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A gyroscope that is rotated to form an ellipse.

Gyroscope

A gyroscope that is rotated to form an ellipse.

Conic sections, cones divided by a plane.

Conic Sections

Conic sections, cones divided by a plane.

"Rear admiral Stringham, born in Middletown, Orange County, N. Y., November 7th, 1798; died in brooklyn, N. Y., February 7th, 1876. He entered the Navy as a midshipman, November 15, 1809, and was in continuous service up to the breaking out of the Civil War in 1861, when he was summoned to Washington to advise upon the preparations for war. He took command of the North Atlantic Blockading Fleet, and planned the expedition to Hatteras Inlet. General Butler accompanied him with 900 men. The squadron bombarded the forts, sailing in an ellipse, by which means it concentrated its fire on the forts, and manoeuvred so skillfully that none of the fleet were hit. Both forts surrendered, and the troops were landed to garrison them on August 29th, 1861. Not one of the Federal troops was injured. This was the first naval victory of any importance. Stringham declined further active service on account of his age, and was retired as a commodore, December 21st, 1861. He was promoted to rear admiral on the retired list, July 16th, 1862."— Frank Leslie, 1896

Admiral Silas H. Stringham

"Rear admiral Stringham, born in Middletown, Orange County, N. Y., November 7th, 1798; died in brooklyn,…

"The elliptical circle being supposed to be the Earth's orbit, with the Sun, S, in one of the foci. Now the spaces, 1, 2, 3, etc., though of different shapes, are of the same dimensions, or contain the same quantity of surface. The Earth, we have already seen, in its journey round the Sun, describes an ellipse, and moves more rapidly in one part of its orbit than in another. But whatever may be its actual velocity, its comparative motion is through equal areas in equal times. Thus its center passes from E to C, and from C to A, in the same period of time, and so of all the other divisions marked in the figure." —Comstock, 1850

Elliptical Orbit

"The elliptical circle being supposed to be the Earth's orbit, with the Sun, S, in one of the foci.…

Every elliptical involution has the property that there are two definite points in the plane from which any two conjugate points are seen under a right angle.

Circular Involution

Every elliptical involution has the property that there are two definite points in the plane from which…

The lines which join corresponding points in an involution on a conic all pass through a fixed point; and reciprocally, the points of intersection of conjugate lines in an involution among tangents to a conic lie on a line.

Conic Involution

The lines which join corresponding points in an involution on a conic all pass through a fixed point;…

The lines joining any point on a conic to the two foci are equally inclined to the tangent and normal at that point. This is an ellipse.

Conic Foci Involution

The lines joining any point on a conic to the two foci are equally inclined to the tangent and normal…

One of the three species of conic sections is the ellipse.

Ellipse

One of the three species of conic sections is the ellipse.

the octant of the wave surface cuts each coordinate plane in a circle and an ellipse.

Octant of Wave Surface

the octant of the wave surface cuts each coordinate plane in a circle and an ellipse.

Each section is an ellipse. The surface is generated by an ellipse moving parallel to itself along two ellipses as directices.

Ellipsoid

Each section is an ellipse. The surface is generated by an ellipse moving parallel to itself along two…

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 2D

Two dimensional view of the cuts required to create the conic sections hyperbola, parabola, ellipse,…

Three dimensional representation of the intersecting planes required to create the conic sections hyperbola, parabola, ellipse, and circle.

Conic Sections 3D

Three dimensional representation of the intersecting planes required to create the conic sections hyperbola,…

Draftsman's first method for creating an ellipse

Ellipse First Method

Draftsman's first method for creating an ellipse

Draftsman's second method for drawing an ellipse

Ellipse Second Method

Draftsman's second method for drawing an ellipse

Draftsman's third method for drawing an ellipse

Ellipse Third Method

Draftsman's third method for drawing an ellipse

Draftsman's fourth method for drawing an ellipse, case 1

Ellipse Fourth Method Case 1

Draftsman's fourth method for drawing an ellipse, case 1

Draftsman's fourth method for drawing an ellipse, case 2

Ellipse Fourth Method Case 2

Draftsman's fourth method for drawing an ellipse, case 2

Draftsman's fourth method for drawing an ellipse, case 3

Ellipse Fourth Method Case 3

Draftsman's fourth method for drawing an ellipse, case 3

Draftsman's fifth method for drawing an ellipse

Ellipse Fifth Method

Draftsman's fifth method for drawing an ellipse

"It is apparent that the auditor, in this case, must be placed in the centre from which the sound proceeds, to receive the greatest effect. But if the shape of the room be elliptical, the sound may be made in one part, and the echo will be heard in another part, because the ellipse has two points, called foci, at one of which, the sound being produced, it will be concentrated at the other." -Comstock 1850

Whispering Gallery

"It is apparent that the auditor, in this case, must be placed in the centre from which the sound proceeds,…

Illustration of ellipse with parts labeled.

