ClipArt ETC
An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer three ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fourth ellipse).

5 Concentric Ellipses

An illustration of 5 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outer two ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the third ellipse).

4 Concentric Ellipses

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which is drawn in the illustration. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes decreases in size in each successive ellipse. The major axis is horizontal for the outmost ellipse and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the second/middle ellipse).

3 Concentric Ellipses

An illustration of 3 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The ellipse on the left has a larger horizontal axis than the ellipse on the right. The ellipse on the left has equal horizontal and vertical axes, making it a circle.

2 Ellipses With Equal Vertical Axes

An illustration of 2 ellipses that have the equal vertical axes, but different horizontal axes. The…

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse inscribed in a rhombus.

Rhombus Circumscribed About an Ellipse

Illustration of a rhombus circumscribed about an ellipse. This could also be described as an ellipse…

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

16 Rotated Concentric Ellipses

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

8 Rotated Concentric Ellipses

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals of 45°. The ellipses are externally tangent to the circle in which they are inscribed.

4 Rotated Concentric Ellipses

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses are externally tangent to the circle in which they are inscribed.

2 Rotated Concentric Ellipses

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses…

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal to the length of the major axis of the ellipse. The ellipse is externally tangent to the circle.

Ellipse Inscribed In A Circle

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal…

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments, are externally tangent to the circle. The illustration could be used as a 3-dimensional drawing of a sphere.

2 Ellipses Inscribed In A Circle

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration showing the definition of an ellipse as a conic section. The section of a right circular cone made by a plane that cuts all the elements of the surface of the cone is an ellipse. The plane is neither parallel nor perpendicular to the axis.

Conic Section Showing An Ellipse

Illustration showing the definition of an ellipse as a conic section. The section of a right circular…

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where the circle intersects the line at D and B, place pins. These pins represent the foci of the ellipse. Use a cord and a pencil to draw the ellipse as shown in figure 60. This illustrates the definition of an ellipse.

Construction Of An Ellipse

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where…

An illustration showing the intersection of a plane and a cone. The cone is intersected by a plane neither parallel to nor perpendicular to the base, nor parallel to a side. Thus forming an ellipse.

Conic Section Showing An Ellipse

An illustration showing the intersection of a plane and a cone. The cone is intersected by a plane neither…

An illustration showing an oval.

Oval

An illustration showing an oval.

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide OA and OB each into three equal parts; draw the quadrant AC. From C, draw the line Cc through the point 1. Through the points 2 draw de at an angle of 45° with the major axis. Then 2 is the center for the ends of the ellipse; e is the center for the arc dc; and C is the center for the arc cf."

Construction Of An Isometric Ellipse

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide…

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles with diameters equal to the long and short axes of the desired ellipse. Draw from o any number of radii, A, B, etc. Draw a line Bb' parallel to n and bb' parallel to m, then b is a point in the desired ellipse.

Construction Of An Ellipse

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles…

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set off from c half the great axis at a and b, which are the two focuses of the ellipse. Take an endless string as long as the three sides in the triangle abc, fix two pins or nails in the focuses, one in a and one in b, lay the string around a and b, stretch it with a pencil d, which then will describe the desired ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using a string. "Having given the two axes, set…

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three equal parts, draw the two circles, and where they intersect one another are the centers for the tangent arcs of the ellipses as shown by the figure."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three…

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off the short axis from A to b, divide b into three equal parts, set off two of these parts from o towards c and c which are the centers for the ends of the ellipse. Make equilateral triangles on cc, when ee will be the centers for the sides of the ellipse. If the long axis is more than twice the short one, this construction will not make a good ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off…

An illustration showing how to construct an ellipse. Given the two axes, set off half the long axis from c to ff, which will be the two focuses in the ellipse. Divide the long axis into any number of parts, say a to be a division point. Take Aa as radius and f as center and describe a circle arc about b, take aB as radius and f as center describe another circle arc about b, then the intersection b is a point in the ellipse, and so the whole ellipse can be constructed."

Construction Of An Ellipse

An illustration showing how to construct an ellipse. Given the two axes, set off half the long axis…

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a semicircle on AB, draw ordinates in the circle at right angle to AB, the corresponding and equal ordinates for the ellipse to be drawn parallel to the lines, and thus the elliptic curve is obtained as shown by the figure."

Construction Of An Ellipse Tangent To Two Parallel Lines

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a…

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Labeled shapes showing various measures of form.

Measures of Form

Labeled shapes showing various measures of form.

Illustration showing an ellipse formed by the intersection of the surface of a cone with a plane neither parallel nor perpendicular to a straight line of the surface of the cone nor the axis.

Ellipse

Illustration showing an ellipse formed by the intersection of the surface of a cone with a plane neither…

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve and two radii to its extremities from the center. Thus, in the figure, CDB is a sector of a circle." -Whitney, 1911

Sector

"In geometry: (a) A plane figure inclosed between the arc of a circle, ellipse, or other central curve…

"Ground Plan of the Colosseum at Rome, with representation of the Tiers of Seats, and of the Substructure. The shape of the amphitheatre was borrowed from that of the theatre. Since no stage was necessary, and with a view to securing as many rows of seats as possible, the semicircular form of the theatre was done away with, and the whole became a circle, or rather an ellipse, which was afterwards the recognized shape for all buildings of this nature, whether at Rome or in the provinces."

