An Introduction to the Theory and Practice of Plain and Spherical ... - Thomas Keith - Βιβλία Google

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THE CONSTRUCTION AND USE OF THE PLAIN

2. Of the logarithmical lines, or GUNTER'S scale

3. The construction of the logarithmical lines on

4. GUNTER'S proportions for using the line of versed

5. Demonstration of GUNTER's proportions (Note) 22 and 23

6. The use of the logarithmical lines on GUNTER'S scale 23

GEOMETRICAL DEFINITIONS AND INTRODUC-

1. Definitions, &c. of angles

2. To erect a perpendicular from a given point in a
given line, or to make a right angle

3. To draw a straight line perpendicular to a given
straight line from a given point without it

4. To make an angle of any proposed number of degrees

upon a given straight line, by the scale of chords

5. An angle being given, to find how many degrees it

contains, by a scale of chords

6. Definitions and general properties of triangles

DEFINITIONS OF PLANE TRIGONOMETRY, &c.

2. Investigation of general rules for calculating the sides

and angles of plane triangles

3. Formulæ for the solutions of the different cases of

right-angled plane triangles

4. Formulæ for the solution of the different cases of

oblique-angled triangles

PRACTICAL RULES FOR THE SOLUTION OF ALL

THE DIFFERENT CASES OF RIGHT-ANGLED

PLANE TRIANGLES, WITH THEIR APPLI-

CATION BY LOGARITHMS

2. Practical rules for solving all the cases of oblique

triangles with their application by logarithms

THE APPLICATION OF PLANE TRIGONOMETRY

TO THE MENSURATION OF DISTANCES,

The subject continued, and more minutely considered

1.. Observations on the admeasurement of a base line

2. Of the errors which occur in taking angles of ele-

vation and depression with a theodolite

84

3. The nature of terrestrial refraction, and its effects on

angles of elevation

4. Of the reduction of angles to the centre of the station 89

5. Of the reduction of angles from one plane to another

6. Of the dip, or depression of the horizon at sea

7. Of the parallax of the celestial bodies

8. Of the admeasurement of altitudes by the barometer

and thermometer

OF THE SIGNS OF TRIGONOMETRICAL QUANTI-

1. General properties of the sines, tangents, chords, &c.

of SINGLE ARCS, with a variety of useful formulæ 102 to 106

2. General properties of the sines, tangents, &c.of DOUBLE

ARCS and of HALF ARCS, with formulæ, &c. 106 to 111

3. General properties of the sines, tangents, &c. of the

SUMS, and of the DIFFERENCES of ARCS, including a

great variety of formulæ

4. General properties of the sines, tangents, &c. of ARCS

in ARITHMETICAL PROGRESSION

5. Of the sines, tangents, &c. of the MULTIPLES of

6. Of the sines and cosines of the POWERS of

7. The determination of the value of the sine and of

the cosine, &c. of any arc, in terms of that arc, by

infinite series, &c.

8. The construction of a table of sines, &c.

DEFINITIONS, &c. OF SPHERICAL ANGLES,

ARCS, AND TRIANGLES

2. Spherical Geometry, or general properties of spheri-

cal angles, arcs, and triangles, &c.

STEREOGRAPHIC PROJECTION

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INVESTIGATION OF GENERAL RULES FOR CAL-

CULATING THE SIDES AND ANGLES OF RIGHT-

ANGLED SPHERICAL TRIANGLES, &c. 165 to 170

2. BARON NAPIER's universal rules for solving right-

angled spherical triangles

Prop. 4. To find the excess of the three angles of a spherical
triangle, above two right angles

5. To reduce the angles of a spherical triangle (whose

sides are very small arcs) to those of a rectilineal tri-

angle, having its sides of equal length with the sides

of the spherical triangle

6. Given two sides of a spherical triangle, and the angle

comprehended between them; to find the angle con-

tained between the chords of these sides, supposing

the chords not to differ materially from the arcs which

7. The angles of elevation of two distant objects being

given, together with the oblique angle contained be-

tween the objects, to find the horizontal angle

THE THEORY OF NAVIGATION.

