A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Σελίδα
... Pole and Polar 104 VIII . The Parabola 112 IX . The Ellipse 141 X. The Ellipse continued . XI . The Hyperbola 168 189 XII . The Hyperbola continued • 203 XIII . General Equation of the Second Degree 227 XIV . Miscellaneous Propositions ...
... Pole and Polar 104 VIII . The Parabola 112 IX . The Ellipse 141 X. The Ellipse continued . XI . The Hyperbola 168 189 XII . The Hyperbola continued • 203 XIII . General Equation of the Second Degree 227 XIV . Miscellaneous Propositions ...
Σελίδα 3
... pole , OX the initial line ; OP the radius vector of the point P , and POX the vectorial angle . 7. The position of any point might be expressed by positive values of the polar co - ordinates and r , since there is here no ambiguity ...
... pole , OX the initial line ; OP the radius vector of the point P , and POX the vectorial angle . 7. The position of any point might be expressed by positive values of the polar co - ordinates and r , since there is here no ambiguity ...
Σελίδα 80
... ; let S be the pole and SA the initial line . Let h , k be the co - ordinates of S referred to 0 ; draw SX ' parallel to OX , and let the angle ASX ' : = α . O N M X X ' Let P be any 80 CHANGE OF ORIGIN AND DIRECTION .
... ; let S be the pole and SA the initial line . Let h , k be the co - ordinates of S referred to 0 ; draw SX ' parallel to OX , and let the angle ASX ' : = α . O N M X X ' Let P be any 80 CHANGE OF ORIGIN AND DIRECTION .
Σελίδα 97
... pole , SX the initial line ; C the centre of the circle , Pany point on its circumference . e Let SC - 1 , CSX = a , so that l , a are the polar co - ordi- nates of C ; let c be the radius of the circle ; and let r , be the polar co ...
... pole , SX the initial line ; C the centre of the circle , Pany point on its circumference . e Let SC - 1 , CSX = a , so that l , a are the polar co - ordi- nates of C ; let c be the radius of the circle ; and let r , be the polar co ...
Σελίδα 98
... pole at an inclination to the initial line , the polar co - ordinates of the middle point of the chord which the circle cuts off from this line are 21 cos 0 2 and 0 ; that is , 7 cos 0 , and 0 . Hence the polar equation to the locus of ...
... pole at an inclination to the initial line , the polar co - ordinates of the middle point of the chord which the circle cuts off from this line are 21 cos 0 2 and 0 ; that is , 7 cos 0 , and 0 . Hence the polar equation to the locus of ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Δημοφιλή αποσπάσματα
Σελίδα 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Σελίδα 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Σελίδα 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.