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• 207

2. GENERAL FORMULÆ for the solution of the different

cases of right-angled spherical triangles 193 to 199

3. General observations on the species and ambiguity

bf the different cases

199

4. Quadrantal, or rectilateral spherical triangles 199

5. GENERAL FORMULÆ for the solutions of the different

cases of oblique-angled spherical triangles 200 to 207

6. General observations on the ambiguity of the

different cases

CHAP. VI. PRACTICAL Rules for the solutions of all the different

cases of RIGHT-ANGLED SPHERICAL TRIANGLES, with

their application by LOGARITHMS

208 to 227

CHAP. VII. PRACTICAL Rules for solving the different cases of

RECTILATERAL or QUADRANTAL SPHERICAL TRI-

ANGLES, with their application by LOGARITHMS 227 to 231

CHAP. VIII. PRACTICAL Rules for solving all the different cases of

OBLIQUE-ANGLED SPHERICAL TRIANGLES with a PER-

PENDICULAR, &c.; and their application by LOGA-

231 to 245

CHAP. IX.

PRACTICAL Rules for solving all the different cases of

OBLIQUE-ANGLED SPHERICAL TRIANGLES without a

PERPENDICULAR, with their application by LOGA-

243 to 260

CHAP. X. 1. ASTRONOMICAL DEFINITIONS AND INTRODUCTORY

260

II. Astronomical definitions

260 to 265

Prob, 1. To turn degrees, or parts of the equator, into time 265

2, To turn time into degrees

3. Given the time under any known meridian to find

the corresponding time at Greenwich

266

4. Given the time at Greenwich to find the correspond-

ing time under any known meridian

268

5. To reduce the declination of the sun, as given in the

Nautical Almanac, to any other meridian, and to any

given time of the day

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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

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

ating

. 275

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

true altitude

276

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

upper limb, to find the true altitude of its centre. 977

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

CHAP XI. THE APPLICATION OF RIGHT ANGLED SPHE-

RICAL TRIANGLES TO ASTRONOMICAL PRO-

BLEMS

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

gitude, to find his right ascension and declination 282

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

ation, to find hisamplitude, ascensional difference, and

the time of his rising and setting

284

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

289

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

292

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

294

6. The difference of longitude between two places, both

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

tance between them, &c.

296

CHAP. XII. THE APPLICATION OF OBLIQUE-ANGLED SPHE-

RICAL TRIANGLES TO ASTRONOMICAL PRO-

BLEMS

• 298

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 298

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-

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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

303

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

planet, being given, to find its right ascension and

declination, et contra

305

11. The right ascensions and declinations of two stars,

or the latitudes and longitudes of two stars being

given, to find their distance

308

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

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

third star

310

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

ation and altitude, to find the azimuth

313

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

ation and altitude, to find the hour of the day 316

14. Continued. The construction of the xvith of the

REQUISITE TABLES, used in finding the latitude by

two altitudes of the sun (Note)

317

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

319

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

the observations, to find the latitude of the place 323

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

326

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

earth's centre

332

17. Continued. Investigation of a GENERAL RULE for

determining the true distance of the moon from the

sun, or from a fixed star

333

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.

337

CHAP. XIII. OF THE FLUXIONAL ANALOGIES OF SPHE-

RICAL TRIANGLES

344

Prop. 1. A preparatory proposition

344

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

345

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

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