A Treatise on Plane and Spherical Trigonometry ... |
Common terms and phrases
1+cos a+b+c altitude angle in terms centre CHAPTER chord complement computed cos.² cos.³ cos.a cos.b cos.c cos.n cosec cot.² cot.c diameter equal equilateral equilateral polygon expression feet Find the area find the cosine Find the number find the sine formulas given angle Given two sides Hence lune negative number of sides oblique-angled perimeter perpendicular plane polar triangle pole quadrant quadrilateral radius regular polyhedrons right angle right-angled triangle secant sides and angles similarly sin.² sin.a sin.b sin.c sine and cosine solid angle sphere spherical polygon spherical triangle SPHERICAL TRIGONOMETRY subtend tangent theorem three angles three sides triangle ABC triangle in terms trigonometrical ratios Trigonometry values whence π π
Popular passages
Page 15 - OH is its cosine ; hence, the sine of an arc is equal to the. sine of its supplement ; and the cosine of an...
Page 129 - 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 118 - 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 57 - 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 120 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 150 - 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 94 - 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 144 - By equating the results and transposing, cos a = cos b cos с — sin b sin с cos A cos b...
Page 120 - 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 120 - 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°.