## 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

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**multiplying**by 10 % or 9. The convenience of a decimal division we have experienced in * Instead of thirds , fourths , & c . , the almost universal practice now is to use decimals of a second , viz . tenths , hundredths , and ... Page 23

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**multiplying**the means and dividing by the first term , we obtain the last RX sin a tan a = cos a that is , the tangent of any arc is equal to radius**multiplied**by the sine divided by the cosine of the same arc . If R be made equal to 1 ... Page 25

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**Multiplying**the expression for the tangent given in Art . 32 by that of the cotangent in Art . 34 , we have whence , and , tan a cot a R1 R2 tan = cot R2 cot = tan when R = 1 the above expressions become 1 tan = cot 1 cot = tan i . e ... Page 27

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**multiplying**the second and third terms , and dividing by the first , in the preceding proportions we have and b = a ...**multiply*** It is important to observe that the same trigonometrical lines of angles or arcs containing the same ... Page 28

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**multiply**the two extremes , and divide by the other mean . When R = 1 we have from proportion ( 3 ) above c = a coS B ( 4 ) -- i . e . either perpendicular side of a right angled triangle , equal to the hypoth . X cos of the adjacent ...### 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.