A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página v
... intersection of the polars of the points , Examples ,. PAGE 3 4 7 9 11 CHAPTER II . SPHERICAL TRIANGLES . Definitions , 12 Colunar or Associated Triangles ,. Parts of a Spherical Triangle , Sphere of Infinite Radius , 13 14 15 • Analogy ...
... intersection of the polars of the points , Examples ,. PAGE 3 4 7 9 11 CHAPTER II . SPHERICAL TRIANGLES . Definitions , 12 Colunar or Associated Triangles ,. Parts of a Spherical Triangle , Sphere of Infinite Radius , 13 14 15 • Analogy ...
Página 4
... intersection , viz . , the axis of the primary . ( 4 ) . If there can be drawn common secondaries to two circles , the planes of those circles are parallel . For , by ( 3 ) , the two circles have the same axis . The distance of any ...
... intersection , viz . , the axis of the primary . ( 4 ) . If there can be drawn common secondaries to two circles , the planes of those circles are parallel . For , by ( 3 ) , the two circles have the same axis . The distance of any ...
Página 5
... intersection . The angle between any two circles , great or small , is measured by the angle between the tangents drawn to them at their point of intersection . The Angle between two Great Circles is equal to- ( 1 ) . The angle between ...
... intersection . The angle between any two circles , great or small , is measured by the angle between the tangents drawn to them at their point of intersection . The Angle between two Great Circles is equal to- ( 1 ) . The angle between ...
Página 7
... intersection of two spherical surfaces is a circle . Consider the triangle ABX formed by joining the centres A and B of the two spheres and any point X on their curve of intersection . The sides of this triangle are given , and the line ...
... intersection of two spherical surfaces is a circle . Consider the triangle ABX formed by joining the centres A and B of the two spheres and any point X on their curve of intersection . The sides of this triangle are given , and the line ...
Página 9
... intersection of two great circles and the are joining their poles are pole and polar with respect to one another . For let A and B be the two points , LO and MO their M L A Fig . 4 . polars , O the point of intersection of the polars ...
... intersection of two great circles and the are joining their poles are pole and polar with respect to one another . For let A and B be the two points , LO and MO their M L A Fig . 4 . polars , O the point of intersection of the polars ...
Otras ediciones - Ver todas
A Treatise On Spherical Trigonometry, by W.J. M'Clelland and T. Preston William John M'Clelland Sin vista previa disponible - 2023 |
A Treatise on Spherical Trigonometry, by W. J. M'Clelland and T. Preston William John M'Clelland Sin vista previa disponible - 2016 |
A Treatise On Spherical Trigonometry, by W.J. M'Clelland and T. Preston William John M'Clelland Sin vista previa disponible - 2023 |
Términos y frases comunes
ambiguity arc joining Art Exam base angles calculate centre Chap cos a sin cos b cos cos(a cos² cosc cosines cot A cot cot B+ cot² denote determine diagonals drawn equation equilateral Examples expression find the locus formula geometrically Given the base Hence hypotenuse internal bisector joining the middle L cot L sin latitude middle points Napier's Analogies notation of Ex opposite angles opposite sides perpendicular plane triangle plano polar triangle pole quadrant radius respectively right angle right-angled triangle Science and Art sec a sec secondaries segments Similarly sin b sin sin c cos sin² sin² a sin² sines small circle solid angle solve the triangle sphere spherical triangle subsidiary angle subtended surface tan² tana tangents Theorem triangle ABC triangle is impossible vertex vertical angle
Pasajes populares
Página 78 - 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 17 - The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal.
Página 17 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Página 28 - Show that any side of a triangle is greater than the difference between the other two sides.
Página 37 - C . cos. a . sin. 6 . cos. c _ — 2 . sin. A . sin. B . sin. C . sin. a . sin. b . sin. c I — 2 sin.
Página 99 - BG; that is, the base is to the sum of the sides as the difference of the sides is to the sum or difference of the segments of the base made by the perpendicular from the vertex, according as the...
Página 114 - 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 39 - Thus the sines of the angles of a spherical triangle are proportional to the sines of the opposite sides.
Página 18 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal.
Página 110 - A = - cos B cos C + sin B sin C cos a. Similarly cos B = - cos C...