Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 páginas |
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... , for the most part , ( I do not say , exclusively ) according to the principles of analysis . Royal Military Academy , Woolwich , Feb , 1816 . OLINTHUS GREGORY , CHAP . I. Preliminary definitions and principles II . General PREFACE .
... , for the most part , ( I do not say , exclusively ) according to the principles of analysis . Royal Military Academy , Woolwich , Feb , 1816 . OLINTHUS GREGORY , CHAP . I. Preliminary definitions and principles II . General PREFACE .
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... CHAP . I. Preliminary definitions and principles II . General properties and mutual relations of the lines and angles of circles and plane triangles III . Solutions of the several cases of plane tri- angles · Page 1 9 24 36 • 61 IV ...
... CHAP . I. Preliminary definitions and principles II . General properties and mutual relations of the lines and angles of circles and plane triangles III . Solutions of the several cases of plane tri- angles · Page 1 9 24 36 • 61 IV ...
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... chap . i . art . 19 , we have , for any arc , COS = ( sin2 ) . This theorem gives , in the pre- sent case , cos 1 ' = 9999999577 . Then , by prop . 12 , cor . 2 , ( A ) , of this chapter , we shall have sin 3 ′ -- 2 cos l ' x sin l'- 2 ...
... chap . i . art . 19 , we have , for any arc , COS = ( sin2 ) . This theorem gives , in the pre- sent case , cos 1 ' = 9999999577 . Then , by prop . 12 , cor . 2 , ( A ) , of this chapter , we shall have sin 3 ′ -- 2 cos l ' x sin l'- 2 ...
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... ( chap . i . 19 ) , COS sin l ' we have tan l ' = cot 89 ° 59 ' cos I ' sin 2 ' tan 2 ' = = cot 89 ° 58 ' cos 2 ' & c . & c . & c . Above 45 ° the process may be considerably simplified by the theorem for the tangents of the sums and ...
... ( chap . i . 19 ) , COS sin l ' we have tan l ' = cot 89 ° 59 ' cos I ' sin 2 ' tan 2 ' = = cot 89 ° 58 ' cos 2 ' & c . & c . & c . Above 45 ° the process may be considerably simplified by the theorem for the tangents of the sums and ...
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... chap . i . 6 ) that for want of a side among the data , the problem thus ex- pressed is unlimited . Our twenty varieties , therefore , only furnish three distinct cases , to the solution of which we shall now proceed . CASE I. 2. When a ...
... chap . i . 6 ) that for want of a side among the data , the problem thus ex- pressed is unlimited . Our twenty varieties , therefore , only furnish three distinct cases , to the solution of which we shall now proceed . CASE I. 2. When a ...
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altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius right angled spherical right angled triangle right ascension right line sec² secant sin A sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith