Spherical Trigonometry ...Macmillian and Company, limited, 1859 - 275 páginas |
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Página 4
... preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ACB . Hence the ...
... preceding Article , the angle between the great circles CD and CE is the angle MON . In the figure to Art . 6 , since PO is perpen- dicular to the plane ACB , every plane which contains PO is at right angles to the plane ACB . Hence the ...
Página 5
... preceding Article . ) For suppose PA and PC to be quadrants and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P is a pole ...
... preceding Article . ) For suppose PA and PC to be quadrants and O the centre of the sphere ; then since PA and PC are quadrants , the angles POC and POA are right angles . Hence PO is at right angles to the plane AOC , and P is a pole ...
Página 8
... preceding Article , the arc AB forms one side of the spherical triangle ABC , and the plane angle AOB is measured by the frac- arc AB tion radius OA and thus the arc AB is proportional to the angle AOB so long as we keep to the same ...
... preceding Article , the arc AB forms one side of the spherical triangle ABC , and the plane angle AOB is measured by the frac- arc AB tion radius OA and thus the arc AB is proportional to the angle AOB so long as we keep to the same ...
Página 9
... preceding Article it will follow that any angle of a spherical triangle is less than two right angles . For suppose a triangle formed by BC , CA and BEDA having the angle BCA greater than two right angles . Then suppose D to denote the ...
... preceding Article it will follow that any angle of a spherical triangle is less than two right angles . For suppose a triangle formed by BC , CA and BEDA having the angle BCA greater than two right angles . Then suppose D to denote the ...
Página 15
... preceding Article by means of the polar triangle . Or thus ; suppose the side AC greater than the side BC , then the angle ABC will be greater than the angle BAC . For the angle ABC cannot be less than the angle BAC by Art . 35 , and ...
... preceding Article by means of the polar triangle . Or thus ; suppose the side AC greater than the side BC , then the angle ABC will be greater than the angle BAC . For the angle ABC cannot be less than the angle BAC by Art . 35 , and ...
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...