The elements of plane trigonometry |
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Página 67
... diff . for 1 " is in this case 67.016 ; 286 286 and = 4-267 = 4.27 nearly , 67.016 Therefore A = 72 ° , 33 ' , 4 " -27 . II . ON THE SOLUTION OF OBLIQUE - ANGLED TRIANGLES . Let two angles and the side between them be given . ( A , C ...
... diff . for 1 " is in this case 67.016 ; 286 286 and = 4-267 = 4.27 nearly , 67.016 Therefore A = 72 ° , 33 ' , 4 " -27 . II . ON THE SOLUTION OF OBLIQUE - ANGLED TRIANGLES . Let two angles and the side between them be given . ( A , C ...
Página 159
... Diff . " , in which the difference is placed opposite to that lo- garithm at which such difference begins . To know what the difference therefore is in any particular case , it is merely requisite to take the number in this line next ...
... Diff . " , in which the difference is placed opposite to that lo- garithm at which such difference begins . To know what the difference therefore is in any particular case , it is merely requisite to take the number in this line next ...
Página 160
... Diff . " 117 , the dif- ference 94 corresponds to the digit 8 , -therefore the significant part of the number sought is 369638 ; also since the given logarithm has 3 for its characteristic , the number required is 3696-38 . Ex . 2 ...
... Diff . " 117 , the dif- ference 94 corresponds to the digit 8 , -therefore the significant part of the number sought is 369638 ; also since the given logarithm has 3 for its characteristic , the number required is 3696-38 . Ex . 2 ...
Página 162
... Diff . " being 118 , the part for a first additional digit 8 is 94 ; and for a first additional digit 6 the part is 71 , and therefore the part when 6 is a second additional digit is is thus performed ; 71 10 > or 7.1 . The operation ...
... Diff . " being 118 , the part for a first additional digit 8 is 94 ; and for a first additional digit 6 the part is 71 , and therefore the part when 6 is a second additional digit is is thus performed ; 71 10 > or 7.1 . The operation ...
Página 165
... Diff . 3650 5622929 3048 3167 3286 3405 3524 3642 3761 3880 3999 119 119 4118 4237 4356 4475 4594 4713 4832 4951 5070 5189 090 11 12 5308 5427 5546 5664 5783 5902 6021 6140 6259 63780803-36 6497 6616 6734 6853 6972 7091 7210 7329 7448 ...
... Diff . 3650 5622929 3048 3167 3286 3405 3524 3642 3761 3880 3999 119 119 4118 4237 4356 4475 4594 4713 4832 4951 5070 5189 090 11 12 5308 5427 5546 5664 5783 5902 6021 6140 6259 63780803-36 6497 6616 6734 6853 6972 7091 7210 7329 7448 ...
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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.