Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 31
... lengths of arcs of great circles drawn from A , B , C perpendicular to the opposite sides , sin a sin 0 = sin b sin p = sin c sin = √ ( 1 − cos3a – cos3b – cos3c + 2 cos a cos b cos c ) . - 16. In a spherical triangle , if 0 , 4 OF ...
... lengths of arcs of great circles drawn from A , B , C perpendicular to the opposite sides , sin a sin 0 = sin b sin p = sin c sin = √ ( 1 − cos3a – cos3b – cos3c + 2 cos a cos b cos c ) . - 16. In a spherical triangle , if 0 , 4 OF ...
Página 44
... length of the arc drawn from Cat right angles to the hypothenuse AB , shew that cot d = √ ( cota + cot3b ) . 2 10. OAA , is a spherical triangle right - angled at A , and acute- angled at A ; the arc A , A , of a great circle is drawn ...
... length of the arc drawn from Cat right angles to the hypothenuse AB , shew that cot d = √ ( cota + cot3b ) . 2 10. OAA , is a spherical triangle right - angled at A , and acute- angled at A ; the arc A , A , of a great circle is drawn ...
Página 53
... length , but presents no difficulty . Before considering the problem generally , we will take the particular case in which a = b ; then A must = B. The first and third of Napier's analogies give cot C = tan A cos a , tanc = tan a cos A ...
... length , but presents no difficulty . Before considering the problem generally , we will take the particular case in which a = b ; then A must = B. The first and third of Napier's analogies give cot C = tan A cos a , tanc = tan a cos A ...
Página 73
... lengths of the sides of the triangles . 105. Given two sides and the included angle of a spherical triangle , to find the angle between the chords of these sides . D B C Let AB , AC be the two sides of the triangle ABC ; let O be the ...
... lengths of the sides of the triangles . 105. Given two sides and the included angle of a spherical triangle , to find the angle between the chords of these sides . D B C Let AB , AC be the two sides of the triangle ABC ; let O be the ...
Página 74
... lengths of the arcs corre- sponding to a and b respectively be a and ß , and r the radius of the α β sphere , we ... length as the arcs of the spherical triangle . Let A , B , C be the angles of the spherical triangle ; a , b , c the ...
... lengths of the arcs corre- sponding to a and b respectively be a and ß , and r the radius of the α β sphere , we ... length as the arcs of the spherical triangle . Let A , B , C be the angles of the spherical triangle ; a , b , c the ...
Otras ediciones - Ver todas
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1949 |
Spherical Trigonometry: For the Use of Colleges and Schools Isaac Todhunter Vista de fragmentos - 1929 |
Términos y frases comunes
A+B+C ambiguity angular points approximately bisecting Cambridge centre circular measure cloth cos b cos cos² cos³ cosine Crown 8vo deduce denote drawn equal angles equilateral example expressed Fcap formulæ formulæ of Art greater Hence hypothenuse inscribed Legendre's Theorem less Let ABC lune meet middle point Napier's analogies Napier's Rules obtained octahedron opposite angle opposite sides parallelopiped perpendicular plane angles plane triangle Plane Trigonometry polar triangle pole polygon preceding article primitive triangle prove quadrant R₁ r₂ radius regular polyhedron respectively right angle right-angled triangles Second Edition shew shewn sides and angles Similarly sin b cos sin b sin sin² sin³ sine solid angle sphere spherical excess spherical triangle Spherical Trigonometry subtended Suppose surface tangent tetrahedron Treatise triangle ABC Trigono Trinity College values π π
Pasajes populares
Página 16 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...
Página 23 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Página 20 - PROCTER— A HISTORY OF THE BOOK OF COMMON PRAYER, with a Rationale of its Offices. By FRANCIS PROCTER, MA Thirteenth Edition, revised and enlarged. Crown 8vo. loг. 6d. PROCTER AND MACLEAR— AN ELEMENTARY INTRODUCTION TO THE BOOK OF COMMON PRAYER.
Página 8 - Christ and other Masters. A Historical Inquiry into some of the Chief Parallelisms and Contrasts between Christianity and the Religious Systems of the Ancient World.
Página 13 - AN ELEMENTARY TREATISE ON THE LUNAR THEORY, with a Brief Sketch of the Problem up to the time of Newton. Second Edition, revised. Crown 8vo. cloth. 5*. 6d. Hemming. — AN ELEMENTARY TREATISE ON THE DIFFERENTIAL AND INTEGRAL CALCULUS, for the Use; of Colleges and Schools.
Página 109 - Life of John Milton, narrated in -Connexion with the Political, Ecclesiastical, and Literary History of his...
Página 15 - Prelector of St. John's College, Cambridge. AN ELEMENTARY TREATISE ON MECHANICS. For the Use of the Junior Classes at the University and the Higher Classes in Schools.
Página 14 - Prize Essay for 1877. 8vC. &r. 6d. SMITH— Works by the Rev. BARNARD SMITH, MA, Rector of Glaston, Rutland, late Fellow and Senior Bursar of St. Peter's College, Cambridge. ARITHMETIC AND ALGEBRA, in their Principles and Application ; with numerous systematically arranged Examples taken from the Cambridge Examination Papers, with especial reference to the Ordinary Examination for the BA Degree.
Página 5 - And an Introduction, explanatory of his position in the Church, with reference to the Parties which divide it. 3 vols. 8vo.
Página 28 - If two triangles have two sides of the one equal to two sides of the...