A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 5
... tangents drawn to them at their point of intersection . The Angle between two Great Circles is equal to- ( 1 ) . The angle between their planes . For the tangents to them at their point of intersection lie in their respective planes and ...
... tangents drawn to them at their point of intersection . The Angle between two Great Circles is equal to- ( 1 ) . The angle between their planes . For the tangents to them at their point of intersection lie in their respective planes and ...
Página 12
... Tangent Circle to the curve . Great and Small Circles are examples of spherical curves . The arcs are generally spoken of as the Sides , and their angles of inclination as the Angles of the Spherical figure . Since , however , three ...
... Tangent Circle to the curve . Great and Small Circles are examples of spherical curves . The arcs are generally spoken of as the Sides , and their angles of inclination as the Angles of the Spherical figure . Since , however , three ...
Página 15
... tangents be drawn to two great circles in their respective planes at the point of intersection ; the plane containing both tan- gents is , with respect to the sphere , the Tangent Plane at the point . Now consider the radius of the ...
... tangents be drawn to two great circles in their respective planes at the point of intersection ; the plane containing both tan- gents is , with respect to the sphere , the Tangent Plane at the point . Now consider the radius of the ...
Página 17
... tangents be drawn to the equal sides from the extremities of the base of the triangle in the planes of those great circles . It is manifest that the intersection of the tangents is a point on both planes , viz . , on their com- mon ...
... tangents be drawn to the equal sides from the extremities of the base of the triangle in the planes of those great circles . It is manifest that the intersection of the tangents is a point on both planes , viz . , on their com- mon ...
Página 29
... tangents to a and b at C. * Since these tangents lie in the planes of the circles to which they are drawn , they will meet the radii OB and * The same result will be obtained if , instead of drawing tangents at C , any point C ' be ...
... tangents to a and b at C. * Since these tangents lie in the planes of the circles to which they are drawn , they will meet the radii OB and * The same result will be obtained if , instead of drawing tangents at C , any point C ' be ...
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...