The elements of plane and spherical trigonometry. [With] Key1868 |
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The Elements of Plane and Spherical Trigonometry. [With] Key William Rossiter No preview available - 2016 |
The Elements of Plane and Spherical Trigonometry. [with] Key William Rossiter No preview available - 2018 |
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1+tan A B C A C BC AC AC Algebra angle increases angled triangle BC AC BC BC calculation centre CHAPTER circle circumference corresponding cos2 cosec cosine cotangent decreases degrees diameter equal equation Euclid Euclid's Elements Example.-Let examples feet Find A C Find the magnitude Find the ratio Find the values formulæ Geometry given to find grades L sin length less logarithms magnitude of angle method minutes perpendicular plane triangles PROP proved quadrant radius A B ratios of 90 Required right angle right-angled triangle secant sides and angles sin b sin sin² sine sine and cosine solid angle solution sphere spherical triangle subtended surface tangent three angles three sides triangle ABC Trigonometry vice versâ ом ОР دو
Popular passages
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 . . _,.