The elements of plane trigonometry |
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Página iii
... FORMULÆ CONNECTING THEM WITH EACH OTHER . 13. Definition of PLANE TRIGONOMETRY .......... 8 14-21 . Definitions of the Goniometrical functions ; their changes of sign and magnitude ........................ . - sin ( 180o - A ) = - · sin ...
... FORMULÆ CONNECTING THEM WITH EACH OTHER . 13. Definition of PLANE TRIGONOMETRY .......... 8 14-21 . Definitions of the Goniometrical functions ; their changes of sign and magnitude ........................ . - sin ( 180o - A ) = - · sin ...
Página iv
John Charles Snowball. ART . FAGE 25. Similar formulæ for Cos A , Tan A , Sec A .... 26. The Sine , Cosine , Tangent , and Secant of an angle expressed in terms of the Complement and the Supplement .......... 27-30 . Formulæ connecting ...
John Charles Snowball. ART . FAGE 25. Similar formulæ for Cos A , Tan A , Sec A .... 26. The Sine , Cosine , Tangent , and Secant of an angle expressed in terms of the Complement and the Supplement .......... 27-30 . Formulæ connecting ...
Página v
... Formulæ which are used in the 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 ...
... Formulæ which are used in the 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 ...
Página vii
... form tables to any other base ......... 142 4-6 . The methods of performing Multiplication , Division , Involution ... formulæ to logarithmic computation . ...... 162 Two pages of Logarithms of Numbers . 164 , 165 APPENDIX II . ON THE ...
... form tables to any other base ......... 142 4-6 . The methods of performing Multiplication , Division , Involution ... formulæ to logarithmic computation . ...... 162 Two pages of Logarithms of Numbers . 164 , 165 APPENDIX II . ON THE ...
Página viii
... Formulæ of Verification ..... IAGE 166 ..... 170 Page of certain Natural and Logarithmic Functions of Angles ............ 173 APPENDIX III . ON THE CONSTRUCTION AND USE OF THE LOGARITHMIC TABLES OF GONIOMETRIC FUNCTIONS . 1-5 . On the ...
... Formulæ of Verification ..... IAGE 166 ..... 170 Page of certain Natural and Logarithmic Functions of Angles ............ 173 APPENDIX III . ON THE CONSTRUCTION AND USE OF THE LOGARITHMIC TABLES OF GONIOMETRIC FUNCTIONS . 1-5 . On the ...
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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.