Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms
Kimber and Conrad, 1810 - Trigonometry - 125 pages
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added arch base called centre circle co-s co-sine AC co-tang common Comp complement consequently COROLLARY describe the circle diameter difference distance draw drawn equal evident excess extremes follows given angle given point gives greater half the difference half the sum Hence hypothenuse inclination intercepted intersect join known less line of measures logarithm manifest meeting minute Moreover oblique opposite parallel passing perpendicular plane of projection plane triangle ABC pole primitive PROB produced projecting point PROP proportion proposed proposition radius rectangle respectively right line RULE secant semi-tangents sides similar sine sine AC sphere supposed tang tangent of half Theor THEOREM triangle ABC fig Trigonometry vertical angle whence
Page 69 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 79 - ... projection is that of a meridian, or one parallel thereto, and the point of sight is assumed at an infinite distance on a line normal to the plane of projection and passing through the center of the sphere. A circle which is parallel to the plane of projection is projected into an equal circle, a circle perpendicular to the plane of projection is projected into a right line equal in length to the diameter of the projected circle; a circle in any other position is projected into an ellipse, whose...
Page 25 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Page 28 - The rectangle of the radius, and sine of the middle part, is equal to the rectangle of the tangents of the two EXTREMES CONJUNCT, and to that of the cosines of the two EXTREMES DISJUNCT.
Page 7 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those...
Page 28 - 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.