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 60 for tan45 + 2 read tan 45 45 them 51 SECTION VI 57 SECTION I 67
 placed at the end of the volume for the general 167 triangles 194 their proof by induction 204

Passatges populars

Pŕgina 102 - 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 The...
Pŕgina 42 - 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.
Pŕgina 70 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Pŕgina 89 - Let a, b, c, be the sides, and A, B, c, the angles of a spherical triangle, as usual.
Pŕgina 80 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Pŕgina 52 - The logarithm of a power of a number is found by multiplying the logarithm of the number by the exponent of the power. For, A« = (10°)
Pŕgina 115 - Б) arc of the same species. 180. In the solution of oblique-angled spherical triangles, there are six cases, the data in them being, respectively, I. Two sides and an angle opposite one of them. II. Two angles and a side opposite one of them. III. Two sides and the included angle. IV. Two angles and the included side. V. The three sides. VI. The three angles. CASE I. 181. Given two sides and an angle opposite one of them. Let there be given, in the oblique- c angled spherical triangle ABC, the sides...
Pŕgina 103 - ... is enabled to solve every case of right-angled triangles. These are known by the name of Napier's Rules for Circular Parts ; and it has been well observed by the late Professor Woodhouse, that, in the whole compass of mathematical science, there cannot be found rules which more completely attain that which is the proper object of all rules, namely, facility and brevity of computation.
Pŕgina 46 - ... and using, in case of need, the auxiliary angles ; with the modifications of the formulae whence they are derived ; and having reference, for convenience of notation, to a spherical triangle ABC, figure 15 or 16, whose sides a, b, c, are respectively opposite to the angles A, B, C.
Pŕgina 94 - ... b) = sec b, cosec ( — b) = — cosec b ; (53) that is, the cosine and secant of the negative of an angle are the same as those of the angle itself ; and the sine, tangent, cotangent, and cosecant of the negative of an angle are the negatives of those of the angle. These results correspond with those obtained geometrically (Art. 68). 80.