Description
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CONTENTS
1. Introduction
2. Coordinates, Lengths of Straight Lines and Areas of
Triangles
Polar coordinates
3. Locus, Equation to a Locus
4. The Straight Line, Rectangular Coordinates
Straight line through two points
Angle between two given straight lines
Conditions that they may be parallel and perpendicular
Length of a perpendicular
Bisectors of angles
5. The Straight Line (Continued)
Polar Equations and Oblique Coordinates
Equations involving an arbitrary constant
Examples of loci
6. On Equations Representing Two or More Straight Lines
Angle between two lines given by one equation
General equation of the second degree
7. Transformation of Coordinates
Invariants
8. The Circle
Equation to a tangent
Pole and polar
Equation to a circle in polar coordinates
Equation referred to oblique axes
Equations in terms of one variable
9. Systems of Circles
Orthogonal circles
Radical axis
Coaxal circles
10. The Parabola
Equation to a tangent
Some properties of the parabola
Pole and polar
Diameters
Equations in terms of one variable
11. The Parabola (Continued)
Loci connected with the parabola
Three normals passing through a given point
Parabola referred to two tangents as axes
12. The Ellipse
Auxiliary circle and eccentric angle
Equation to a tangent
Some properties of the ellipse
Pole and polar
Conjugate diameters
Four normals through any point
Examples of loci
13. The Hyperbola
Asymptotes
Equation referred to the asymptotes as axes
One variable. Examples
14. Polar Equation of a Conic Section, Its Focus being the Pole
Polar equation to a tangent, polar, and normal
15. General Equation of the Second Degree, Tracing of Curves
Particular cases of conic sections
Transformation of equation to centre as origin
Equation to asymptotes
Tracing a parabola
Tracing a central conic
Eccentricity and foci of general conic
16. The General Conic
Tangent
Conjugate diameters
Conics through the intersections of two conics
The equation S = uv
General equation to the pair of tangents drawn from
any point
The director circle
The foci
The axes
Lengths of straight lines drawn in given directions
to meet the conic.
Conics passing through four points
Conics touching four lines
The conic LM = R2
17. Miscellaneous Propositions
On the four normals from any point to a central conic
Confocal conics
Circles of curvature and contact of the third order
Envelopes
Answers
1. Introduction
2. Coordinates, Lengths of Straight Lines and Areas of
Triangles
Polar coordinates
3. Locus, Equation to a Locus
4. The Straight Line, Rectangular Coordinates
Straight line through two points
Angle between two given straight lines
Conditions that they may be parallel and perpendicular
Length of a perpendicular
Bisectors of angles
5. The Straight Line (Continued)
Polar Equations and Oblique Coordinates
Equations involving an arbitrary constant
Examples of loci
6. On Equations Representing Two or More Straight Lines
Angle between two lines given by one equation
General equation of the second degree
7. Transformation of Coordinates
Invariants
8. The Circle
Equation to a tangent
Pole and polar
Equation to a circle in polar coordinates
Equation referred to oblique axes
Equations in terms of one variable
9. Systems of Circles
Orthogonal circles
Radical axis
Coaxal circles
10. The Parabola
Equation to a tangent
Some properties of the parabola
Pole and polar
Diameters
Equations in terms of one variable
11. The Parabola (Continued)
Loci connected with the parabola
Three normals passing through a given point
Parabola referred to two tangents as axes
12. The Ellipse
Auxiliary circle and eccentric angle
Equation to a tangent
Some properties of the ellipse
Pole and polar
Conjugate diameters
Four normals through any point
Examples of loci
13. The Hyperbola
Asymptotes
Equation referred to the asymptotes as axes
One variable. Examples
14. Polar Equation of a Conic Section, Its Focus being the Pole
Polar equation to a tangent, polar, and normal
15. General Equation of the Second Degree, Tracing of Curves
Particular cases of conic sections
Transformation of equation to centre as origin
Equation to asymptotes
Tracing a parabola
Tracing a central conic
Eccentricity and foci of general conic
16. The General Conic
Tangent
Conjugate diameters
Conics through the intersections of two conics
The equation S = uv
General equation to the pair of tangents drawn from
any point
The director circle
The foci
The axes
Lengths of straight lines drawn in given directions
to meet the conic.
Conics passing through four points
Conics touching four lines
The conic LM = R2
17. Miscellaneous Propositions
On the four normals from any point to a central conic
Confocal conics
Circles of curvature and contact of the third order
Envelopes
Answers
