The elements of plane and spherical trigonometry. [With] Key

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Page 147 - ... the sum of the three angles of a spherical triangle is greater than two right angles.
Page 11 - Triangles and parallelograms of the same altitude are to one another as their bases.
Page 149 - A. {cos a = cos b cos c + sin b sin c cos A. cos b = cos a cos c + sin a sin c cos B. cos c = cos a cos b + sin a sin b cos C.
Page 121 - The area of the surface of a sphere is equal to the product of the diameter by the circumference of a great circle. Let...
Page 120 - horizon" be given to the plane passing through our eye which is produced to the (extremities of the) universe, and separates off the segment which we see above the earth. The horizon is a circle; for, if a sphere be cut by a plane, the section is a circle. Let the name "meridian circle...
Page 99 - the square of the hypothenuse equals the sum of the squares of the other two sides,
Page 120 - ... impossible. Cor. 3. The centre of a sphere, and the centre of any small circle of that sphere, are in a straight line perpendicular to the plane of the circle. Cor. 4. The square of the radius of any small circle is equal to the square of the radius of the sphere diminished by the square of the distance from the centre of the sphere to the plane of the circle (B. IV., P. XI., C. 1): hence, circles which are equally distant from the centre, are equal ; and of two circles which are unequally distant...
Page 108 - Given, two sides and the angle opposite to one of them, to find the angle opposite to the other side.
Page 53 - The value of the sine of an angle increases from 0 to 1 as the angle increases from 0 to 90░...
Page 156 - В sin (A — B) = sin A cos В — cos A sin В cos (A — B) = cos A cos В + sin A sin В . ,-.. tan A + tan В . . _,.

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