A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 21
... internal bisector of the vertical angle passes through a fixed point . ( Cf. Prop . ( 11 ) ) . 20. Theorem . - The great circle bisecting the sides of a triangle intersects the base 90 ° distant from its middle point . Let ABC ( fig ...
... internal bisector of the vertical angle passes through a fixed point . ( Cf. Prop . ( 11 ) ) . 20. Theorem . - The great circle bisecting the sides of a triangle intersects the base 90 ° distant from its middle point . Let ABC ( fig ...
Página 38
... internal and external vertical angle are to one another as the sines of the adjacent sides . ( Cf. Euc . VI . , 111. ) 5. The bisector of the base divides the vertical angle into two parts , the ratio of whose sines is the inverse ratio ...
... internal and external vertical angle are to one another as the sines of the adjacent sides . ( Cf. Euc . VI . , 111. ) 5. The bisector of the base divides the vertical angle into two parts , the ratio of whose sines is the inverse ratio ...
Página 45
... internal bisector of the angle C make an angle with the opposite side , we have C cos + cos A cos = sin A sin cos b ; by Art . 26 ( 1 ) . 2 and also C C cos + cos B cos = sin B sin cos a . 2 Adding these equations , we eliminate 0 , and ...
... internal bisector of the angle C make an angle with the opposite side , we have C cos + cos A cos = sin A sin cos b ; by Art . 26 ( 1 ) . 2 and also C C cos + cos B cos = sin B sin cos a . 2 Adding these equations , we eliminate 0 , and ...
Página 46
... internal , bisector of C ] . 4. Prove the relation - COS B sin ( a + b ) sin c = 0 . COS A Σ 1 + cos C 5. If a great circle passes through the vertex C , making angles a and B with the sides a and b , the angle 0 , which it makes with ...
... internal , bisector of C ] . 4. Prove the relation - COS B sin ( a + b ) sin c = 0 . COS A Σ 1 + cos C 5. If a great circle passes through the vertex C , making angles a and B with the sides a and b , the angle 0 , which it makes with ...
Página 47
... bisector of the vertical angle makes with the base . If i be the length of the internal bisector , we have C cos A + cos e cos eos B - cos e cos 2 cos i = C sin sin sin sin 2 therefore , cos A ~ cos B cos @ = 2 cos 10. If e ' denote the ...
... bisector of the vertical angle makes with the base . If i be the length of the internal bisector , we have C cos A + cos e cos eos B - cos e cos 2 cos i = C sin sin sin sin 2 therefore , cos A ~ cos B cos @ = 2 cos 10. If e ' denote 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...