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ABDP base bisecting chord circle passing co-s co-sine AC co-tangent of half common logarithm common section Comp complement COROLL COROLLARY describe the circle equal to half extremes gent given angle given circle given point half the difference half the sum half the vertical Hence hyperbolic logarithm inclination intersect less circle line of measures manifest oblique opposite OREM original circle parallel perpendicular plane of projection plane triangle ABC primitive PROB produced projected circle projected pole projecting point PROP radius rectangle right angles right line right-angled spherical triangle SCHOLIUM secant semi-tangents sides similar triangles sine 59 sine AC sphere spherical angle spherical triangle ABC sum or difference tang tangent of half THEOREM triangle ABC fig Trigonometry versed sine vertical angle whence
Σελίδα 1 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Σελίδα 3 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.
Σελίδα 75 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 85 - ... 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...
Σελίδα 31 - The cotangent of half the sum of the angles at the base, Is to the tangent of half their difference...
Σελίδα 34 - 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.
Σελίδα 13 - 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...