A treatise on spherical trigonometry, by W.J. M'Clelland and T. Preston, Parte1 |
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Página vi
... angle in terms of the sides , 36 Rule of Sines . Examples , 37 Geometrical proof of the Rule of Sines , 39 Expressions for sin A , cos A , and tan A in terms of the sides , 40 ... RIGHT - ANGLED TRIANGLES . SECTION I. vi Contents .
... angle in terms of the sides , 36 Rule of Sines . Examples , 37 Geometrical proof of the Rule of Sines , 39 Expressions for sin A , cos A , and tan A in terms of the sides , 40 ... RIGHT - ANGLED TRIANGLES . SECTION I. vi Contents .
Página vii
William John M'Clelland. CHAPTER IV . RIGHT - ANGLED TRIANGLES . SECTION I. — Geometrical Deduction of Formulae ... angle . CASE V. Having given a side and the adjacent angle . Examples , 88 CASE VI . - Having given a side and the ...
William John M'Clelland. CHAPTER IV . RIGHT - ANGLED TRIANGLES . SECTION I. — Geometrical Deduction of Formulae ... angle . CASE V. Having given a side and the adjacent angle . Examples , 88 CASE VI . - Having given a side and the ...
Página 4
... right angles . These latter are called Secondaries ; e.g. parallels of latitude are primaries , and the meridians ... Angle between Two Great Circles . Example . 10 4 The Sphere . Primary and Secondary Circles,
... right angles . These latter are called Secondaries ; e.g. parallels of latitude are primaries , and the meridians ... Angle between Two Great Circles . Example . 10 4 The Sphere . Primary and Secondary Circles,
Página 10
... right angles . 5a . Draw a great circle cutting two given circles , great or ... angle passes through the pole of the in- ternal bisector ; and conversely ... angle between their planes is twice the complement of their spherical radius ...
... right angles . 5a . Draw a great circle cutting two given circles , great or ... angle passes through the pole of the in- ternal bisector ; and conversely ... angle between their planes is twice the complement of their spherical radius ...
Página 13
... right angles . 2. Each angle is less than two right angles . For if possible let ABC be a spherical triangle , having an angle at A greater than two right angles . Continue the arc BA to the point X on the side BC . Then BX is a ...
... right angles . 2. Each angle is less than two right angles . For if possible let ABC be a spherical triangle , having an angle at A greater than two right angles . Continue the arc BA to the point X on the side BC . Then BX is a ...
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...