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The Contents of this Book.
V
PART I. CHA P. I.
CONCERNING the Principles of the Doctrine of the Sphere, and Spherical Projection and Trigono
metry, in fifty four Definitions
Chap. II.
Page 1
Containeth twelve Theorems ferving to the Orthographic
Projection of the Sphere, called the Analemma, in
Plano
Chap. III.
10
Containeth Problems of the Orthographic Projection, viz.
19
Prob. 1. To defcribe an Ellipfis
Prob. 2. To divide a Right Circle into its proper Degrees
20
Prob. 3. To divide an Oblique Circle into its proper De
grees
21
Prob. 4. To project the Sphere on the Solftitial Colure 22
Prob. 5. To defcribe the Hour Circles, Azimuths, &c. 24
Prob. 6. To divide the Ecliptic into the twelve Signs of
the Zodiac
25
Prob. 7. To annex the Calendar to the Analemma ibid.
Prob. 8. To fhew the Ufes of this Projection in general 26
Prob. 9. To exhibit a Synopfis of the Aftronomical Affecti
ons of the Heavens for any given Time thereby 28
Prob. 10. To reprefent the fixed Stars on this Projection
7
Chap. IV.
Containeth eleven Theorems ferving to the Stereographic
Projection of the Sphere in Plano
Chap. V.
30
Containeth Problems of the Stereographic Projection, viz.
42
ibid.
Prob. 1. To find the Pole of any Great Circle
Prob. 2. To defcribe, or lay down, any Spherical Angle
43
Prob. 3. To draw a Great Circle through any given
Point, fo as to contain any given Angle with the Pri
mitive
44
Prob. 4. To defcribe a Great Circle through any two
Points given within the Primitive
Prob. 5. To measure any Spherical Angle
Prob. 6. To divide any Great Circle into its
Prob. 7. To draw any parallel Circle
45
46
proper De
48

49
Prob. 8. To draw a Great Circle perpendicular to any
other
Prob. 9. To graduate any leffer Oblique Circle
Chap. VI.
51
52
53
55
The Stereographic Projection of the Sphere on the Planes
of feveral Great Circles of the Sphere
Viz. 1. On the Plane of the General Meridian
2. On the Plane of the Horizon of London
3. On the Plane of the Ecliptic
4. On the Plane of the Equinoctial
5. On the Plane of the Tropic of Capricorn
6. On the Plane of any Oblique Circle
Chap. VII.
56
62
65
68
70
Containeth Forty One Theorems for the Explication of the
Doctrine of Spherical Triangles in general; by which
is fhewn the Reason of the feveral Canons for their
Solution
74
Chap.
Chap. VIII.
Of the Nature, Cafes, Analogies, and various Methods
of Solving Rightangled Spherical Triangles; with a
Synopfis of the Whole Doctrine
Chap. IX.
98
Method 1. Of folving Rightangled Spherical Triangles
by the Logarithmetic Canon of Sines and Tangents
Method 9 and 10. By the Orthographic and Stereogra
phic Planifpheres
Chap. XVIII.
161
Of the Doctrine of Obliqueangled Spherical Triangles;
a Synopfis of the fix Cafes thereof; the Method of
Solving them by letting fall a Perpendicular; and
Rules for folving all kind of Ambiguities attending
them
Chap. XIX.
166
Method of folving Oblique Spherical Triangles without a
Perpendicular with a proper Scheme for the Demon
ftration thereof
;
a 2
* 18
Chap. XX.
The Solution of the fix Cafes of Oblique Triangles by Ste
reographic Projection
Chap. XXI.
200
Tha Menfuration of the Area of a Spherical Triangle ;
and the Completion of a folid Body; with Examples
of each
208
PART II.
CHAP. I.
Containing the Application of Spherical Trigonometry
to Aftronomy; in all the practical Problems of the
Sun, Moon, and Stars; with Tables of the Sun's Mo
tion, for Years, Months, Days, Hours, Minutes, and
Seconds. The Problems are as follow
213
Viz. Prob. 1. To find the Sun's Place at any time by
the Tables
221
224
Prob. 2. To find the Latitude of any Place
Prob 3. To find the Sun's Greatest Declination 225
Prob. 4. To find the Sun's Prefent Declination 226
Prob. 5. To find the Sun's Right Afcenfion 227
Prob. 6. To find the Sun's Place, and Right Afcen fion otherwise ibid.
Prob. 7. To find the Angle of the Sun's Pofition 228
Prob. 8. To find the Sun's Amplitude of Rifing
and Setting ibid.
Prob. 9. To find the Afcenfional Difference; or the
true Time of the Sun's Rifing and Setting 230
Prob. 10. To find the Sun's Oblique Afcenfion and
Defcenfion
231
Prob. 11. To find the Time the Sun is due Eaft or
West
232
Prob. 12. To find his Altitude when due Eaft or
Weft
233
Prob.
Prob. 13. To find the Sun's Azimuth at the Hour
of fix
Prob. 14. To find his Altitude at the Hour of fix
234
235
Prob. 15. To find the Sun's Altitude at any time
of Day 236
Prob. 16. To find the Hour of the Day 240
Prob. 17. To find the Sun's Azimuth at any time
241
243
Prob. 18. To find the Sun's Apparent Rifing, Set
ting, and Amplitude
Prob. 19. To find the Beginning and End of Twi
light
246
Prob. 20. To find the Declination of a Star or
Planet
Prob. 21. To find its Right Afcenfion
248
251
Prob. 22. To find its Longitude and Latitude 252
Prob. 23. To find the Hour of the Night
254
Prob. 24. To find the Culminating Point in the
Ecliptic
Prob. 25. To find the Meridian Angle
256
257
Prob. 26. To find the Declination of the Culmina ting Point
Prob. 27. To find the Altitude thereof
258
Prob. 28. To find the Altitude of the Nonagefima
Prob. 29. To find the Place thereof in the Ecliptic
259
Prob. 30. To find the Cufp of the Afcendant, or
Horoscope
260
Prob. 31. To find the Parallactic Angle ibid. Prob. 32. To find the Cofmical Rifing of a Star, 261
&c.
Prob. 33. To find the Time of its Cofmical Setting
263
Prob. 34. To find the time of its Achronical Rifing
and Setting
264