The Elements of Spherical Trigonometry |
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Common terms and phrases
adjacent angle agrees with equation bcos called circle circumference comp complements of BC cos b cos cos c sin cos² cosb cosc cosines cot a cot cot BC Csin disjoined extremes conjunct extremes disjunct find the angle find the hypothenuse formula Given the side Given the three greater than 90 hence hypothenuse BC icosahedron less than 90 log cos log cot log sin BC logarithm middle Napier's Analogies oblique angles octahedron opposite angles perpendicular plane angles Plane Trigonometry polar triangle pole polygon QUADRANTAL TRIANGLES radius regular polyhedron right-angled spherical triangle right-angled triangle side AC sin a sin sin c cos sin sin sin sin(a sin² a sin² sines six right solid angle solution sphere spherical triangle surface taking the complements three angles three circular three sides triangle ABC triangle is equal
Popular passages
Page 4 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.
Page 2 - ... the sum of the three angles of a spherical triangle is greater than two right angles.
Page 27 - The sum of any two sides is greater than the third side, and their difference is less than the third side.
Page 45 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 12 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 27 - The sum of any two angles is greater than the supplement of the third angle.
Page 46 - I made use of for finding the excess of the sum of the three angles of a spherical triangle above 180°, (which since that time has been quoted as Gen.
Page 27 - The sum of the three angles is greater than two right angles and less than six right angles.
Page 46 - Roy's rule, and given by him in the Philosophical Transactions for 1790, p. 171 ; it is, however, due to the late Mr. Isaac Dalby, who was then General Roy's assistant in the Trigonometrical Survey, and for several years the entire conductor of the mathematical department.
Page 60 - ... that the sum of all the angles of the triangles is equal to the sum of the angles of the polygon ; therefore the surface of the polygon is...