A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página 2
... perpendicular from C on AB . It is obvious that as ACB revolves round AB , the point C describes a circle round D as centre ; and also that O , the middle point of AB , being equally distant from all points on ACB , is the centre of the ...
... perpendicular from C on AB . It is obvious that as ACB revolves round AB , the point C describes a circle round D as centre ; and also that O , the middle point of AB , being equally distant from all points on ACB , is the centre of the ...
Página 3
... perpendicular to the plane of CC ' , for CD remained per- pendicular to AB during its entire revolution . Hence the Axis of a circle may be defined as the diameter * The following method of looking at this question is also instructive ...
... perpendicular to the plane of CC ' , for CD remained per- pendicular to AB during its entire revolution . Hence the Axis of a circle may be defined as the diameter * The following method of looking at this question is also instructive ...
Página 4
William John M'Clelland. of the sphere perpendicular to the plane of the circle , or the line joining the centre of the sphere with the pole of the circle . Cor . The pole of a circle is equidistant from all points on the circumference ...
William John M'Clelland. of the sphere perpendicular to the plane of the circle , or the line joining the centre of the sphere with the pole of the circle . Cor . The pole of a circle is equidistant from all points on the circumference ...
Página 5
... perpendicular to their common diameter . ( 2 ) . The arc intercepted by them on the great circle to which they are secondaries . For if AC and BC ( fig . 2 ) be secondaries to AB they C Α α B Fig . 2 . are perpendicular to AB , and are ...
... perpendicular to their common diameter . ( 2 ) . The arc intercepted by them on the great circle to which they are secondaries . For if AC and BC ( fig . 2 ) be secondaries to AB they C Α α B Fig . 2 . are perpendicular to AB , and are ...
Página 6
... perpendicular to the planes of the circles , and the angle between the perpendiculars to two planes is equal to the angle between the planes . Hence , by drawing a great circle parallel to a small circle , we see that the angle between ...
... perpendicular to the planes of the circles , and the angle between the perpendiculars to two planes is equal to the angle between the planes . Hence , by drawing a great circle parallel to a small circle , we see that the angle between ...
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...