper, 1830 - 306 páginas |
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Página 23
... secant , cosecant , tangent , and cotangent are determined from them . 38. We see , in examining the figure , that if the point B coincides with the point A , or the arc AB = 0 , the sin . AB becomes -0 , the tang . AB becomes = 0 , the ...
... secant , cosecant , tangent , and cotangent are determined from them . 38. We see , in examining the figure , that if the point B coincides with the point A , or the arc AB = 0 , the sin . AB becomes -0 , the tang . AB becomes = 0 , the ...
Página 24
... secants and cosecants are usually omitted , being readily found from those of the cosine and sine ( 37 ) . 41. If the values of the sine , cosine , tangent , and secant be known for arcs or angles less than 90 ° , they are also known ...
... secants and cosecants are usually omitted , being readily found from those of the cosine and sine ( 37 ) . 41. If the values of the sine , cosine , tangent , and secant be known for arcs or angles less than 90 ° , they are also known ...
Página 29
... secants and cosecants are omitted in the table , being easily found from the cosines and sines . R ? For , sec . = ( 37 ; or , taking the logarithms : log.sec . = 2 log . R - log . cos . = 20 - log . cos ; that is , the logarithmic secant ...
... secants and cosecants are omitted in the table , being easily found from the cosines and sines . R ? For , sec . = ( 37 ; or , taking the logarithms : log.sec . = 2 log . R - log . cos . = 20 - log . cos ; that is , the logarithmic secant ...
Página 122
... secants BE and DF are very small in respect of the diameter of the earth , they may be neglected without sensible error : the expressions above will then become , AE = BE X2EC , and AF2 = DF X2FC , AE ? AF : or , BE = 2E C ; and DF ...
... secants BE and DF are very small in respect of the diameter of the earth , they may be neglected without sensible error : the expressions above will then become , AE = BE X2EC , and AF2 = DF X2FC , AE ? AF : or , BE = 2E C ; and DF ...
Página 134
... secant planes , being lines of the surface , will indicate its form at the places of section , and , as the curves are more or less numerous , the form of the surface will be more or less accurately ascertained . If such a system of ...
... secant planes , being lines of the surface , will indicate its form at the places of section , and , as the curves are more or less numerous , the form of the surface will be more or less accurately ascertained . If such a system of ...
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Página 57 - 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.
Página 15 - FRACTION is a negative number, and is one more than the number of ciphers between the decimal point and the first significant Jigure.
Página 15 - The characteristic of a number less than 1 is found by subtracting from 9 the number of ciphers between the decimal point and the first significant digit, and writing — 10 after the result.
Página 102 - The line so determined makes, with the true meridian, an angle equal to the azimuth of the pole star; and from this line the variation of the needle is readily determined, even without tracing the true meridian on the ground. Place the compass upon this line, turn the sights in the direction of It, and note the angle shown by the needle. Now, if the elongation at the time of observation...
Página 21 - The circumference of every circle is supposed to be divided into 360 equal parts called degrees, each degree into 60 equal parts called minutes, each minute into 60 equal parts called seconds.
Página 97 - But the star being at a distance from the pole equal to 1° 30' nearly. It performs a revolution about the pole in a circle, the polar distance of which is 1° 30': the time of revolution is 23 h. and 56 min. To the eye of an observer this star is continually in motion, and is due north but twice in 23 h. 56 min.; and is then said to be on the meridian. Now, when It departs from the meridian it apparently moves east or west for 5 h.
Página 100 - ... 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 of the pole-star, as shown by the tables of elongations, let the theodolite be placed at a convenient point and leveled. Let the board be placed about one foot in front of the theodolite, a lamp or candle placed on the shelf at its lower edge; and let the board be slipped up or down, until the pole-star can be seen...
Página 2 - An Act for the Encouragement of Learning, by securing the copies of Maps, Charts, and Books, to the authors and proprietors of such copies during the time* therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
Página 100 - Let the board be placed about one foot in front of the theodolite, a lamp or candle placed on the shelf at its lower edge ; and let the board be slipped up or down, until the pole-star can be seen through the hole. The light reflected from the paper will show the cross hairs in the telescope of the theodolite. Then, let the vertical spider's line be brought exactly upon the pole-star, and, if it is an eastern elongation that is to be observed, and the star has not yet reached the most easterly point,...
Página 100 - ... to coincide with the vertical hair. Then mark the point directly under the theodolite; the line passing through this point and the staff makes an angle with the true meridian equal to the azimuth of the pole-star. From the table of azimuths, take the azimuth corresponding to the year and nearest latitude. If the observed elongation was east, the true meridian lies on the west of the line which has been found, and makes with it an angle equal to the azimuth. If the elongation was west, the true...