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Illustration of half of an ellipse. "The ordinates of two corresponding points in an ellipse and its auxiliary circle are in the ratio b:a."

Corresponding Points in an Ellipse and Circle

Illustration of half of an ellipse. "The ordinates of two corresponding points in an ellipse and its…

Illustration showing that if one diameter is conjugate to a second, the second is conjugate to the first.

Conjugate Diameters of an Ellipse

Illustration showing that if one diameter is conjugate to a second, the second is conjugate to the first.

Illustration of half of an ellipse and its auxiliary circle used to construct an ellipse by points, having given its two axes.

Construction of an Ellipse

Illustration of half of an ellipse and its auxiliary circle used to construct an ellipse by points,…

Illustration of half of an ellipse. "If d denotes the abscissa of a point of an ellipse, r and r' its focal radii, then r'=a+ed, r=a-ed."

Focal Radii of an Ellipse

Illustration of half of an ellipse. "If d denotes the abscissa of a point of an ellipse, r and r' its…

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the angle between one of the focal radii and the other produced, every point in this line except P is without the curve."

Line Bisecting Angle Between Focal Radii on Ellipse

Illustration of half of an ellipse. "If through a point P of an ellipse a line is drawn bisecting the…

Illustration of half of an ellipse. The square of the ordinate of a point in an ellipse is to the product of the segments of the major axis made by the ordinate as the square of b to the square of a.

Ordinate and Major Axis of Ellipse

Illustration of half of an ellipse. The square of the ordinate of a point in an ellipse is to the product…

Illustration showing that tangents drawn at the ends of any diameter are parallel to each other.

Parallel Tangents to an Ellipse

Illustration showing that tangents drawn at the ends of any diameter are parallel to each other.

Illustration of half of an ellipse. "The sum of the distances of any point from the foci of an ellipse is greater than or less than 2a, according as the point is without or within the curve."

Point Distances to Foci on Ellipse

Illustration of half of an ellipse. "The sum of the distances of any point from the foci of an ellipse…

Illustration of how to draw a tangent to an ellipse from an external point.

Tangent From External Point to an Ellipse

Illustration of how to draw a tangent to an ellipse from an external point.

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting the external angle between the focal radii is a tangent."

Tangent to an Ellipse

Diagram an ellipse with a tangent line that illustrates "A line through a point on the ellipse and bisecting…

Illustration showing the tangents drawn at two corresponding points of an ellipse and its auxiliary circle cut the major axis produced at the same point.

Tangents to an Ellipse

Illustration showing the tangents drawn at two corresponding points of an ellipse and its auxiliary…

Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola a line is drawn bisecting the angle between the focal radii, every point in this line except P is on the convex side of the curve.

Line Bisecting Angle Between Focal Radii in Hyperbola

Illustration of a hyperbola with a line bisecting the focal radii. "If through a point P of an hyperbola…

Illustration of a point on a hyperbola. "If d denotes the abscissa (x-coordinate) of a point of an hyperbola, r and r' its focal radii, then r = ed - a, and r' = ed + a."

Point on a Hyperbola

Illustration of a point on a hyperbola. "If d denotes the abscissa (x-coordinate) of a point of an hyperbola,…

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola and bisecting the internal angle between the focal radii is a tangent."

Tangent to a Hyperbola

Diagram part of a hyperbola with a tangent line that illustrates "A line through a point on the hyperbola…