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 37
... diff . of logs . As the number 3905073 is too large to be found in the tables , the method of finding its logarithm from the tables must be postponed till the explanation of such cases , further in advance . Before explaining other ...
... diff . of logs . As the number 3905073 is too large to be found in the tables , the method of finding its logarithm from the tables must be postponed till the explanation of such cases , further in advance . Before explaining other ...
Page 40
... diff . of numbers . hence , 100 : diff . of logs . ⚫00005 ⚫00005 X 42 diff . of num . 42 diff . of logs . x x = = 0000210 100 adding this to the logarithm of 843700 which is 5.92619 the sum , rejecting the two last places 10 which go ...
... diff . of numbers . hence , 100 : diff . of logs . ⚫00005 ⚫00005 X 42 diff . of num . 42 diff . of logs . x x = = 0000210 100 adding this to the logarithm of 843700 which is 5.92619 the sum , rejecting the two last places 10 which go ...
Page 42
... diff . of logs . 00005 diff . of num . 42 diff . of logs . 000021 Instead of the 42 being given and the 000021 required as before , the 000021 is now given and the 42 required . The first term of the proportion is 100 or 1000 , & c ...
... diff . of logs . 00005 diff . of num . 42 diff . of logs . 000021 Instead of the 42 being given and the 000021 required as before , the 000021 is now given and the 42 required . The first term of the proportion is 100 or 1000 , & c ...
Page 43
... diff . and divide by the diff . number in the mar- gin , which is 6 . 6 ) 300 Annex the quotient 50 to the number 7392 before found , and you have the number required corresponding to the given logarithm , namely , 739250. This number ...
... diff . and divide by the diff . number in the mar- gin , which is 6 . 6 ) 300 Annex the quotient 50 to the number 7392 before found , and you have the number required corresponding to the given logarithm , namely , 739250. This number ...
Page 44
... diff . ( 100 above ) is not found exactly in the little table , take the nearest number to it , and take the ... Diff . 0-4971499 4971371 128 nearest to which in the little table is diff . with cipher annexed nearest to this in the ...
... diff . ( 100 above ) is not found exactly in the little table , take the nearest number to it , and take the ... Diff . 0-4971499 4971371 128 nearest to which in the little table is diff . with cipher annexed nearest to this in the ...
Contents
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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.