## An Elementary Treatise of Spherical Geometry and Trigonometry ... |

### Other editions - View all

An Elementary Treatise of Spherical Geometry and Trigonometry Anthony Dumond Stanley No preview available - 2015 |

An Elementary Treatise of Spherical Geometry and Trigonometry Anthony D. Stanley No preview available - 2017 |

### Common terms and phrases

a=cos a=cot B cot AB+BC adjacent angle ABC angle ACB angle opposite arcs b=cos b=sin BC and B'C C+sin C=cos C=sin circumference common section comp complemental computed corresponding cos C=cos cosec cosine distance drawn equal spheres equal to A'B given gles Hence hypotenuse included angle intersection Let ABC lune measures middle Napier's rule Napier's theorem oblique angles opposite angles opposite side pole of AC polygon quadrant radii radius remaining sides right angles right-angled spherical triangle right-angled triangle severally equal side AC side opposite sides AB sides and angles sin b sin sin BC sin(A+B sine sine of AC smaller sphere sphere whose center spherical angle spherical polygon spherical triangle Spherical Trigonometry supplements tangent tangent of half three quantities three sides tri-quadrantal triangle trian triangle ABC trigonometry unequal vertex whence wherefore

### Popular passages

Page 50 - ... fourth, if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...

Page 106 - In any plane triangle, the sum of any two sides is to their difference, as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 94 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...

Page 51 - DEF, having two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, are themselves equal (Prop.

Page 96 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides...

Page 8 - Axis of a great circle of a sphere is that diameter of the sphere which is perpendicular to the plane of the circle.

Page 27 - Therefore, if two triangles have two sides and the included angle of one, equal to two sides and the included angle of the other, the two triangles are equal in all respects.

Page 96 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.

Page 27 - If two angles of a spherical triangle are equal, the sides opposite these angles are equal and the triangle is isosceles. In the spherical triangle ABC, let the angle B equal the angle C. To prove that AC = AB. Proof. Let the A A'B'C