The Complete Mathematical and General Navigation Tables: Including Every Table Necessary to be Used with the Nautical Almanac in Finding the Latitude and Longitude : with Their Description and Use, Comprising the Principles of Their Construction, and Their Direct Application to Plane and Spherical Trigonometry, Navigation, Nautical Astronomy, Dialling, Practical Gunnery, Mensuration, Guaging &c. &c, Volum 1

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Baldwin and Cradock, 1828 - 664 sider
 

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Table Page xxv Correction of the logarithmic difference for the suns or stars appa rent altitude
51
Correction of the logarithmic difference for a planets apparent altitude
52
Natural versed sines and natural sines
53
IX
74
Proportional logarithms
75
Logarithmic half elapsed time
84
Logarithmic middle time
86
Logarithmic rising
87
To reduce points of the compass to degrees and conversely
89
Logarithmic secants to every second in the semicircle
90
Logarithmic sines to every second in the semicircle
93
Logarithmic tangents to every second in the semicircle
97
To reduce the time of the moons passage over the meridian of Greenwich to the time of her passage over any other meridian
100
Correction to be applied to the time of the moons reduced transit in finding the time of high water at any given place
102
Reduction of the moons horizontal parallax on account of the spheroidal figure of the earth
104
Reduction of terrestrial latitude on account of the spheroidal figure of the earth
105
A general traverse table or difference of latitude and departure
106
Meridional parts
113
The mean right ascensions and declinations of the principal fixed stars
114
Acceleration of the fixed stars or to reduce sidereal time into mean solar time
117
To reduce mean solar time into sidereal time
119
Altitude of a celestial object when its centre is in the prime ver tical most proper for determining the apparent time with the greatest accuracy
120
XLIX Amplitudes of a celestial object reckoned from the true east or west point of the horizon
122
To find the times of the rising and setting of a celestial object
123
For computing the meridional altitude of a celestial object the latitude and the declination being of the same name
138
The miles and parts of a mile in a degree of longitude at every degree of latitude
144
A concise system of decimal arithmetic
156
Solution of PRob LEMs IN PLAN E AND SPHERICAL TRIGono
168
Spherical trigonometry solution of right angled triangles 181
181
isation
211
i
223
Solution of problems relative to the errors of the log line and
272
Problem Page
394
Solution of PRoBLEMs RELAT1 v E to FINDING THE ALTIt UD Es
403
Solution of PROBLEMs RELATIVE to THE LoNGITUDE
413
Given the latitude of a place and the observed altitude of
420
Of reducing the apparent to the true central
436
Method W Of reducing the apparent to the true central
441
Of reducing the apparent to the true central
450
Given the observed distance between the moon and sun a fixed
470
Solution of Problems RELATIve to the VARIAtion of
483
Ill To find the variation of the compass by observations of a circum
492
Given the true course between two places and the variation
496
Given the latitude of a place and the height of the eye above
504
moons rising and setting
511
Given the latitude and the suns declination to find the interval
520
Solution of PROBLEMs Relative to the MENsu Ration
528
tances between those objects taken at any point in the same
536
Given the height of the eye to find the distance of the visible
544
To find the distance of an object by observing the interval
552
find its weight
560
Problem Page
564
To find the velocity of any shot or shell
571
elevation 576 Given the elevation for one range to find the elevation for another
577
Given the inclination of the plane the elevation of the piece
582
the impetus to find the range 582 Given the inclination of the plane the elevation of the piece
583
the horizontal range
590
Solution of PROBLEMs IN GAUGING
596
tvtion of Miscellaneous Problems
607
To find the distance of the sun from the earth
614
of the earth
649
Solution of Us EFUL AstroNoMICAL PROBLEMs
672
doctrine of compound interest
687
Description and use of the general victualling table
717

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Side 13 - Given two sides and the included angle, to find the third side and the remaining angles. The sum of the required angles is found by subtracting the given angle from 180°. The difference of the required angles is then found by Theorem II. Half the difference added to half the sum gives the greater angle, and, subtracted, gives the less angle.
Side 478 - AZIMUTH, in astronomy, an arch of the horizon, intercepted between the meridian of the place and the azimuth, or vertical circle passing through the centre of the object, which...
Side 206 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; each minute into 60 equal parts called seconds.
Side 57 - And, if the logarithm of any number be divided by the index of its root, the quotient will be equal to the logarithm of that root. Thus the index or logarithm of 64 is 6 ; and, if this number be divided by 2, the quotient will be = 3, which is the logarithm of 8, or the square root of 64.
Side 57 - Also, between the mean, thus found, .and the nearest extreme, find another geometrical mean, in the same manner ; and so on, till you are arrived within the proposed limit of the number whose logarithm is sought.
Side 481 - ... reckoned from the north in north latitude, but from the south in south latitude. » In observations of the altitude of the sun'< loiter limb (by afore enervation) it is u«u»l to »<M 12' for tic cBecl of dip, parallax, ami sern diameter.
Side 153 - When there happens to be a remainder after the division ; or when the decimal places in the divisor are more than those in the dividend ; then ciphers may be annexed to the dividend, and the quotient carried on as far as required.
Side 675 - The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy.
Side 643 - ... position with respect to a luminous body, can cast a circular shadow ; likewise all calculations of eclipses, and of the places of the planets, are made upon supposition that the earth is a sphere, and they all answer to the true times when accurately calculated. When an eclipse of the moon happens, it is observed sooner by those who live eastward than by those who live westward ; and, by frequent experience, astronomers have determined that, for every fifteen degrees difference of longitude,...
Side 177 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

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