The elements of plane trigonometry |
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Página 122
... changed into - 0 , the sine of continues of the same mag- nitude , but changes its sign , -a result which cannot take place if the series contain either constant terms , or terms involving even powers of the angle . Let therefore Sin 0 ...
... changed into - 0 , the sine of continues of the same mag- nitude , but changes its sign , -a result which cannot take place if the series contain either constant terms , or terms involving even powers of the angle . Let therefore Sin 0 ...
Página 123
... changed into - 0 . Let ... Cos = a + ɑ2 Ø2 + α1 Ø1 + And if o be written for 0 , this equation becomes , 1 = a ; Cos e = 1 + a2 93 + a1 01 + ...... Adding these values of Sin and Cos 9 , we have 1 + 0 + a¿02 + a ̧Ð3 + a ̧01 + ... = cos ...
... changed into - 0 . Let ... Cos = a + ɑ2 Ø2 + α1 Ø1 + And if o be written for 0 , this equation becomes , 1 = a ; Cos e = 1 + a2 93 + a1 01 + ...... Adding these values of Sin and Cos 9 , we have 1 + 0 + a¿02 + a ̧Ð3 + a ̧01 + ... = cos ...
Página 129
... changed ; for the product of the roots with their signs changed ( -q ) remains the same , and the sum of their roots with their signs changed ( the coefficient of the second term ) changes its sign , but continues of the same magnitude ...
... changed ; for the product of the roots with their signs changed ( -q ) remains the same , and the sum of their roots with their signs changed ( the coefficient of the second term ) changes its sign , but continues of the same magnitude ...
Página 130
... changed . ( Wood's Algebra , Art . 281. ) In the last two cases , if 49 be > 1 , let 4q = ( sec 0 ) 2 ; p3 p2 then ∞ = Ρ - • { 1+ ± √ − [ ( sec 0 ) 2 − 1 ] Ρ = 2 { 1 + tan 0√ - 1 } , 2 and both roots of the equation are impossible ...
... changed . ( Wood's Algebra , Art . 281. ) In the last two cases , if 49 be > 1 , let 4q = ( sec 0 ) 2 ; p3 p2 then ∞ = Ρ - • { 1+ ± √ − [ ( sec 0 ) 2 − 1 ] Ρ = 2 { 1 + tan 0√ - 1 } , 2 and both roots of the equation are impossible ...
Página 199
... changed to a from the south , and the shadow to B'o from the north , and the kite was raised as much above 45 ° as it had before been below Shew that 0 ° being the angular eleva- tion of the Sun , and 45o - 4o that of the kite at first ...
... changed to a from the south , and the shadow to B'o from the north , and the kite was raised as much above 45 ° as it had before been below Shew that 0 ° being the angular eleva- tion of the Sun , and 45o - 4o that of the kite at first ...
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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.