A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 6
... subtending any angle at its centre D , and let AB be an arc of a great circle subtending an equal angle at its centre O , then if the cir- cles be placed parallel , so that they may have a common pole at C , O will be the centre of the ...
... subtending any angle at its centre D , and let AB be an arc of a great circle subtending an equal angle at its centre O , then if the cir- cles be placed parallel , so that they may have a common pole at C , O will be the centre of the ...
Página 8
... subtends a solid angle at that point , the solid angle being enclosed by the lines drawn from the point to the contour of the surface . B C B Fig . 3 . Let ABCD ( fig . 3 ) be any surface or plane area . From any point O draw lines OA ...
... subtends a solid angle at that point , the solid angle being enclosed by the lines drawn from the point to the contour of the surface . B C B Fig . 3 . Let ABCD ( fig . 3 ) be any surface or plane area . From any point O draw lines OA ...
Página 9
... subtends at the centre . Since the radius of the sphere is unity , its area is 4π ; hence the solid angle subtended at O by the nth part of the surface of the sphere is 4π n · Example . The solid angle at a corner of a cube is П 12 ...
... subtends at the centre . Since the radius of the sphere is unity , its area is 4π ; hence the solid angle subtended at O by the nth part of the surface of the sphere is 4π n · Example . The solid angle at a corner of a cube is П 12 ...
Página 11
... subtended at the centre of a circle , great or small , by two points on it , is equal to the angle subtended by them at its pole . ( Art . 6. ) 14. If through the centre O of a sphere a line be drawn parallel to a chord AB of a ...
... subtended at the centre of a circle , great or small , by two points on it , is equal to the angle subtended by them at its pole . ( Art . 6. ) 14. If through the centre O of a sphere a line be drawn parallel to a chord AB of a ...
Página 14
... subtend at the centre , C α b B A Fig . 6 . and the angles BAC , ABC , and BCA between the sides are equal to the angles between the planes containing the solid angle at O ( Chap . I. , Art . 6 ) . The notation for the parts of a ...
... subtend at the centre , C α b B A Fig . 6 . and the angles BAC , ABC , and BCA between the sides are equal to the angles between the planes containing the solid angle at O ( Chap . I. , Art . 6 ) . The notation for the parts of a ...
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...