A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 10
... external bisector of an angle 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 ...
... external bisector of an angle 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 ...
Página 19
... external and one internal , are concurrent . ( Euc . IV . v . ) [ The points of concurrence are the poles of the small circles touching the sides of the triangle . ] ( 10 ) . The arcs of great circles bisecting c 2 Plane and Spherical ...
... external and one internal , are concurrent . ( Euc . IV . v . ) [ The points of concurrence are the poles of the small circles touching the sides of the triangle . ] ( 10 ) . The arcs of great circles bisecting c 2 Plane and Spherical ...
Página 20
... external bisector of the vertical angle always passes through a fixed point . ( Dublin University Exam . Papers . ) For , let ABC ( fig . 9 ) be a triangle having the given A X B Fig 9 . base AB . Upon AB construct an isosceles triangle ...
... external bisector of the vertical angle always passes through a fixed point . ( Dublin University Exam . Papers . ) For , let ABC ( fig . 9 ) be a triangle having the given A X B Fig 9 . base AB . Upon AB construct an isosceles triangle ...
Página 38
... 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 of the sines ...
... 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 of the sines ...
Página 46
... external , instead of the 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 ...
... external , instead of the 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 ...
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...