The elements of plane trigonometry |
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Página iv
... : Tan - 1 = 1 t1 = to tit2 47 t1 67. Tan - 1 t1- tan - 1 t1 = tan - 1 - t2 + tan - 1 1 + t1 to to - tz 1+ tots + ... + tan - 1 48 • 1+ t - tỉ · 68. Examples ......... 48 ART . CHAPTER IV . ON THE SOLUTION OF TRIANGLES iv INDEX .
... : Tan - 1 = 1 t1 = to tit2 47 t1 67. Tan - 1 t1- tan - 1 t1 = tan - 1 - t2 + tan - 1 1 + t1 to to - tz 1+ tots + ... + tan - 1 48 • 1+ t - tỉ · 68. Examples ......... 48 ART . CHAPTER IV . ON THE SOLUTION OF TRIANGLES iv INDEX .
Página v
... solution of triangles 79-81 . The solution of right - angled triangles 82-88 . The solution of oblique - angled triangles 89. Examples ... ........................ 90. The area of a triangle in terms of the sides sin B. sin C sin ( B + ...
... solution of triangles 79-81 . The solution of right - angled triangles 82-88 . The solution of oblique - angled triangles 89. Examples ... ........................ 90. The area of a triangle in terms of the sides sin B. sin C sin ( B + ...
Página vi
... expand , independently of Demoivre's principle , Sine and Cos in terms of 0 ........... 132 , 133. The summation of some Trigonometrical series . ............. 121 122 124 ART . CHAPTER VII . ON THE SOLUTION OF EQUATIONS vi INDEX .
... expand , independently of Demoivre's principle , Sine and Cos in terms of 0 ........... 132 , 133. The summation of some Trigonometrical series . ............. 121 122 124 ART . CHAPTER VII . ON THE SOLUTION OF EQUATIONS vi INDEX .
Página vii
John Charles Snowball. ART . CHAPTER VII . ON THE SOLUTION OF EQUATIONS AND THE RESOLUTION OF CERTAIN EXPRESSIONS INTO FACTORS . 134. To solve a quadratic equation ........ 135 , 136. To solve a cubic equation .. PAGE 128 131 n - 137-140 ...
John Charles Snowball. ART . CHAPTER VII . ON THE SOLUTION OF EQUATIONS AND THE RESOLUTION OF CERTAIN EXPRESSIONS INTO FACTORS . 134. To solve a quadratic equation ........ 135 , 136. To solve a cubic equation .. PAGE 128 131 n - 137-140 ...
Página 8
... solution of plane recti- lineal figures . 14. Let a straight line revolve from the fixed line AB round the point A , in the direction of the letters B , D , B ' , D ' , and let there be A degrees in the angle BAC . D D D B ' B B BBN ...
... solution of plane recti- lineal figures . 14. Let a straight line revolve from the fixed line AB round the point A , in the direction of the letters B , D , B ' , D ' , and let there be A degrees in the angle BAC . D D D B ' B B BBN ...
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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.