A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 11
... prove the relations : - - a . sin BC sin AD + sin CA sin BD + sin AB sin CD = 0 . 8 ° . sin BC cos AD + sin CA cos BD + sin AB cos CD = 0 , CHAPTER II . SPHERICAL TRIANGLES . 13. In the present Examples . 11 Examples,
... prove the relations : - - a . sin BC sin AD + sin CA sin BD + sin AB sin CD = 0 . 8 ° . sin BC cos AD + sin CA cos BD + sin AB cos CD = 0 , CHAPTER II . SPHERICAL TRIANGLES . 13. In the present Examples . 11 Examples,
Página 37
... prove that sin a sin a = sin b sin B sin c sin y = For ( Art . 27 , Ex . 3 ) , sin a = = = 2n . sin b sin C , sin ẞ = sin c sin A , sin y sin a sin B ; therefore , & c . ( Art . 30 ( 3 ) ) . Remark . - The rule of sines follows at once ...
... prove that sin a sin a = sin b sin B sin c sin y = For ( Art . 27 , Ex . 3 ) , sin a = = = 2n . sin b sin C , sin ẞ = sin c sin A , sin y sin a sin B ; therefore , & c . ( Art . 30 ( 3 ) ) . Remark . - The rule of sines follows at once ...
Página 38
... prove that sin AM ' sin BM ' :: sin2 b sin2 a . : 7. If p1 , p2 , be the perpendiculars drawn from the mid - point M of the base of a spherical triangle on the great circle bisectors of the vertical angle A , and pз the perpendicular ...
... prove that sin AM ' sin BM ' :: sin2 b sin2 a . : 7. If p1 , p2 , be the perpendiculars drawn from the mid - point M of the base of a spherical triangle on the great circle bisectors of the vertical angle A , and pз the perpendicular ...
Página 42
... Prove that 8n3 = sin2 a sin2 b sin2 c sin A sin B sin C. 3. Prove that A B cot : cot 2 - : cot 2 = 2 4. Prove that 5. Prove that tan 312 B - - sin ( sa ) sin ( s — b ) : sin ( s — c ) . C tan == sin ( s - a ) sin s B sin sin C 2 sin ...
... Prove that 8n3 = sin2 a sin2 b sin2 c sin A sin B sin C. 3. Prove that A B cot : cot 2 - : cot 2 = 2 4. Prove that 5. Prove that tan 312 B - - sin ( sa ) sin ( s — b ) : sin ( s — c ) . C tan == sin ( s - a ) sin s B sin sin C 2 sin ...
Página 43
William John M'Clelland. 6. Prove that 2 sin a . B C COS COS 2 sin s = A sin n2 = sin s 7. Prove that A B sin a sin b sin c . sin sin · sin 2 8. Prove that B sin ( s - b ) sin 2 COS COS 2 sin c COS NOTE . * - By the aid of a similar ...
William John M'Clelland. 6. Prove that 2 sin a . B C COS COS 2 sin s = A sin n2 = sin s 7. Prove that A B sin a sin b sin c . sin sin · sin 2 8. Prove that B sin ( s - b ) sin 2 COS COS 2 sin c COS NOTE . * - By the aid of a similar ...
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...