A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Resultados 1-5 de 14
Página 11
... calculated on a sphere of given radius . 13. The angle 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 ...
... calculated on a sphere of given radius . 13. The angle 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 ...
Página 74
... calculating the sum of the angles , having given two sides and the included angle , or by the aid of Art . 30 , the three sides of a spherical triangle will be afterwards proved as Cagnoli's Theorem . 29. Prove that 1 + cos a - cos b 74 ...
... calculating the sum of the angles , having given two sides and the included angle , or by the aid of Art . 30 , the three sides of a spherical triangle will be afterwards proved as Cagnoli's Theorem . 29. Prove that 1 + cos a - cos b 74 ...
Página 100
... calculate the segments a and c - x of the base made by the perpendicular on it from the vertex . Ans . tan A sin x = tan B sin ( c - x ) . 15. What is the shortest distance between two places on the earth's sur- face - one in latitude ...
... calculate the segments a and c - x of the base made by the perpendicular on it from the vertex . Ans . tan A sin x = tan B sin ( c - x ) . 15. What is the shortest distance between two places on the earth's sur- face - one in latitude ...
Página 106
... calculated is utilized in the calculation of each angle . The logarithmic form of the above equation is L tan A 2 = - - 10 - L sin ( sa ) + 1⁄2 { L sin ( s − a ) + L sin ( s − b ) + L sin ( s - c ) - L sin s } . Examples . ( 1 ) ...
... calculated is utilized in the calculation of each angle . The logarithmic form of the above equation is L tan A 2 = - - 10 - L sin ( sa ) + 1⁄2 { L sin ( s − a ) + L sin ( s − b ) + L sin ( s - c ) - L sin s } . Examples . ( 1 ) ...
Página 110
... calculated from two separate equations , one giving half the sum and the other half the difference of those angles . The formulæ to be employed have been arrived at on p . 43 ( Note to Ex . 8 ) . They have , moreover , been demonstrated ...
... calculated from two separate equations , one giving half the sum and the other half the difference of those angles . The formulæ to be employed have been arrived at on p . 43 ( Note to Ex . 8 ) . They have , moreover , been demonstrated ...
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...