ClipArt ETC

This mathematics ClipArt gallery offers 87 illustrations of analytical geometry, which is also called coordinate geometry, Cartesian geometry, algebraic geometry, or simply analytic geometry. It is the study of geometry using principles of algebra.

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of two rolling bodies is not a constant, the pitch lines take, the conditions of pure rolling contact should be fulfilled, namely, the point of contact must be on the line of centres, and the rolling arcs must be of equal length.

Rolling of Non-cylindrical Surfaces

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of…

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.

A straight line through the origin of a coordinate plane.

The Origin

A straight line through the origin of a coordinate plane.

Illustration showing a Cassinian Oval.

Cassinian Oval

Illustration showing a Cassinian Oval.

An alternate form of the perpendicular distance method.

Alternate Form, Perpendicular Distance

An alternate form of the perpendicular distance method.

A coordinate planes with the quadrants labeled showing which value (x or y) is positive or negative.

Coordinate Plane

A coordinate planes with the quadrants labeled showing which value (x or y) is positive or negative.

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Coordinate Plane

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Finding the equation of a line drawn through a given point at a given direction.

Given Point

Finding the equation of a line drawn through a given point at a given direction.

Constructing the polar of a given point P with respect to a circle.

Polar of Point

Constructing the polar of a given point P with respect to a circle.

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs of tangents at the extremities of the chords will all lie on a fixed straight line.

Polar Property

If the chords of a circle are drawn through a fixed point, then the points of intersection of the pairs…

Given any three circles, the common chords meet at one point.

Radical Center of 3 Circles

Given any three circles, the common chords meet at one point.

Showing how to find points on a coordinate plane. Also, shows an example of the midpoint formula.

Point Ratio

Showing how to find points on a coordinate plane. Also, shows an example of the midpoint formula.

Illustration "where ad is the given resultant, if the two components have the magnitudes represented by ac and ab, the directions ac and ab would solve the problem, or the direction ac<sub>1</sub> and ab<sub>1</sub> would equally well fulfil (sic) the conditions."

Vector Addition Given Resultant

Illustration "where ad is the given resultant, if the two components have the magnitudes represented…

Illustration used to resolve a motion into two components, one of which is perpendicular, and the other parallel, to a given line, as ef. Vector ad represents the motion; ab = ad cos(dab), the component parallel to ef; and ac = ad sin(dab), the components perpendicular to ef.

Vector Motion Into Two Components - Resultant

Illustration used to resolve a motion into two components, one of which is perpendicular, and the other…

Illustration for rigidly-connected points. "If two points are so connected that their distance apart is invariable and if their velocities are resolved into components at right angles to and along the straight line connecting them, the components along this line of connection must be equal, otherwise the distance between the points would change."

Velocities Of Rigidly-connected Points

Illustration for rigidly-connected points. "If two points are so connected that their distance apart…

Illustration for rigidly-connected points. In the series of links shown, c and d are fixed axes and f slides on the line ff<sub>1</sub>.

Velocities Of Rigidly-connected Points

Illustration for rigidly-connected points. In the series of links shown, c and d are fixed axes and…

Illustration showing a section of the rolling surfaces by a plane perpendicular to their straight line of contact.

Section of Rolling Surfaces

Illustration showing a section of the rolling surfaces by a plane perpendicular to their straight line…

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the shaft, and C1, 2, 3, et., is the center line of the shaft. From o, set off the small distance oa; and set off a1 - R. Set off the same small distance from a to b, and make b2 = R. Continue in the same way with the other points, and the anti-friction curve is thus constructed.

Construction Of Shield's Anti-friction Curve

An illustration showing how to construct Shield's anti-friction curve. "R represents the radius of the…

Any system of coordinate axes to another set which is parallel to the former, but with different origins.

Axes Shift

Any system of coordinate axes to another set which is parallel to the former, but with different origins.

An illustration showing how to construct an arithmetic spiral. "Given the pitch p and angle v, divide them into an equal number of equal parts, say 6; make 01 = 01, 02 = 02, 03 = 03, 04 = 04, 05 = 05, and 06 = the pitch p; then join the points 1, 2, 3, 4, 5 and 6, which will form the spiral required."

Construction Of An Arithmetic Spiral

An illustration showing how to construct an arithmetic spiral. "Given the pitch p and angle v, divide…

The straight line is the simplest type of locus and the simplest first degree equation.

Straight Line

The straight line is the simplest type of locus and the simplest first degree equation.

Illustration showing a tractrix curve.

Tractrix

Illustration showing a tractrix curve.

Transformation of coordinates to new axes.

Transform Coordinates

Transformation of coordinates to new axes.

Illustration showing the motion of translation of two parallel motions.

Motion of Translation

Illustration showing the motion of translation of two parallel motions.

Illustration showing how to find the cubed roots of unity by applying DeMoivre's Theorem.

Cubed Roots of Unity

Illustration showing how to find the cubed roots of unity by applying DeMoivre's Theorem.

Illustration showing how to find the fifth roots of unity by applying DeMoivre's Theorem.

Fifth Roots of Unity

Illustration showing how to find the fifth roots of unity by applying DeMoivre's Theorem.

Illustration showing two component forces ab and ac acting upon point a. The result is the vector ad (the diagonal of the parallelogram).

Vector Addition

Illustration showing two component forces ab and ac acting upon point a. The result is the vector ad…