A Treatise on Trigonometry, Plane and Spherical: With Its Application to Navigation and Surveying, Nautical and Practical Astronomy and Geodesy, with Logarithmic, Trigonometrical, and Nautical Tables ...G.P. Putnam, 1851 - 372 pages |
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Page 25
... quotient of the sine and cosine , and that therefore when the sine and cosine have contrary signs , the tangent and cotangent will be negative . This occurs in the second and fourth quadrants . It appears hence , that the cotangent ...
... quotient of the sine and cosine , and that therefore when the sine and cosine have contrary signs , the tangent and cotangent will be negative . This occurs in the second and fourth quadrants . It appears hence , that the cotangent ...
Page 37
... quotient . - b'- = n n Since l ' is the exponent of the power to which it is necessary to raise b the base , in order to produce it follows that — l ' is the loga- n N n ' rithm of i . e . the logarithm of the quotient is equal to the ...
... quotient . - b'- = n n Since l ' is the exponent of the power to which it is necessary to raise b the base , in order to produce it follows that — l ' is the loga- n N n ' rithm of i . e . the logarithm of the quotient is equal to the ...
Page 39
... quotient of the numerator divided by the denominator , applying the rule for division by logarithms , the greater logarithm would have to be subtracted from the lesser , and the remainder would of course be negative . From the above ...
... quotient of the numerator divided by the denominator , applying the rule for division by logarithms , the greater logarithm would have to be subtracted from the lesser , and the remainder would of course be negative . From the above ...
Page 40
... quotient would have extended three places beyond the usual . Had they differed by 10 , the quotient would have extended one place beyond . The inaccuracy of this method increases with the number of additional figures beyond four , in ...
... quotient would have extended three places beyond the usual . Had they differed by 10 , the quotient would have extended one place beyond . The inaccuracy of this method increases with the number of additional figures beyond four , in ...
Page 42
... quotient figure without annexing a cipher to the dividend , this quotient figure must be added to the last figure of the number taken from the table . Should it be necessary to annex two ciphers before obtaining a quotient figure , a ...
... quotient figure without annexing a cipher to the dividend , this quotient figure must be added to the last figure of the number taken from the table . Should it be necessary to annex two ciphers before obtaining a quotient figure , a ...
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Common terms and phrases
altitude azimuth called celestial sphere centre circle colatitude collimation column comp computed correction corresponding cos² cosc cosec cotangent course decimal declination departure determined diagram diff difference of latitude difference of longitude divided equal equation error EXAMPLE expressed feet formula Geom given number hence horizontal hour angle hypothenuse instrument intersection limb logarithm longitude means measured meridian miles multiplied Nautical Almanac number of degrees object observed obtained parallax parallel perpendicular plane sailing plane triangle polar pole proportion quadrant quotient radius right angled triangle right ascension sailing screw secant second member semidiameter ship side opposite siderial sin a sin sin² sine and cosine sine of half solution sphere spherical triangle spherical trigonometry spirit level star subtracting supporting axis tangent telescope transit trigonometrical lines vernier vertical wire zenith distance
Popular passages
Page 204 - ... 6. The latitude of a place is its distance north or south of the equator, measured on the meridian of the place.
Page 136 - The sine of half the sum of two angles of a spherical triangle is to the sine of half their difference as the tangent of half the interjacent side is to the tangent of half the difference of the other two sides.
Page 33 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 86 - When a ray of light passes from one medium to another, it is refracted so that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities in the two media.
Page 79 - 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 66 - 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 arc is equal to the cosine of its supplement* Furthermore...
Page 219 - Then, along the horizontal line, and under the given difference of latitude, is inserted the proper correction to be added to the middle latitude to obtain the latitude in which the meridian distance is accurately equal to the departure. Thus, if the middle latitude be 37°, and the difference of latitude 18°, the correction will be found on page 94, and is equal to 0° 40'. EXAMPLES. 1. A ship, in latitude 51° 18...
Page 213 - A2,lay off the distance BC = 23 miles; in the direction parallel to A3, lay off CD = 36 ; in the direction parallel to A4, lay off DE = 12 miles ; and, lastly, in the direction parallel to A5, lay off EF = 41 ; then F will be the place of the ship at the end of the traverse ; consequently, AF will be the distance made good, and the angle FAS the direct course ; applying, therefore, the distance AF to the scale of equal parts, we shall find it reach from 0 to 62| ; and applying the distance Sa to...
Page 284 - ZP. Now, in the triangle PSS', we have given two sides and the included angle to find the third side SS', and one of the remaining angles, say the angle PSS'.
Page 13 - SINE of an arc, or of the angle measured by that arc, is the perpendicular let fall from one extremity of the arc, upon the diameter passing through the other extremity. The COSINE is the distance from the centre to the foot of the sine.