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
... Circle 25 58 Transformation of Co - ordinates 76 84 • VII . Radical Axis . 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 ...
... Circle 25 58 Transformation of Co - ordinates 76 84 • VII . Radical Axis . 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 ...
Σελίδα 74
... circle and the circum- scribed circle is a ( cos B - cos C ) + B ( cos C - cos A ) + y ( cos A — cos B ) = 0 . 16. If the equations to the sides of a triangle ABC be u = 0 , v = 0 , w = 0 , and to the sides of a triangle A'B'C ' , u = a ...
... circle and the circum- scribed circle is a ( cos B - cos C ) + B ( cos C - cos A ) + y ( cos A — cos B ) = 0 . 16. If the equations to the sides of a triangle ABC be u = 0 , v = 0 , w = 0 , and to the sides of a triangle A'B'C ' , u = a ...
Σελίδα 75
... circle , O the centre of the escribed circle which touches BC . The line 00 ' meets BC in D , and any straight line drawn through D meets AC in E and AB in F. The lines OF and O'E meet in P , and the lines OE and O'F in Q. Shew that A ...
... circle , O the centre of the escribed circle which touches BC . The line 00 ' meets BC in D , and any straight line drawn through D meets AC in E and AB in F. The lines OF and O'E meet in P , and the lines OE and O'F in Q. Shew that A ...
Σελίδα 83
... the same point referred to another system of oblique axes , and shew that x = mx + ny ' , m2 + m2 n2 + n 12 / 2 - - 1 1 y = m'x ' + n'y ' , = mm nn ' CHAPTER VI . THE CIRCLE . 88. WE now proceed 6-2 OF THE CO - ORDINATES . 83.
... the same point referred to another system of oblique axes , and shew that x = mx + ny ' , m2 + m2 n2 + n 12 / 2 - - 1 1 y = m'x ' + n'y ' , = mm nn ' CHAPTER VI . THE CIRCLE . 88. WE now proceed 6-2 OF THE CO - ORDINATES . 83.
Σελίδα 84
... circle , with which we shall commence . To find the equation to the circle referred to any rectangular axes . D N M X Let C be the centre of the circle ; P any point on its cir- cumference . Let c be the radius of the circle ; a , b the ...
... circle , with which we shall commence . To find the equation to the circle referred to any rectangular axes . D N M X Let C be the centre of the circle ; P any point on its cir- cumference . Let c be the radius of the circle ; a , b the ...
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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.