The elements of plane trigonometry |
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Página 117
... pole , and being measured from that vertex which is the further from the focus ; .. r = a . √√1 − e2 . { 1 + 2b . cos 0 + 2b2 . cos 20 + ... } , - where b = e 1 + √ 1 − e2 - € - 128. To expand 1 ( 1 e cos 0 ) in a series of the co ...
... pole , and being measured from that vertex which is the further from the focus ; .. r = a . √√1 − e2 . { 1 + 2b . cos 0 + 2b2 . cos 20 + ... } , - where b = e 1 + √ 1 − e2 - € - 128. To expand 1 ( 1 e cos 0 ) in a series of the co ...
Página 205
... pole is a right angle ... 3 10 , 11. Methods of finding the Pole of a circle ............. 12. The arc joining the Poles of two great circles subtends the angle at which the circles are inclined to each other ........ ........... 13 ...
... pole is a right angle ... 3 10 , 11. Methods of finding the Pole of a circle ............. 12. The arc joining the Poles of two great circles subtends the angle at which the circles are inclined to each other ........ ........... 13 ...
Página 3
... poles of the circle AFC , and the straight line BOD is called the axis of the circle AFC . 8. The pole of a circle is equally distant from every point in its circumference . ( Fig . Art . 2. ) Join B with F any point in AFCG . Then ...
... poles of the circle AFC , and the straight line BOD is called the axis of the circle AFC . 8. The pole of a circle is equally distant from every point in its circumference . ( Fig . Art . 2. ) Join B with F any point in AFCG . Then ...
Página 4
... pole of the circle ; whether the distance be estimated by the length of a straight line joining the point with the pole , or by the arc of a great circle connecting the same points , or by the angle which this arc subtends at the centre ...
... pole of the circle ; whether the distance be estimated by the length of a straight line joining the point with the pole , or by the arc of a great circle connecting the same points , or by the angle which this arc subtends at the centre ...
Página 5
... pole of AFC . COR . Hence also it appears , that the intersection of two arcs drawn at right angles to a given circle through any two points in it , is the pole of that circle . 12. The angle subtended at the centre of the sphere by the ...
... pole of AFC . COR . Hence also it appears , that the intersection of two arcs drawn at right angles to a given circle through any two points in it , is the pole of that circle . 12. The angle subtended at the centre of the sphere by 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.