Elements of Trigonometry, Plane and Spherical: Adapted to the Present State of Analysis : to which is Added, Their Application to the Principles of Navigation and Nautical Astronomy : with Logarithmic, Trigonometrical, and Nautical Tables, for Use of Colleges and Academies

Forside
Wiley & Putnam, 1838 - 307 sider
 

Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

Innhold

Middle latitude sailing
141
Mercators sailing
145
CHAP 2 NAUTICAL ASTRONOMY 103 Introductory
149
Definitions
150
Corrections to be applied to the observed altitudes of celestial objects
152
Dip or depression of the horizon
153
Refraction
155
Parallax
157
Examples of corrections
158
Method of determining the latitude at sea by the meridian altitude
161
Examples
166
On finding the longitude by the lunar observations
171
Variation of the compass
177
Formulae for the tangent of the sum and difference of two arcs
180
Value of the sine and cosine of 45
181
Sine of 300 and secant of 60
182
Construction of table of sines c
183
MISCELLANEOUS TRIGONOMETRICAL INQUIRIES 122 Introductory
185
Use of the arithmetical complement
189
Quadrantal triangles
195
Formulae to be employed instead of Napiers rules in certain cases where great accuracy is required
199
Two sides and the included angle of a spherical triangle being given to find the third side directly
201
Two angles and the interjacent side being given to find the third angle
202
Rules relative to ambiguous cases
203
Determination of the effect of minute errors in data
205
Example in the measurement of distances
63
A side and the opposite angle being two of the given parts
64
Two angles and the interjacent side being given
65
Example in the measurement of heights the bases of which are in accessible
66
Two sides and the angle opposite one of them being given an am biguous case
67
Derivation of a formula for the cosine of an angle in terms of the three sides of a triangle
68
and 70 Derivation of formulae for the sine and cosine of the
69
and difference of two arcs Derivation of formula for the sine and cosine of an arc in terms of half the arc 62 64
72

Andre utgaver - Vis alle

Vanlige uttrykk og setninger

Populære avsnitt

Side 201 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Side 126 - The latitude of a place is its distance from the equator, measured on the meridian of the place, and is north or south according as the place lies north or south of the equator.
Side 78 - 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.
Side 35 - 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.
Side 83 - An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
Side 17 - The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right.hand column, belong to the degrees below.
Side 14 - 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.
Side 174 - A' . cos z =— .- — ;t cos A cos A ' and in the triangle mzs, cos d — sin « sin a' cos z = cos a cos a hence, for the determination of D, we have this equation, viz., cos D — sin A sin A' cos d — sin a sin a
Side 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...
Side 162 - S"Z and declination S"E, and it is north. We have here assumed the north to be the elevated pole, but if the south be the elevated pole, then we must write south for north, and north for south. Hence the following rule for all cases. 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, if of different names, their difference...

Bibliografisk informasjon