CHAPTER I. Definitions and Plane sailing

CHAP, II. Parallel and Middle Latitude sailing

CHAP. III. Mercator's sailing

I. A Table of the LOGARITHMS of numbers, from an

unit to ten thousand

II. A Table of NATURAL SINEs to every degree and

minute of the quadrant

III. A Table of LOGARITHMICAL SINES and TANGENTS to

every degree and minute of the quadrant 418 to 440

IV. A Table of the REFRACTION in altitude of the heavenly

V. A Table of the depression or DIP of the horizon of

VI. A Table of the sun's PARALLAX in altitude

VII. A Table of the augmentation of the moon's semi-

VIII. A Table of the right ascensions and declinations

of thirty-six principal fixed stars, corrected to the

beginning of the year 1822

Five copper-plates at the end of the book.

Prob. 6. To reduce the declination of the moon, as given in

the Nautical Almanac, to any other meridian, and to

any given time of the day

7. To find the time of a star's culminating, or coming

to the meridian of Greenwich

s. To find the time of the moon, or any planet's culmin-

9. Given the observed altitude of a fixed star to find its

10. Given the observed altitude of the sun's lower or

upper limb, to find the true altitude of its centre . 277

11. Given the observed altitude of the moon's lower or

upper limb, to find the true altitude of its centre. 278

12. Given the sun's meridian altitude to find the latitude

of the place of observation

THE APPLICATION OF RIGHT ANGLED SPHE-

RICAL TRIANGLES TO ASTRONOMICAL PRO-

Prob. 1. Given the obliquity of the ecliptic and the sun's lon-

gitude, to find his right ascension and declination

2. Given the latitude of the place, and the sun's declin-

ation, to find his amplitude, ascensional difference, and

the time of his rising and setting

3. The latitude of the place, and the sun's (or a star's)

declination being given, to find the altitude and azi-

muth, &c. at six o'clock

4. The latitude of a place, and the declination of the sun

(or of a star) being given; to find the altitude, and

the times when it will be due east and west

5. Given the latitude of the place, and the sun's altitude,

when on the equinoctial, to find his azimuth and the

hour of the day

6. The difference of longitude between two places, both

in one parallel of latitude, being given, to find the dis-

tance between them, &c.

THE APPLICATION OF OBLIQUE-ANGLED SPHE-

RICAL TRIANGLES TO ASTRONOMICAL PRO-

Prob. 7. Given the sun's declination, and the latitude of the

place, to find the apparent time of day-break in the

morning, and the end of twilight in the evening

8. Given the day of the mouth, the latitude of the place,

the horizontal refraction, and the sun's horizontal

parallax, to find the apparent time of his centre ap-

pearing in the eastern or western part of the horizon 30

Prob. 9. Given the latitude of the place, the day of the month,

the moon's horizontal parallax and refraction, to find

the time of her rising

10. The latitude and longitude of a fixed star, or of a

planet, being given, to find its right ascension and

declination, et contra

11. The right ascensions and declinations of two stars,

or the latitudes and longitudes of two stars being

given, to find their distance

12. The places of two stars being given, and their dis-

tances from a third star, to find the place of this

13. Given the latitude of the place, the sun's declin-

ation and altitude, to find the azimuth

14. Given the latitude of the place, the sun's declin-

ation and altitude, to find the hour of the day

14. Continued. The construction of the xvith of the

REQUISITE TABLES, used in finding the latitude by

two altitudes of the sun (Note)

15. Given the latitude of the place, the declination and

the altitude of a known fixed star, to find the hour

of the night when the observation was made

16. Given two altitudes of the sun and the time between

the observations, to find the latitude of the place

16. Continued. A GENERAL RULE for finding the latitude

by two altitudes of the sun, the elapsed time and the

sun's declination being given

17. Given the apparent distance of the moon from the

sún, or from a star, and their apparent zenith dis-

tances, to find their true distance, as seen from the

17. Continued. Investigation of a GENERAL RULE for

determining the true distance of the moon from the

sun, or from a fixed star

18. The latitude of a place and its longitude by account,

the distance between the sun and the moon, or the

moon and a star in the NAUTICAL ALMANAC being

given, to find the correct longitude.

CHAP. XIII. OF THE FLUXIONAL ANALOGIES OF SPHE-

RICAL TRIANGLES

Prop. 1. A preparatory proposition

2. To find the fluxions of the several parts of a RIGHT-

ANGLED spherical triangle, when one of its oblique

angles is a constant quantity

3. To find the fluxions of the several parts of a RIGHT-

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