A treatise on spherical trigonometry, and its application to geodesy and astronomy, with numerous examples. By John Casey.

Contents. ix
PAGE.
SECTION II.-First class continued,... 32
The right-angled triangle,... 32
Comparison of formulie for right-angled triangles, plane an
spherical,.... 34
Napier's rules,. 35
Exercises VII.,... 36
Quadrantal triangles,... 38
SECTION III.-Second Class,. 39
Formulae containing five elements,..39
Napier's analogies,... 39
Exercises VIII.,.... 40
SECTION IV.-Third class,...... 40
Delambre's analogies,........ 40
Historical sketch of Delambre's analogies,...41
Reidt's analogies,........ 41
Other applications of Delambre's analogies,. 43
Lhuilier's theorem,.. 44
The Lhuilierian function L,.... 44
The double value of,........ 44
Exercises IX.,.. 45
Breitschneider's analogies,..... 47
CHAPTER III.
SOLUTION OF SPHERICAL TRIANGLES.
Preliminary observations,..48
Use of auxiliary angles,......48
SECTION I.-The right-angled triangle,.. 49
Six cases of right-angled triangles,.... 49
First case.-Being given c and a, to calculate b, A, B, 49
Type of the calculation,. 50
Exercises X.,... 50
Second case.-Being given c, A, to calculate b, a, B,.. 50
Type of the calculation,........ 51
Exercises XI.,..51
Third case.-Being given a, b, to calculate A, B, c,. 51
Exercises XII.,... 52
Fourth case.-Being given a, A, to find c, b, B,.. 52
Exercises XIII.,.... 53
Fifth case.-Being given a, B, to find b, A,... 53
Exercises XIV.,.... 53
Sixth case.-Being given A, B, to find a, b, c.. 53
Exercises XV.,..54
Solution of quadrantal triangles,... 54