A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 2
... equal parts , and the curve of section is called a Great Circle . When its plane does not pass through the centre it is called a Small Circle . Example . The Meridians , Equator , and Ecliptic , are great circles . The Parallels of ...
... equal parts , and the curve of section is called a Great Circle . When its plane does not pass through the centre it is called a Small Circle . Example . The Meridians , Equator , and Ecliptic , are great circles . The Parallels of ...
Página 5
... equal to- ( 1 ) . The angle between their planes . For the tangents to them at their point of intersection lie in their respective planes and are perpendicular to their common diameter . ( 2 ) . The arc intercepted by them on the great ...
... equal to- ( 1 ) . The angle between their planes . For the tangents to them at their point of intersection lie in their respective planes and are perpendicular to their common diameter . ( 2 ) . The arc intercepted by them on the great ...
Página 6
... equal to the angular distance between the poles of the circles . 7. To compare the length of the arc of a small circle sub- tending any angle at its centre , with the arc of a great circle subtending an equal angle at the centre of the ...
... equal to the angular distance between the poles of the circles . 7. To compare the length of the arc of a small circle sub- tending any angle at its centre , with the arc of a great circle subtending an equal angle at the centre of the ...
Página 7
William John M'Clelland. measured on the parallel , is equal to the difference of lon- gitude ( AB ) multiplied by the cosine of the latitude . 8. The Lune . — A Lune is a portion of the surface of a sphere enclosed by two great circles ...
William John M'Clelland. measured on the parallel , is equal to the difference of lon- gitude ( AB ) multiplied by the cosine of the latitude . 8. The Lune . — A Lune is a portion of the surface of a sphere enclosed by two great circles ...
Página 10
... equal small circles are drawn touching each other : show that the angle between their planes is twice the complement ... equal to twice the spherical radius of either small circle , and the lines drawn to the point of contact of the ...
... equal small circles are drawn touching each other : show that the angle between their planes is twice the complement ... equal to twice the spherical radius of either small circle , and the lines drawn to the point of contact of the ...
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...