A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 2
... passes through O it divides the sphere into two equal parts , and the curve of section is called a Great Circle . When its plane does not pass ... passing through them . For , when the radius of a sphere is indefinitely 2 The Sphere .
... passes through O it divides the sphere into two equal parts , and the curve of section is called a Great Circle . When its plane does not pass ... passing through them . For , when the radius of a sphere is indefinitely 2 The Sphere .
Página 3
... passing through two points on it becomes a right line joining two points in a plane ; but the right line joining two points is the shortest distance between them ; therefore , etc. * It is for this reason , and because only one great ...
... passing through two points on it becomes a right line joining two points in a plane ; but the right line joining two points is the shortest distance between them ; therefore , etc. * It is for this reason , and because only one great ...
Página 8
... passing through the boundary of the plane area ) . These lines form a kind of irregular cone , having its vertex at 0 , and enclosing the surface ABCD . The solid angle of this cone is the solid angle which ABCD subtends at O. To ...
... passing through the boundary of the plane area ) . These lines form a kind of irregular cone , having its vertex at 0 , and enclosing the surface ABCD . The solid angle of this cone is the solid angle which ABCD subtends at O. To ...
Página 10
... passes through the pole of the in- ternal bisector ; and conversely . 10. If two great circles are equally inclined to a third , their poles are equidistant from the pole of the third . 11. Two equal small circles are drawn touching ...
... passes through the pole of the in- ternal bisector ; and conversely . 10. If two great circles are equally inclined to a third , their poles are equidistant from the pole of the third . 11. Two equal small circles are drawn touching ...
Página 13
... passing through the points ( see Chap . I. Art . 3 ) . Examples . 1. Each side of a spherical triangle is less than two right angles . 2. Each angle is less than two right angles . For if possible let ABC be a spherical triangle ...
... passing through the points ( see Chap . I. Art . 3 ) . Examples . 1. Each side of a spherical triangle is less than two right angles . 2. Each angle is less than two right angles . For if possible let ABC be a spherical triangle ...
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...