The Second [-fifth and Sixth] Part of A Course of Mathematics: Adapted to the Method of Instruction in the American Colleges

Howe & Spalding, S. Converse, printer, 1824

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 Section 1 Methods of calculating by logarithms 17 VIII 29 TRIGONOMETRY 49 Explanation of the Trigonometrical 58 Solutions of Right angled Triangles 73 Solutions of Oblique angled Triangles 80 Geometrical Construction of Triangles 91
 Notes 137 Table of Natural Sines and Tangents 147 32 153 Section I 15 Plane Sailing 24 Surveying a field by measuring round 57 Qther methods of surveying 86 The Magnetic Needle 92

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«Š’›Õ… 75 - C' (89) (90) (91) (92) (93) 112. 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.Ģ
«Š’›Õ… 49 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.Ģ
«Š’›Õ… 108 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.Ģ
«Š’›Õ… 89 - III. Two sides and the included angle being given ; to find the other side and angles. Draw one of the given sides. From one end of it lay off the given angle, and draw the other given side. Then connect the extremities of this and the first line. Ex. 1. Given the angle A 26į 14', the side b 78, and the side c 106 ; to find B, C, and a.Ģ
«Š’›Õ… 125 - 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.Ģ
«Š’›Õ… 36 - Icosaedron, whose sides are four triangles ; six squares ; eight triangles ; twelve pentagons ; twenty triangles.* Besides these five, there can be no other regular solids. The only plane figures which can form such solids, are triangles, squares, and pentagons. For the plane angles which contain any solid angle, are together less than four right angles or 360į. (Sup. Euc. 21, 2.) And the least number which can form a solid angle is three.Ģ
«Š’›Õ… 50 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.Ģ
«Š’›Õ… 129 - In any triangle, twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides, and the square of the base, as the radius to the cosine of the angle included by the two sides. Let ABC be any triangle, 2AB.BC is to the difference between AB2+BC2 and AC2 as radius to cos.Ģ