A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página viii
... drawn , read are drawn . " " " " 63 , Ex . 1 , for Euclid I. , read Euclid III . " " 68 , Ex . 7 , for fig . 18 , read fig . 19 . 140 153 SPHERICAL TRIGONOMETRY . CHAPTER I. THE SPHERE . 1. A viii Contents .
... drawn , read are drawn . " " " " 63 , Ex . 1 , for Euclid I. , read Euclid III . " " 68 , Ex . 7 , for fig . 18 , read fig . 19 . 140 153 SPHERICAL TRIGONOMETRY . CHAPTER I. THE SPHERE . 1. A viii Contents .
Página 1
... drawn from the centre of a sphere to the surface is called a Radius , and any straight line drawn through the centre and terminated both ways by the sur- face is called a Diameter . A sphere may be generated by the revolution of a semi ...
... drawn from the centre of a sphere to the surface is called a Radius , and any straight line drawn through the centre and terminated both ways by the sur- face is called a Diameter . A sphere may be generated by the revolution of a semi ...
Página 2
... drawn through two given points on the surface of a sphere ; for its plane must also pass through the centre ; and three points not in the same right line are sufficient to determine a plane com- pletely . If the two given points be ...
... drawn through two given points on the surface of a sphere ; for its plane must also pass through the centre ; and three points not in the same right line are sufficient to determine a plane com- pletely . If the two given points be ...
Página 3
... drawn through two points that distances on the sur- face of a sphere are measured along arcs of great circles . Advantage is taken of this property of the great circle in Navigation . 4. Axes and Poles . - The line AB ( fig . 1 ) is ...
... drawn through two points that distances on the sur- face of a sphere are measured along arcs of great circles . Advantage is taken of this property of the great circle in Navigation . 4. Axes and Poles . - The line AB ( fig . 1 ) is ...
Página 4
... drawn common secondaries to two circles , the planes of those circles are parallel . For , by ( 3 ) , the two circles have the same axis . The distance of any point on the surface of a sphere from a circle traced thereon is measured by ...
... drawn common secondaries to two circles , the planes of those circles are parallel . For , by ( 3 ) , the two circles have the same axis . The distance of any point on the surface of a sphere from a circle traced thereon is measured by ...
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...