The elements of plane trigonometry |
Dentro del libro
Resultados 1-5 de 59
Página vi
... nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε - 0√ = 1 ) . Sin 03.V - 1 . ( e - T _ 6-0 √ = ï ) . 101 102 104 104 106 118 . 107 1 Tan0 = · 20 √ T +1 119. GREGORIE'S SERIES ; 0 120. EULER'S SERIES to ...
... nearly ......... Cos 0 = 3. ( co√ = 1 · § . ( e® √ = 1 + € - 0 √ = 1 ) . + ε - 0√ = 1 ) . Sin 03.V - 1 . ( e - T _ 6-0 √ = ï ) . 101 102 104 104 106 118 . 107 1 Tan0 = · 20 √ T +1 119. GREGORIE'S SERIES ; 0 120. EULER'S SERIES to ...
Página 43
... nearly equal to 2n + 1.90 ° , n being an integer ) , SA 2 tan A. tan is a very small quantity , and may be ne- glected in comparison with unity . We have therefore , when these two conditions are fulfilled , and not otherwise , — △ sin ...
... nearly equal to 2n + 1.90 ° , n being an integer ) , SA 2 tan A. tan is a very small quantity , and may be ne- glected in comparison with unity . We have therefore , when these two conditions are fulfilled , and not otherwise , — △ sin ...
Página 44
... nearly ) , cot A. tan SA 2 neglected with respect to unity ; and we then have , may be A cos A = - - sin A. sin & A . NOTE . It must be carefully borne in mind , that unless , ( 1 ) , A be a very small angle , and , ( 2 ) , A be ...
... nearly ) , cot A. tan SA 2 neglected with respect to unity ; and we then have , may be A cos A = - - sin A. sin & A . NOTE . It must be carefully borne in mind , that unless , ( 1 ) , A be a very small angle , and , ( 2 ) , A be ...
Página 45
... nearly equal to n.90o ) , cot A. tan SA 2 and tan A. tan ASA will both be very small , and may be neglected when compared with unity . case therefore we have In this A sec A = tan A. sec A. tan SA . NOTE . It is to be remarked , that ...
... nearly equal to n.90o ) , cot A. tan SA 2 and tan A. tan ASA will both be very small , and may be neglected when compared with unity . case therefore we have In this A sec A = tan A. sec A. tan SA . NOTE . It is to be remarked , that ...
Página 46
... nearly equal to a right angle . 64. For a given small increment of A , the increment of the sine is > - the ... nearly a multiple of 90o . For Asin Acos A. sin 84 , if A be not nearly ( 2n + 1 ) 90o . Art . 60. Cor . A cos Asin A. sin SA ...
... nearly equal to a right angle . 64. For a given small increment of A , the increment of the sine is > - the ... nearly a multiple of 90o . For Asin Acos A. sin 84 , if A be not nearly ( 2n + 1 ) 90o . Art . 60. Cor . A cos Asin A. sin SA ...
Otras ediciones - Ver todas
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
Pasajes populares
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.