Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions |
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Other editions - View all
Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions Briot,Bouquet No preview available - 2018 |
Briot and Bouquet's Elements of Analytical Geometry of Two Dimensions Briot,Bouquet No preview available - 2018 |
Common terms and phrases
abscissa angular coefficient arbitrary parameter asymptotes Ax² axes circumscribed co-ordinates coincide condition conic section conjugate diameters constant constructed corresponding Cy² described determine different from zero directrix distance draw ellipse equa equal equation find the locus fixed point foci focus F formulas function given points given straight lines harmonic conjugates homogeneous homogeneous co-ordinates homogeneous function homographic hyperbola imaginary infinite branches infinity inscribed length M₁ major axis mid-point negative obtained ordinate parabola parallel perpendicular plane point F point of contact point of intersection polar polynomial positive preceding projection quantity radical axis radius vector ratio rectangular reduced represents respect revolve roots satisfy secant second degree sides sin² situated Suppose tangent tangents drawn theorem tion triangle variable vertex vertices whence it follows x-axis y-axis y₁
Popular passages
Page 548 - Find the locus of a point, the square of whose distance from a given point is proportional to its distance from a given right line.
Page 547 - Prove algebraically that the angles in the same segment of a circle are equal, and that the angle in a semicircle is a right angle.
Page 19 - Tlte parabola is a curve every point of which is equally distant from a fixed point called the focus and a fixed line called the directrix.
Page 556 - The radius of the circle, which touches an hyperbola and its asymptotes, is equal to that part of the latus rectum produced which is intercepted between the curve and the asymptote.
Page 557 - If normals be drawn to an ellipse from a given point within it, the points where they meet the curve will all lie in an equilateral hyperbola which passes through the given point, and has its asymptotes parallel to the axes of the ellipse.
Page 552 - V. 21. Find the radius of a circle inscribed in a semi-ellipse, touching the axis minor. 22. From the point where the circle on the major axis is intersected by the minor axis produced, a tangent is drawn to the ellipse; find the point of contact. 23. If from the extremities of the minor axis two straight lines be drawn through any point in the ellipse, and intersect the axis major in Q and R, then CQ. CR=CA'.
Page 73 - B. Constructions. 1. Bisect a line segment and draw the perpendicular bisector. 2. Bisect an angle. 3. Construct a perpendicular to a given line through a given point. 4. Construct an angle equal to a given angle. 5. Through a given point draw a straight line parallel to a given straight line. 6.
Page 548 - If through any point in the arc of a quadrant whose radius is R, two circles be drawn touching the bounding radii of the quadrant, and r, r' be the radii of these circles : shew that rr'= S*.
Page 552 - The circle described on any radius vector SP of an ellipse as diameter, will touch the circle on the axis major. 17. Find where the tangents from the foot of the directrix will meet the hyperbola, and what angle they will make with the transverse axis. 18. Find the equation to the tangent at the extremity of the 3?
Page 541 - Determine the point of intersection of the two lines (3y - x = 0) and (2x + y = 1). 7. Find the equation to the straight line which passes through the point of intersection of the straight lines x - 2y - a = 0, x + 3y - 2a = 0, and is parallel to the line 3x + 4y = 0.