## A treatise on plane and spherical trigonometry |

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A.cos base called centre CHAPTER chord circle complement computed cos.a cos.b cos.c cosec described diameter difference dividing draw drawn edges English equal equation Examples expression faces feet figure Find the area find the sine formulas four fourth French given greater Hence included increases infinite inscribed known less lines log.c logarithmic measure meet minutes multiple nearly negative observed obtain opposite perimeter plane pole polygon positive prove quadrant quantities radius regular remaining respectively right angle rules secant sides signs similarly sin.a sin.b sin.c sine and cosine solid solution sphere spherical triangle subtend supplement surface tangent theorem third triangle in terms Trigonometry values whence

### Popular passages

Page 13 - OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an...

Page 127 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 116 - Every section of a sphere, made by a plane, is a circle, Let AMB be a section, made by a plane, in the sphere whose centre is C.

Page 55 - The area of a triangle is equal to half the product of any two of its sides multiplied by the sine of the included angle, radius being unity.

Page 118 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.

Page 148 - The area of a spherical triangle is proportional to the excess of the sum of its angles over two right angles (called the spherical excess).

Page 92 - Show that the area of a regular polygon inscribed in a circle is a mean proportional between the areas of an inscribed and circumscribing polygon of half the number of sides.

Page 142 - By equating the results and transposing, cos a = cos b cos с — sin b sin с cos A cos b...

Page 118 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.

Page 118 - Each side of a spherical triangle is less than the sum of 'the other two sides. 48. The sum of the sides of a spherical polygon is less than 360°. 49. The sum of the angles of a spherical triangle is greater than 180° and less tha'n 540°.