The elements of plane trigonometry |
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Página 202
... 1105 , 1107 , 110 ( 3 ) . From 1102 , and 11067 , find L tan 15o . ( 4 ) . ] { ( 1+ N ) 2 . ( 1 − 1+ N 2 1 - N N ) 2 1960 N2 == + 1.2 N1 N6 + 3.4 5.6 + ... } . THE ELEMENTS OF SPHERICAL TRIGONOMETRY . BY J. C. SNOWBALL 202.
... 1105 , 1107 , 110 ( 3 ) . From 1102 , and 11067 , find L tan 15o . ( 4 ) . ] { ( 1+ N ) 2 . ( 1 − 1+ N 2 1 - N N ) 2 1960 N2 == + 1.2 N1 N6 + 3.4 5.6 + ... } . THE ELEMENTS OF SPHERICAL TRIGONOMETRY . BY J. C. SNOWBALL 202.
Página 203
... COLLEGE , CAMBRIDGE . SECOND EDITION . CAMBRIDGE : PRINTED BY JOHN W. PARKER , UNIVERSITY PRINTER . T. STEVENSON , CAMBRIDGE ; A. H. BAILY & Co. , LONDON . M.DCCC.XXXVII . SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES.
... COLLEGE , CAMBRIDGE . SECOND EDITION . CAMBRIDGE : PRINTED BY JOHN W. PARKER , UNIVERSITY PRINTER . T. STEVENSON , CAMBRIDGE ; A. H. BAILY & Co. , LONDON . M.DCCC.XXXVII . SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES.
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John Charles Snowball. 1 SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES.
John Charles Snowball. 1 SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES.
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John Charles Snowball. SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES OF SPHERICAL TRIANGLES . PAGE ART . 1. DEF . A Sphere .......... 2 , 3. Every section of a sphere made by a plane is a circle . 1 1 4. Objects of ...
John Charles Snowball. SPHERICAL TRIGONOMETRY . INDEX . CHAPTER I. ON CERTAIN PROPERTIES OF SPHERICAL TRIANGLES . PAGE ART . 1. DEF . A Sphere .......... 2 , 3. Every section of a sphere made by a plane is a circle . 1 1 4. Objects of ...
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John Charles Snowball. CHAPTER II . FORMULE CONNECTING THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE . ART . 28 . Sin A sin B sin a sin b sin c sin C = PAGE 15 29. Cos A. sin b . sin c = cos acos b . cos c .... 16 30 , 31 . Sin c . cos A ...
John Charles Snowball. CHAPTER II . FORMULE CONNECTING THE SIDES AND ANGLES OF A SPHERICAL TRIANGLE . ART . 28 . Sin A sin B sin a sin b sin c sin C = PAGE 15 29. Cos A. sin b . sin c = cos acos b . cos c .... 16 30 , 31 . Sin c . cos A ...
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Términos y frases comunes
A₁ AC AC angle containing Asin base C₁ centre circle coefficient cosec cosines decimal determined Diff difference digit equal errors Eucl expression formulæ given goniometric functions greater Hence increment integer last Article less m₁ magnitude mantissa measured Napier's rules nearly negative number of seconds P₁ perpendicular plane triangle planes AOB polar triangle pole polygon positive proved quantity radius Regular Polyhedron right angles right-angled triangle S₁ secants shew shewn Similarly sin A sin sines sines and cosines small angle solid angle sphere spherical excess spherical triangle SPHERICAL TRIGONOMETRY subtended subtraction tabular logarithmic tangents THEOREM triangle ABC triangle whose sides TRIGONOMETRY versin Wherefore π π
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Página 141 - Logarithm of a number to a given base is the index of the power to which the base must be raised to give the number.
Página 10 - Any two sides of a spherical triangle are together greater than the third, and the sum of the three sides is less than the circumference of a great circle.
Página 56 - Mathematics which treats of the solution of plane triangles. In every plane triangle there are six parts : three sides and three angles. When three of these parts are given, one being a side, the remaining parts may be found by computation. The operation of finding the unknown parts is called the solution of the triangle.
Página 57 - ... the three interior angles of a triangle are together equal to two right angles.
Página 12 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Página 143 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 27 - For example, let it be required to prove the formula sin ( A - B) = sin A. cos В - cos A. sin В from the annexed figure, where ВАC' = A, and C'AD — В ; each angle being greater than a right angle.
Página 5 - ... stretched taut from one point to the other. The string will not lie on the parallel, but will evidently be in a plane which passes through the centre of the sphere. If the two points be on a meridian, the stretched string will lie on the meridian. By angular distance between two points on a sphere is meant the angle subtended at the centre of the sphere by the arc joining the given points. Thus in Fig. 4 the angle NOA is the angular distance of A from N.
Página 6 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Página 200 - Three circles whose radii are a, b, c touch each other externally ; prove that the tangents at the points of contact meet in a point whose distance from any one of them is (aba Nj a+b + cj 12.