The elements of plane trigonometry |
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Página v
... angle , to determine the number 87 The number of degrees , and seconds , subtended by an arc which is equal to the radius 88 103. Comparison of the unit of measurement in the two methods of esti- mating the magnitude of an angle ...
... angle , to determine the number 87 The number of degrees , and seconds , subtended by an arc which is equal to the radius 88 103. Comparison of the unit of measurement in the two methods of esti- mating the magnitude of an angle ...
Página vi
... number of seconds contained in an angle which is ex- pressed by the circular measure .......... 114 1 127. To expand 1 - e.cos 0 in a series of the cosines of 0 and its multiples ... 115 128. To expand 1 , ( 1 - e . cos 0 ) . 117 129 ...
... number of seconds contained in an angle which is ex- pressed by the circular measure .......... 114 1 127. To expand 1 - e.cos 0 in a series of the cosines of 0 and its multiples ... 115 128. To expand 1 , ( 1 - e . cos 0 ) . 117 129 ...
Página 5
... seconds ; and so on ; and the divisions are thus marked , 269 , 24 , 32 ... number of degrees and grades contained in the same angle BAC . ( Art . 14 ... how many degrees and minutes 5 The relation between the degrees and the grades which ...
... seconds ; and so on ; and the divisions are thus marked , 269 , 24 , 32 ... number of degrees and grades contained in the same angle BAC . ( Art . 14 ... how many degrees and minutes 5 The relation between the degrees and the grades which ...
Página 70
... number of degrees and minutes exactly , the additional seconds have to be determined on the principle that the increment of the tabular logarithm varies as the increment of the angle . But when the angle is equal to ( 2n + 1 ) . 90 ...
... number of degrees and minutes exactly , the additional seconds have to be determined on the principle that the increment of the tabular logarithm varies as the increment of the angle . But when the angle is equal to ( 2n + 1 ) . 90 ...
Página 88
... seconds required are 57 ° , 17 ′ , 44 " 77 . COR . It is often necessary to know the number of seconds subtended by an arc which is equal to the radius . The number of degrees subtended = 57.29577 minutes 3437.7462 60 60 number of seconds ...
... seconds required are 57 ° , 17 ′ , 44 " 77 . COR . It is often necessary to know the number of seconds subtended by an arc which is equal to the radius . The number of degrees subtended = 57.29577 minutes 3437.7462 60 60 number of seconds ...
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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.