Plane and Spherical Trigonometry

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Ginn, 1876 - 163 sider
 

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Side 44 - Its peculiarities are the rigorous use of the Doctrine of Limits, as a foundation of the subject, and as preliminary to the adoption of the more direct and practically convenient infinitesimal notation and nomenclature ; the early introduction of a few simple formulas and methods for integrating ; a rather elaborate treatment of the use of infinitesimals in pure geometry ; and the attempt to excite and keep up the interest of the student by bringing in throughout the whole book, and not merely at...
Side 91 - From a station B at the base of a mountain its summit A is seen at an elevation of 60°; after walking one mile towards the summit up a plane making an angle of 30° with the horizon to another station C, the angle BCA is observed to be 135°.
Side 20 - ... 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.
Side 73 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Side 46 - By [2]. [18]. and [19]. we have. — sin (a ± ß) sin a cos ß ± cos a sin ß cos (a ± ß) cos acoeß Т sin a sin ß Divide both numerator and denominator by cos a cos |3.
Side 69 - Having measured a distance of 200 feet, in a direct horizontal line, from the bottom of a steeple, the angle of elevation of its top, taken at that distance, was found to be 47° 30'; from hence it is required to find the height of the steeple.
Side 44 - Mailing price, 55 cents ; for introduction, 50 cents. rPHE design of the author has been to give to students a more complete and accurate knowledge of the nature and use of Logarithms than they can acquire from the cursory study commonly bestowed on this subject.

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