A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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... parabola , ellipse , and hyperbola , have been separately considered before the discussion of the general equation of the second degree , from the belief that the subject is thus presented in its most accessible form to students in the ...
... parabola , ellipse , and hyperbola , have been separately considered before the discussion of the general equation of the second degree , from the belief that the subject is thus presented in its most accessible form to students in the ...
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... 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 247 XV . Abridged Notation 274 ...
... 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 247 XV . Abridged Notation 274 ...
Página 111
... two given points ; shew that the lines which join the points of intersection of the fixed circle with each circle of the series all meet in a point . CHAPTER VIII . THE PARABOLA . 123. THERE are three MISCELLANEOUS EXAMPLES . 111.
... two given points ; shew that the lines which join the points of intersection of the fixed circle with each circle of the series all meet in a point . CHAPTER VIII . THE PARABOLA . 123. THERE are three MISCELLANEOUS EXAMPLES . 111.
Página 112
... parabola , an ellipse , an hyperbola , a circle , two straight lines , one straight line , or a point . Hence the term conic section is applied to the parabola , ellipse , and hyperbola — and may be extended to include the circle , two ...
... parabola , an ellipse , an hyperbola , a circle , two straight lines , one straight line , or a point . Hence the term conic section is applied to the parabola , ellipse , and hyperbola — and may be extended to include the circle , two ...
Página 113
... parabola with the assumed origin and axes . The curve cuts the axis of x at a point A which bisects OS ; for when y = 0 in ( 1 ) , we have x = a . The equation will be simplified if we put the origin at A ; let x ' = AM , then x ' = x ...
... parabola with the assumed origin and axes . The curve cuts the axis of x at a point A which bisects OS ; for when y = 0 in ( 1 ) , we have x = a . The equation will be simplified if we put the origin at A ; let x ' = AM , then x ' = x ...
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Términos y frases comunes
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
Pasajes populares
Página 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 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.
Página 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.
Página 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.
Página 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.