The elements of plane trigonometry |
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Página viii
... GONIOMETRIC FUNCTIONS . 1-5 . On the determination from the angles of the logarithms of gonio- metric functions ........ 174 6 , 7. The increment of a tabular logarithmic function of an angle varies , with certain exceptions , as the ...
... GONIOMETRIC FUNCTIONS . 1-5 . On the determination from the angles of the logarithms of gonio- metric functions ........ 174 6 , 7. The increment of a tabular logarithmic function of an angle varies , with certain exceptions , as the ...
Página 166
... goniometric functions are sometimes said to be radius of 10000 ; " the meaning of this expression we will explain . If with C as centre , and radius CA , an arc AB be described , and BN , AT be to CA , the lines NB , CN , AT , CT , AN ...
... goniometric functions are sometimes said to be radius of 10000 ; " the meaning of this expression we will explain . If with C as centre , and radius CA , an arc AB be described , and BN , AT be to CA , the lines NB , CN , AT , CT , AN ...
Página 171
... goniometric functions are correctly given by the tables . 10 . The values of the goniometric functions having been 171.
... goniometric functions are correctly given by the tables . 10 . The values of the goniometric functions having been 171.
Página 172
... goniometric functions , mathematical calculations are most fre- quently made . A page from Sherwin's Logarithmic Tables , corrected in some places , is here subjoined , the natural cosines , tangents , secants , and cosecants being ...
... goniometric functions , mathematical calculations are most fre- quently made . A page from Sherwin's Logarithmic Tables , corrected in some places , is here subjoined , the natural cosines , tangents , secants , and cosecants being ...
Página 173
... 9-9784111 5 9-9783702 4 10-0217117 29.9782883 2 6-8169-9782474 6-8509-9782063 9-9783293 3 Co - sines . L. Sec . Co - tans . Co - secants . L. Sine . M 72 Degrees . APPENDIX III . ON THE LOGARITHMIC TABLES OF GONIOMETRIC FUNCTIONS.
... 9-9784111 5 9-9783702 4 10-0217117 29.9782883 2 6-8169-9782474 6-8509-9782063 9-9783293 3 Co - sines . L. Sec . Co - tans . Co - secants . L. Sine . M 72 Degrees . APPENDIX III . ON THE LOGARITHMIC TABLES OF GONIOMETRIC FUNCTIONS.
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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.