A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
Dentro del libro
Resultados 1-5 de 22
Página 22
... a triangle may be conveniently obtained by drawing great circles through the vertices perpendicular to the opposite sides A'B'C ' . Produce the side B'C ' ( if 22 Spherical Triangles . Polar Triangles Reciprocal and Supplemental Relations,
... a triangle may be conveniently obtained by drawing great circles through the vertices perpendicular to the opposite sides A'B'C ' . Produce the side B'C ' ( if 22 Spherical Triangles . Polar Triangles Reciprocal and Supplemental Relations,
Página 24
... obtained in the previous Article may be further exemplified , as follows : - ( 1 ) . It has been seen that two sides of a triangle are greater than the third : thus b + c > a . Applying this inequality to the sides of the supple- mental ...
... obtained in the previous Article may be further exemplified , as follows : - ( 1 ) . It has been seen that two sides of a triangle are greater than the third : thus b + c > a . Applying this inequality to the sides of the supple- mental ...
Página 29
... obtained if , instead of drawing tangents at C , any point C ' be taken on OC , and lines C'D ' and C'E ' be drawn perpen- dicular to it , meeting OB and OA in D ' and E ' , respectively . OA in D and E respectively , and the angle ( 29 ) ...
... obtained if , instead of drawing tangents at C , any point C ' be taken on OC , and lines C'D ' and C'E ' be drawn perpen- dicular to it , meeting OB and OA in D ' and E ' , respectively . OA in D and E respectively , and the angle ( 29 ) ...
Página 30
... obtain the angles in terms of the sides . Thus : COS A - cos a cos b cos c - sin b sin c • COS B cos b = COS C COs a COS C = sin c sin a COS C cos a cos b sin a sin b ( 2 ) . These results are of special importance , and the student ...
... obtain the angles in terms of the sides . Thus : COS A - cos a cos b cos c - sin b sin c • COS B cos b = COS C COs a COS C = sin c sin a COS C cos a cos b sin a sin b ( 2 ) . These results are of special importance , and the student ...
Página 41
... obtain A sin A 2 tan sin ( sb ) sin ( s – c ) 2 sin s sin ( s - a ) " COS with similar expressions for tan NOTE.- A A sin A = 2 sin COS = 2 2 ( 6 ) B C and tan ( 7 ) 2 2 2 sin b sin c sin s sin ( sa ) sin ( sb ) sin ( sc ) ; ( From ( 5 ) ...
... obtain A sin A 2 tan sin ( sb ) sin ( s – c ) 2 sin s sin ( s - a ) " COS with similar expressions for tan NOTE.- A A sin A = 2 sin COS = 2 2 ( 6 ) B C and tan ( 7 ) 2 2 2 sin b sin c sin s sin ( sa ) sin ( sb ) sin ( sc ) ; ( From ( 5 ) ...
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...