Variation of the sine for values of the arc from zero to 360°, Method from an arc> 90° to find one < 90° having the same sine, Variations in the value of the tangent for arcs from zero up to 360°, Variation of the secant for variation of the arc from zero to 360°, Exercises in the trigonometric functions, Derivation of formulas for the solution of right angled plane triangles, Description and mode of using the trigonometric tables of Callet, Method of finding the degrees, minutes, and seconds corresponding to any SOLUTION OF Right Angled TRIANGLES BY THE AID OF LOGARITHMS, Exercises in ditto, Practical examples, Practical exercises, . Use of the arithmetical complement, SOLUTION OF OBLIQUE ANGLED PLANE TRIANGLES, Practical problems, . Deduction of the formula for the cosine of an angle in terms of the three sides of a triangle Example under the above formula, Blank form for the same, Derivation of formulas for the sum and difference of the sines of two arcs and their ratio, Demonstration of formula to be used in the last case, when only the Of the sine and cosine of 45°. Of the sine, &c., of 300 and 60°, Extension of the demonstration for sine and cosine of (ab) to all the Forms for the sum and difference of the sines and cosines of two arcs, Table of forms for the trigonometric lines in the different quadrants, Forms for trigonometric lines of arcs greater than 360°, Table of formulas expressing the most useful general relations of arcs, Evasion of tabular errors for very large or very small angles, Resolution of quadratic equations trigonometrically, ib. Of a formula for the cosine of half an angle in terms of the three sides, Formulas for the sine and tangent of half an angle in terms of the three New mode of deriving Napier's analogies from the Gauss equations, Geographic example of the application of Napier's Analogies, . Astronomic example of the same, viz. the determination of the latitude and longitude of a heavenly body from its right ascension and decli- Mode of solution when two sides and the included angle are given, and the ib. Mode of applying electro-magnetism to record the observation, . Mode of solution when two angles and the included side, the unknown Napier's rules for the solution of right angled triangles, Astronomical example, from the sun's right ascension and declination, to find his longitude, . Exercises in right angled spherical trigonometry, Astronomical Problem. Given the sun's declination, to find the time of his |