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 |
From inside the book
Results 1-5 of 37
Page 60
... comp . log . b 10 log . b . Now add this arith . comp . to some other log . as log . a , the result will be = log a 10 log b subtract 10 and there remains — log a log b - The same result as would tracting log . b from log . a . have ...
... comp . log . b 10 log . b . Now add this arith . comp . to some other log . as log . a , the result will be = log a 10 log b subtract 10 and there remains — log a log b - The same result as would tracting log . b from log . a . have ...
Page 61
... comp log . sin 35 ° = 0.241409 Sum rejecting 10 from characteristic 1.417500 = log . 26.15 Applying it to the last example of Art . 61 we have log . tan . 30 ° 9.761439 log . 200 2.301030 0.000000 * ar . comp log . 101o sum rejec . 10 ...
... comp log . sin 35 ° = 0.241409 Sum rejecting 10 from characteristic 1.417500 = log . 26.15 Applying it to the last example of Art . 61 we have log . tan . 30 ° 9.761439 log . 200 2.301030 0.000000 * ar . comp log . 101o sum rejec . 10 ...
Page 62
... comp . log . 1010 log . 0.000000 1000 = 3.000000 log . tan . 77 ° 30 ′ = 10.654245 3.654245 = log . 4510.71 feet . ' Therefore the distance of the ship is 4510.71 feet , or a little over of a mile . SOLUTION OF PLANE TRIANGLES IN ...
... comp . log . 1010 log . 0.000000 1000 = 3.000000 log . tan . 77 ° 30 ′ = 10.654245 3.654245 = log . 4510.71 feet . ' Therefore the distance of the ship is 4510.71 feet , or a little over of a mile . SOLUTION OF PLANE TRIANGLES IN ...
Page 63
... 30 ° , the side opposite 1000 yards , and another angle 102 ° , the side opposite to which is required . Then sin 30 ° : sin 102 ° 1000 length of causeway required . Arith . comp . log . sin 30 ° 0.301030 OBLIQUE ANGLED TRIANGLES . 63.
... 30 ° , the side opposite 1000 yards , and another angle 102 ° , the side opposite to which is required . Then sin 30 ° : sin 102 ° 1000 length of causeway required . Arith . comp . log . sin 30 ° 0.301030 OBLIQUE ANGLED TRIANGLES . 63.
Page 64
... comp . log . sin 30 ° 0.301030 ( Art . 15 ) log . sin 102 ° log . sin 78 ° = log . 1000 9.990404 = : 3.000000 3.291434 - log.of1956 The length of the causeway must be 1956 yards . 65. This proportion is also applicable to the case where ...
... comp . log . sin 30 ° 0.301030 ( Art . 15 ) log . sin 102 ° log . sin 78 ° = log . 1000 9.990404 = : 3.000000 3.291434 - log.of1956 The length of the causeway must be 1956 yards . 65. This proportion is also applicable to the case where ...
Other editions - View all
Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ... Charles William Hackley No preview available - 2016 |
Elements of Trigonometry, Plane and Spherical: Adapted to the Present State ... Charles William Hackley No preview available - 2016 |
Common terms and phrases
adjacent apparent altitude applied arith called celestial sphere centre chord circle colatitude comp complement correction cosecant decimal declination departure determine diff difference of latitude difference of longitude direct course dist divided ecliptic equation EXAMPLE expressed formula Geom given number given side Greenwich hence horizon hour angle hypothenuse included angle meridian altitude middle latitude miles multiply Napier's rules Nautical Almanac number of degrees observed altitude obtained parallax in altitude parallel parallel sailing perpendicular plane sailing plane triangle polar triangle pole Prop proportion quadrant quantity quotient radius right angled triangle right ascension secant second member semidiameter ship side opposite sin a sin sine and cosine solution spherical triangle spherical trigonometry substituting subtract tance Tang tangent three sides tion trigonometrical lines true altitude tude
Popular passages
Page 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.
Page 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.
Page 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.
Page 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.
Page 83 - An oblique equator is a great circle the plane of which is perpendicular to the axis of an oblique projection.
Page 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.
Page 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.
Page 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
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 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...