## 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

Page 281

...

...

**Call the zenith distance north or south , according as the zenith is north or south of the object . If**the zenith distance and declination be of the same name , that is , both north or both south , their sum will be the latitude ; but ...### Contents

217 | |

219 | |

227 | |

244 | |

250 | |

262 | |

269 | |

276 | |

50 | |

72 | |

80 | |

87 | |

97 | |

114 | |

136 | |

143 | |

147 | |

150 | |

151 | |

165 | |

172 | |

174 | |

182 | |

184 | |

194 | |

211 | |

215 | |

277 | |

287 | |

293 | |

299 | |

301 | |

311 | |

318 | |

324 | |

330 | |

337 | |

343 | |

351 | |

352 | |

358 | |

364 | |

370 | |

111 | |

112 | |

### Other editions - View all

### Common terms and phrases

altitude applied azimuth called centre colatitude collimation column comp computed correction corresponding cos² cosc cosec cotangent course declination deduced determined diagram diff difference of latitude dist divided equal equation error EXAMPLE expressed feet formula Geom Greenwich hence horizontal hour angle hypothenuse intersection interval limb logarithm longitude measured meridian transit middle wire miles multiplied Napier's rules Nautical Almanac number of degrees object observed obtained parallax parallel passing perpendicular plane sailing plane triangle pole proportion quadrant radius refraction right angled triangle right ascension sailed screw secant second member semidiameter ship side opposite siderial sin a sin sin² sine sine and cosine solution sphere spherical triangle spherical trigonometry spirit level star subtracting supporting axis tangent telescope theodolite transit instrument trigonometrical lines vernier vertical circle zenith distance zero

### 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.