The elements of plane trigonometry |
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Página 6
... neglecting the thou- sandth parts of a second . Ex . 2. Find how many grades and minutes are contained in the angle 24o , 51 ' , 45 " . First reducing the minutes and seconds to the decimal parts of a degree , 60 ) 45 " . 60 ) 51′.75 ...
... neglecting the thou- sandth parts of a second . Ex . 2. Find how many grades and minutes are contained in the angle 24o , 51 ' , 45 " . First reducing the minutes and seconds to the decimal parts of a degree , 60 ) 45 " . 60 ) 51′.75 ...
Página 120
... neglecting the second and all the succeeding terms of the expansion , as being small when compared with 1 , we have for a first approximation , ( representing by y , this first ap- proximation to the real value of y ) , 2 и y1 = = 2 tan ...
... neglecting the second and all the succeeding terms of the expansion , as being small when compared with 1 , we have for a first approximation , ( representing by y , this first ap- proximation to the real value of y ) , 2 и y1 = = 2 tan ...
Página 121
... . sin x . cos m + cos z . cos n , when y and n are very small , that n cos m y = n . 1 + - • cot x y • cot x = -n . n y 2 - - . ( cos m - . cotz ) - ( 1 - 2. cota ) , nearly ; 2 • n whence , neglecting cot ≈ with respect to cos 121.
... . sin x . cos m + cos z . cos n , when y and n are very small , that n cos m y = n . 1 + - • cot x y • cot x = -n . n y 2 - - . ( cos m - . cotz ) - ( 1 - 2. cota ) , nearly ; 2 • n whence , neglecting cot ≈ with respect to cos 121.
Página 122
... neglecting powers of n above the second . The number of seconds in y is y sin 1 " n cos m n2 = + • sin 1 " 2. sin 1 " cot x . ( sin m ) 2 , the terms of this expression are , as in Ex . 1 , determined sepa- rately by means of logarithms ...
... neglecting powers of n above the second . The number of seconds in y is y sin 1 " n cos m n2 = + • sin 1 " 2. sin 1 " cot x . ( sin m ) 2 , the terms of this expression are , as in Ex . 1 , determined sepa- rately by means of logarithms ...
Página 158
... neglecting the 10n succeeding terms as being small compared with the first term , becomes α nearly . = 1 , 10 ̊ 10n ' - Similarly , m , – m1 = 110 ( n + 1 ) − 1 , n = - .. m - mi = ( m2 — m1 ) - • a 10 1 • 1 le 10 n Whence m may be ...
... neglecting the 10n succeeding terms as being small compared with the first term , becomes α nearly . = 1 , 10 ̊ 10n ' - Similarly , m , – m1 = 110 ( n + 1 ) − 1 , n = - .. m - mi = ( m2 — m1 ) - • a 10 1 • 1 le 10 n Whence m may be ...
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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
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.