Ellipse With Parts Labeled

Illustration of ellipse with parts labeled.

Illustration of a ellipse with squares drawn to demonstrate area.

Area of Ellipse

Illustration of a ellipse with squares drawn to demonstrate area.

A graph of tan ellipse with Foci and Center.

Graph of Ellipse with Foci and Center Labeled

A graph of tan ellipse with Foci and Center.

Second layer of muscles of the back. Labels: 1, trapezius; 2, a portion of the ten dinous ellipse formed by the trapezius on both sides; 3, spine of scapula; 4, latissimus dorsi; 5, deltoid; 6, infra-spinatus and teres minor; 7, external oblique; 8, gluteus medius; 9, gluteus magnus; 10, levator scapulae; 11, rhomboideus minor; 12, rhomboideus major; 13, splenius capitis; 14, splenius colli; 15, portion of origin of latissimus dorsi; 16, serratus inferior posticus; 17, supra-spinatus; 18, infra-spinatus; 19, teres minor; 20, teres major; 21, long head of triceps extensor cubiti; 22, serratus major anticus; 23, internal oblique.

Muscles of the Back

Second layer of muscles of the back. Labels: 1, trapezius; 2, a portion of the ten dinous ellipse formed…

A flashcard featuring an illustration of a Circle

Flashcard of a Circle

A flashcard featuring an illustration of a Circle

A flashcard featuring an illustration of an Ellipse

Flashcard of an Ellipse

A flashcard featuring an illustration of an Ellipse

Illustration showing the definition of an ellipse. "An ellipse is a curve which is the locus of a point that moves in a plane so that the sum of its distances from two fixed points in the plane is constant." The foci and major axis is drawn.

Demonstration of Ellipse Definition

Illustration showing the definition of an ellipse. "An ellipse is a curve which is the locus of a point…

Illustration of an ellipse with foci F' and F, major axis A' to A, minor axis B' to B, and center O.

Ellipse With Parts Labeled

Illustration of an ellipse with foci F' and F, major axis A' to A, minor axis B' to B, and center O.

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. "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 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. 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 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 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 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.

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 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 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 used to show that the area of an ellipse is equal to pi times a times b.

Area of an Ellipse

Illustration of half of an ellipse used to show that the area of an ellipse is equal to pi times a times…

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."

Conic Section Showing an Ellipse

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

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."

Conic Section Showing an Ellipse

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

Illustration showing the definition of an hyperbola as a conic section. "The section of a right circular cone made by a plane that cuts both nappes of the cone is a hyperbola." A double right circular cone with a plane parallel to the axis cutting through the cones.

Conic Section Showing an Hyperbola

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

Illustration of an ellipse with major and minor axes, foci, and points on the ellipse. "An ellipse is a plane figure bounded by a curved line, to any point of which the sum of the distances from two fixed points within, called the foci, is equal to the sum of the distances from the foci to any other point on the curve."

Ellipse

Illustration of an ellipse with major and minor axes, foci, and points on the ellipse. "An ellipse is…

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder greatly inclined to a plane.

Projection of Cylinder

Illustration of the method of finding the projection, in the form of an ellipse, of the top of a cylinder…

Illustration showing the definition of an ellipse as a conic section. The plane cuts the cone obliquely.

Conic Section Showing Ellipse

Illustration showing the definition of an ellipse as a conic section. The plane cuts the cone obliquely.

Illustration showing an ellipse (and circle) as a section from a cylinder.

Section of a Cylinder Showing an Ellipse

Illustration showing an ellipse (and circle) as a section from a cylinder.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of an ellipse.

Ellipse

Illustration of an ellipse.

Illustration of six concentric ellipses.

6 Concentric Ellipses

Illustration of six concentric ellipses.

Illustration of five concentric ellipses.

5 Concentric Ellipses

Illustration of five concentric ellipses.

Illustration of four concentric ellipses.

4 Concentric Ellipses

Illustration of four concentric ellipses.

Illustration of three concentric ellipses.

3 Concentric Ellipses

Illustration of three concentric ellipses.

Illustration of two concentric ellipses.

2 Concentric Ellipses

Illustration of two concentric ellipses.

Illustration of an ellipse with major and minor axes.

Ellipse With Axes

Illustration of an ellipse with major and minor axes.

An illustration of 4 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive 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 3 concentric ellipses that are tangent at the end points of the vertical axes. The horizontal axes (the major axes of the ellipses) decreases in size in each successive ellipse. The major axis equals the minor axis in the smallest ellipse, thus forming a circle.

3 Concentric Ellipses

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

An illustration of 6 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 four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes. The…

An illustration of 6 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 four ellipses and vertical for the innermost ellipse. When the major and minor axes are equal, the result is a circle (as in the fifth ellipse).

6 Concentric Ellipses

An illustration of 6 concentric ellipses that are tangent at the end points of the vertical axes, which…

An illustration of 5 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 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. The…