## A Treatise on Plane and Spherical Trigonometry |

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according adjacent angle applied becomes CHAPTER Check circle computation considered constant corresponding cos A sin cos b cos cos² cosc cosec deduce denote determined develop difference differential divided employed equal equations EXAMPLE expressed factors formulæ functions given gives greater half increments less than 90 log cot logarithms manner means methods middle multiple Napier's nearly negative obtained opposite perpendicular plane triangle polar triangle positive preceding problem quadrant radius reduced relations right angle right triangles Rules second member sides similar simple sin b sin sin c cos sin x sin² sin³ sine sine and cosine solution solve sphere spherical triangle substituting successively tables taken tangent third Trig trigonometric values whence

### Popular passages

Page 151 - Spherical Triangle the cosine of any side is equal to the product of the cosines of the other two sides, plus the product of the sines of those sides into the cosine of their included angle ; that is, (1) cos a = cos b...

Page 169 - The sine of any middle part is equal to the product of the tangents of the Adjacent parts. RULE II. The sine of any middle part is equal to the product of the cosines of the opposite parts.

Page 2 - Union, in the Clerk's Office of the District Court of the Eastern District of Pennsylvania. PREFACE.

Page 58 - 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.

Page 229 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.

Page 64 - As the sine of the angle opposite the given side, is to the sine of the angle opposite the required side ; so is the given side to the required side.

Page 15 - The sum of the two acute angles of a right triangle is equal to one right angle, or 90°.

Page 65 - The side opposite the given angle is to the side opposite the required angle as the sine of the given angle is to the Bine of the required angle.

Page 181 - ... cos a = cos b cos с + sin b sin с cos A ; (2) cos b = cos a cos с + sin a sin с cos в ; ^ A. (3) cos с = cos a cos b + sin a sin b cos C.

Page 150 - The law of sines states that in any spherical triangle the sines of the sides are proportional to the sines of their opposite angles: sin a _ sin b __ sin c _ sin A sin B sin C...