The elements of plane trigonometry |
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Página 76
... centre C of these circles . Draw CD perpendicular to AB . D B Then AD = DB , and CD is the radius of the inscribed circle . Let r = CD , and R = AC . Now the sum of all the angles which the sides subtend at C = n × ACB = 360 ° ; 360o ...
... centre C of these circles . Draw CD perpendicular to AB . D B Then AD = DB , and CD is the radius of the inscribed circle . Let r = CD , and R = AC . Now the sum of all the angles which the sides subtend at C = n × ACB = 360 ° ; 360o ...
Página 77
... centre is C ; AB a side of the in- scribed regular polygon of n sides ; CE at right angles to AB , and therefore bisecting it ; FG a tangent through E ; then FG is a side of the circumscribed polygon of n sides . Let CA = r . ADB = 2 AD ...
... centre is C ; AB a side of the in- scribed regular polygon of n sides ; CE at right angles to AB , and therefore bisecting it ; FG a tangent through E ; then FG is a side of the circumscribed polygon of n sides . Let CA = r . ADB = 2 AD ...
Página 78
... angles A and B meet in O , and from O draw OD , OE , OF perpendiculars to the sides . Then , Euclid Iv . 4 , O is the centre of the inscribed circle , and r its radius = OD OE = OF = B E Now , Area of △ ABC = △ AOB + 78.
... angles A and B meet in O , and from O draw OD , OE , OF perpendiculars to the sides . Then , Euclid Iv . 4 , O is the centre of the inscribed circle , and r its radius = OD OE = OF = B E Now , Area of △ ABC = △ AOB + 78.
Página 79
... centre of the circumscribed circle ; and R , its radius , = OA = OB = OC . Euclid IV . 5 . Area of ABC AC . AB . sin A , Art . 90 . = And A = BOC , Euclid 111. 20 ; ... Sin A = sin BOC = sin BOE = 2 bc .. R = - α b +2 = r • S ; 2 BE a ...
... centre of the circumscribed circle ; and R , its radius , = OA = OB = OC . Euclid IV . 5 . Area of ABC AC . AB . sin A , Art . 90 . = And A = BOC , Euclid 111. 20 ; ... Sin A = sin BOC = sin BOE = 2 bc .. R = - α b +2 = r • S ; 2 BE a ...
Página 85
... centres of the circles . 360 ° Then ACB : = = Lacb , n and ACB , acb are similar triangles ; R 7 ° = AB n . AB ab = P = C - X n.ab p C - x .. R.c-R.xr.Cr . X. Now since R. c , r . C are constant , and R. x , r . X are variable , we must ...
... centres of the circles . 360 ° Then ACB : = = Lacb , n and ACB , acb are similar triangles ; R 7 ° = AB n . AB ab = P = C - X n.ab p C - x .. R.c-R.xr.Cr . X. Now since R. c , r . C are constant , and R. x , r . X are variable , we must ...
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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.