The elements of plane trigonometry |
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Página v
... opposite angles are supplements to each other 79 CHAPTER V. 97 , 98. THE USE OF SUBSIDIARY ANGLES ; and EXAMPLES ...... CHAPTER VI . ANALYTICAL TRIGONOMETRY . 81 100 . 99. The circumference of a circle varies as the radius Arc radius 85 ...
... opposite angles are supplements to each other 79 CHAPTER V. 97 , 98. THE USE OF SUBSIDIARY ANGLES ; and EXAMPLES ...... CHAPTER VI . ANALYTICAL TRIGONOMETRY . 81 100 . 99. The circumference of a circle varies as the radius Arc radius 85 ...
Página 21
... opposite to the greater angle , ( Eucl . 1. 19. ) ; .. AN NC ; AN NC > AC AC ' or cos Asin A. Similarly , for angles between 45 ° and 90o , it may be shewn that the cosine is less than the sine . 32. To find the sines , cosines , and ...
... opposite to the greater angle , ( Eucl . 1. 19. ) ; .. AN NC ; AN NC > AC AC ' or cos Asin A. Similarly , for angles between 45 ° and 90o , it may be shewn that the cosine is less than the sine . 32. To find the sines , cosines , and ...
Página 56
... opposite to the angles A , B , C , by the letters a , b , c . 70. The sines of the angles of a triangle are propor- tional to the sides respectively opposite . Let ABC be the triangle . Draw CD perpendicular to AB , or AB produced ...
... opposite to the angles A , B , C , by the letters a , b , c . 70. The sines of the angles of a triangle are propor- tional to the sides respectively opposite . Let ABC be the triangle . Draw CD perpendicular to AB , or AB produced ...
Página 57
... opposite to it , it might be proved that , sin A sin C a C Wherefore , sin A sin B sin C ; a b с the magnitudes of the lines a , b , c , being represented by the number of units of length they respectively contain ; for otherwise sin ...
... opposite to it , it might be proved that , sin A sin C a C Wherefore , sin A sin B sin C ; a b с the magnitudes of the lines a , b , c , being represented by the number of units of length they respectively contain ; for otherwise sin ...
Página 58
... opposite to one of them ( a , b , A ) , the triangle can be determined only in the case where the side opposite to the given angle is the greater of the two sides which are given ; i . e . when a is greater than b . The equations of the ...
... opposite to one of them ( a , b , A ) , the triangle can be determined only in the case where the side opposite to the given angle is the greater of the two sides which are given ; i . e . when a is greater than b . The equations of 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
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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.