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A treatise on plane and spherical trigonometry: including the construction ...
Uten tilgangsbegrensning - 1860
ABDP adjacent angle angled spherical triangle base bisect C.cos C.sin centre circle Art common section cone conical surface consequently construction cosec cosine cotan cotan BAC directrix distance ecliptic ellipse equal equation given angle greater axis Hence hyperbola hypothenuse intersection join latus rectum less circle Let ABC line of measures logarithms meet opposite ordinate original circle parabola parallel perpendicular plane of projection primitive circle projected circle projected pole projecting point Q. E. D. Art Q. E. D. Cor quadrant radius right angled spherical right ascension right line secant semicircle semitangent sides similar triangles sine sphere spherical angle tan AC tangent tangent of half touches the circle triangle ABC vertex vertical angle whence wherefore
Side 39 - In the same way it may be proved that a : b : : sin. A : sin. B, and these two proportions may be written a : 6 : c : : sin. A : sin. B : sin. C. THEOREM III. t8. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference. By Theorem II. we have a : b : : sin. A : sin. B.
Side 78 - Required the height and distance of the steeple. Ans. Height, 210.4 feet; distance, 250.8 feet. 14. Two pulleys, whose diameters are 6 inches and 4 feet 3 inches, respectively, are placed at a distance of 3 feet 6 inches from centre to centre. What must be the length of a belt which shall connect them, by passing around their circumferences, without crossing...
Side 78 - From the top of a tower, whose height is 108 feet, the angles of depression of the top and bottom of a vertical column standing in the horizontal plane are found to be 30° and 60° respectively ; required the height of the column.
Side 80 - Ans. 41.9968. 6. tin a level garden there are two lofty firs, having their tops ornamented with gilt balls, one is 100 feet high, the other 80, and they are 120 feet distant at the bottom ; now the owner wants to place a fountain in a right line between the trees, to be equally distant from the top of each...
Side 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Side 98 - In a right angled spherical triangle, the rectangle under the radius and the sine of the middle part, is equal to the rectangle under the tangents of the adjacent parts ; or', to the rectangle under the cosines of the opposite parts.
Side 36 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Side 117 - The straight line joining the vertex and the centre of the base is called the axis of the cone.
Side 40 - Def. 10. 1.) If then CE is made radius, GE is the tangent of GCE, (Art. 84.) that is, the tangent of half the sum of the angles opposite to AB and AC. If from the greater of the two angles ACB and ABC, there be taken ACD their half sum ; the remaining angle ECB will be their half difference.