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 |
From inside the book
Results 1-5 of 33
Page ix
... negative arcs , ib . • 15 16 Definition of tangent , ib . • Variations in the value of the tangent for arcs from zero up to 360 ° , Definition of the secant , Variation of the secant for variation of the arc from zero to 360 ° , ib . 18 ...
... negative arcs , ib . • 15 16 Definition of tangent , ib . • Variations in the value of the tangent for arcs from zero up to 360 ° , Definition of the secant , Variation of the secant for variation of the arc from zero to 360 ° , ib . 18 ...
Page 16
... negative . * THE TANGENT . 19. The tangent of an arc is a perpendicular drawn to the radius at one extremity of the arc , and terminated by the radius produced , which passes through the other extremity . In the annexed dia- gram AT is ...
... negative . * THE TANGENT . 19. The tangent of an arc is a perpendicular drawn to the radius at one extremity of the arc , and terminated by the radius produced , which passes through the other extremity . In the annexed dia- gram AT is ...
Page 17
... negative . When the arc is 180 ° , the negative tangent , which became shorter and shorter as the second extremity of the arc approached this point , again reduces to 0 . Beyond 180 ° , or in the third quadrant , the tangent is cut off ...
... negative . When the arc is 180 ° , the negative tangent , which became shorter and shorter as the second extremity of the arc approached this point , again reduces to 0 . Beyond 180 ° , or in the third quadrant , the tangent is cut off ...
Page 18
... negative , as may be seen from the annexed diagram . 20. The least value of the tangent is 0. The greatest value is ∞ . So that the tan- gent has all possible values . B But these it has , if we do not regard the sign , in the M T A ...
... negative , as may be seen from the annexed diagram . 20. The least value of the tangent is 0. The greatest value is ∞ . So that the tan- gent has all possible values . B But these it has , if we do not regard the sign , in the M T A ...
Page 19
... negative . In the fourth quad- rant the secant is again estimated towards the second extremity of the arc , and is therefore positive . The vertical diameter separates the positive from the negative secants , the positive being in the ...
... negative . In the fourth quad- rant the secant is again estimated towards the second extremity of the arc , and is therefore positive . The vertical diameter separates the positive from the negative secants , the positive being 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.