Ground Plan of the Colosseum

"Ground Plan of the Colosseum at Rome, with representation of the Tiers of Seats, and of the Substructure.…

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate end, B, of the transverse axis, called the eccentric angle of the point H." -Whitney, 1911

Eccentric Angle

"In geometry, an angle connected with an ellipse and defined as ... angle BCL, reckoned from one determinate…

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that the distance between the axes O<SUB>1</SUB> and O<SUB>2</SUB> is equal to the major axis of the ellipses, we shall find that they will be in contact on the line of centres and that the rolling arcs are of equal length."

Rolling of Equal Ellipses

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that…

Illustration used to show how to draw an egg-shaped oval when given the diameters.

Construction Of Oval

Illustration used to show how to draw an egg-shaped oval when given the diameters.

Illustration used to show how to draw an ellipse when given the diameters.

Construction Of Ellipse

Illustration used to show how to draw an ellipse when given the diameters.

Illustration used to show how to draw an ellipse by circular arcs.

Construction Of Ellipse

Illustration used to show how to draw an ellipse by circular arcs.

Illustration of a cylinder cut by a plane making an angle of 57&deg; with the base.

Plane Intersecting A Cylinder

Illustration of a cylinder cut by a plane making an angle of 57° with the base.

Illustration of a cone cut by a plane that is not parallel to the base and does not intersect the base.

Conic Section Ellipse

Illustration of a cone cut by a plane that is not parallel to the base and does not intersect the base.

An elliptical shape of a shield or escutcheon in heraldry.

Elliptical Shield

An elliptical shape of a shield or escutcheon in heraldry.

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Cone depicting Conic Sections

Diagram of a cone with spheres and cut by a plane to depict the conic sections.

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle, ellipse.

Cone depicting Conic Sections

Diagram of a cone with inscribed spheres and cut by various planes to depict the conic sections: circle,…

Diagram of an ellipse that can used to illustrate the definition. "The constant ration between the distances of a point on an ellipse from the focus and the directrix equals the linear eccentricity divided by the semi major axis."

Definition of Ellipse

Diagram of an ellipse that can used to illustrate the definition. "The constant ration between the distances…

Diagram of an ellipse that can used to illustrate the different parts. Segment MN is the major axis, segment CD is the conjugate (minor) axis, and point O is the center of the ellipse. Both foci are also labeled in the illustration.

Parts of Ellipse

Diagram of an ellipse that can used to illustrate the different parts. Segment MN is the major axis,…

Diagram that illustrates "The algebraic sum of the distances of any point from the foci of a conic is greater or less than 2a, according as the point is without or within the curve."

Foci Distances on an Ellipse

Diagram that illustrates "The algebraic sum of the distances of any point from the foci of a conic is…

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…

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis (2a).

Construction of an Ellipse

Diagram showing how to construct an ellipse when given the two foci and the length of the major axis…

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis (2a).

Construction of a Hyperbola

Diagram showing how to construct a hyperbola when given the two foci and the length of the major axis…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus is outside the circle, we get a hyperbola. If it's inside the circle, we get an ellipse. If the auxiliary circle is a straight line (radius is infinite), we get a parabola.

Construction of a Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. If the focus…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is on the left of the auxiliary circle, thus producing a very obtuse hyperbola.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. The focus is…

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus moves inside the circle the ellipse broadens out until the focus reaches the center and becomes a circle.

Focus In Auxiliary Circle of Conic

Diagram showing how to construct a conic when given the focus and the auxiliary circle. As the focus…

Illustration used to draw a an ellipse using string and pins.

Construction of Ellipse Using String

Illustration used to draw a an ellipse using string and pins.

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters equal to the minor and major axes of the ellipse.

Construction of Ellipse by Describing Circles

Illustration used to draw a an ellipse using string and pins by describing a circles with diameters…

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Construction of Ellipse

Illustration used to draw a an ellipse with major axis AB and minor axis CD.

Color flag of Guam. Territorial flag is dark blue with a narrow red border on all four sides; centered is a red-bordered, pointed, vertical ellipse containing a beach scene, outrigger canoe with sail, and a palm tree with the word GUAM superimposed in bold red letters; US flag is the national flag.

Flag of Guam, 2009

Color flag of Guam. Territorial flag is dark blue with a narrow red border on all four sides; centered…

Black and white outline flag of Guam. Territorial flag is dark blue with a narrow red border on all four sides; centered is a red-bordered, pointed, vertical ellipse containing a beach scene, outrigger canoe with sail, and a palm tree with the word GUAM superimposed in bold red letters; US flag is the national flag

Flag of Guam, 2009

Black and white outline flag of Guam. Territorial flag is dark blue with a narrow red border on all…

Oval with dotted vertical and horizontal lines that are lines of symmetry.

Lines of Symmetry, Oval With

Oval with dotted vertical and horizontal lines that are lines of symmetry.

An ellipse French curve, or irregular curve, is used to draw short elliptical radius curves by using points.

Ellipse Curve French Curves

An ellipse French curve, or irregular curve, is used to draw short elliptical radius curves by using…

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing characteristics of each shape.

Conic Section Using Ellipse

The cone is sliced by a ellipse by making an angle within the plane. This can be drawn with knowing…

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines will determine the points on the curve.

Determining Points on Ellipse Using Circles

Using C as a center, draw two circles with different diameters. The intersection of the diameter lines…