This mathematics ClipArt gallery offers 48 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 the periodic center of motion as it often happens when two positions of a line are known and they are moving in the same plane and we wish to find an axis about which this line could revolve to occupy the two given positions.

Periodic Center of Motion

Illustration showing the periodic center of motion as it often happens when two positions of a line…

Aronhold stated if any three bodies have plane motion their three virtual centers are three points on one straight line

Centrodes

Aronhold stated if any three bodies have plane motion their three virtual centers are three points on…

Illustration showing a centroid, "the curve passing through the successive positions of the instantaneous centre of a body having a combined motion of rotation and translation is called a centroid." A smooth curve passes through the successive positions of the instantaneous centers (all the centers marked o)will be the centroid ab.

Centroid

Illustration showing a centroid, "the curve passing through the successive positions of the instantaneous…

Intersection of lines between a circle and its polar point.

Circle Polar Point

Intersection of lines between a circle and its polar point.

Illustration showing complex numbers with a modulus equal to unity. The lines representing these numbers terminate in points lying on the circumference of a circle whose radius is unity.

Geometric Inspection of Complex Numbers

Illustration showing complex numbers with a modulus equal to unity. The lines representing these numbers…

Illustration showing a conchoid, "a curve, shell-like in flexure (whence the name), invented by Nicomedes in the 2nd century B.C., and used by him for finding two mean proportionals."

Conchoid

Illustration showing a conchoid, "a curve, shell-like in flexure (whence the name), invented by Nicomedes…

Instantaneous axis of two cones, each with angular velocity

Conic Motion

Instantaneous axis of two cones, each with angular velocity

Illustration showing conchoidal curves.

Conchoidal Curves

Illustration showing conchoidal curves.

Illustration showing conchoidal curves.

Conchoidal Curves

Illustration showing conchoidal curves.

Illustration showing confocal curves.

Confocal Curves

Illustration showing confocal curves.

Illustration showing equilateral curves.

Equilateral Curves

Illustration showing equilateral curves.

"Since these curves are not closed, one pair cannot be used for continuous motion; but a pair of such curves may be well adapted to sectional wheels requiring a varying angular velocity." This figure shows an example of the process.

Motion of Open Curves

"Since these curves are not closed, one pair cannot be used for continuous motion; but a pair of such…

Illustration showing Pascal's Volute curves.

Pascal's Volute Curves

Illustration showing Pascal's Volute curves.

Illustration showing trajectory curves.

Trajectory Curves

Illustration showing trajectory curves.

Illustration showing a cycloid curve. "The curve generated by a point in the plane of a circle when the circle is rolled along a straight line and always in the same plane."

Cycloid

Illustration showing a cycloid curve. "The curve generated by a point in the plane of a circle when…

Illustration showing a cycloid curve. "The curve generated by a point in the plane of a circle when the circle is rolled along a straight line and always in the same plane."

Cycloid

Illustration showing a cycloid curve. "The curve generated by a point in the plane of a circle when…

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle and base line C into a number of equal parts, draw through the division point the ordinates and abscissas, make aa' = 1d, bb' = 2'e, cc = 3f, then ab' and c' are points in the cycloid. In the Epicycloid and Hypocycloid the abscissas are circles and the ordinates are radii to one common center."

Construction Of A Cycloid

An illustration showing how to construct a cycloid. "The circumference C=3.14D. Divide the rolling circle…

Illustration showing cycloid curves. "The curve generated by a point in the plane of a circle when the circle is rolled along a straight line and always in the same plane."

Cycloids

Illustration showing cycloid curves. "The curve generated by a point in the plane of a circle when the…

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…

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and radius r. Divide the angle v into a number of equal parts, draw the radii and tangents for each part, divide the pitch p into an equal number of equal parts, then the first tangent will be one part, second two parts, third three parts, etc., and so the Evolute is traced."

Construction Of An Evolute Of A Circle

An illustration showing how to construct an evolute of a circle. "Given the pitch p, the angle v, and…

"Folium of Descartes, with its asymptote. The equation is (4-y)(y-1)<sup>2</sup> = 3x<sup>2</sup>y ... In geometry, a plane cubic curve having a crunode, and one real inflexion, which lies at infinity.

Folium of Descartes

"Folium of Descartes, with its asymptote. The equation is (4-y)(y-1)2 = 3x2y ... In geometry, a plane…

Generating a hyperbola from two equal and parallel circular disks.

Generate Hyperbola

Generating a hyperbola from two equal and parallel circular disks.

Three dimensional representation of a variable hyperbola moving parallel to itself along the parabolas as directrices.

Hyperbolic Parabaloid

Three dimensional representation of a variable hyperbola moving parallel to itself along the parabolas…

Two dimensional representation of variable hyperbola moving parallel to itself along the parabolas as directrices.

Hyperbolic Parabaloid

Two dimensional representation of variable hyperbola moving parallel to itself along the parabolas as…

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale measurements the same as any ordinary drawing, and gives a clear representation of the object. It is easily learned. All horizontal rectangular lines are drawn at an angle of 30&deg;. All circles are ellipses of proportion, as shown."

Construction Using Isometric Perspective

An illustration showing how to use isometric perspective. "This kind of perspective admits of scale…

The aggregate of the components of momentum.

Components of Momentum

The aggregate of the components of momentum.

Illustration showing two points a and b to be in the same plane and parallel.

Motions Of 2 Points In Same Plane And Parallel

Illustration showing two points a and b to be in the same plane and parallel.

Illustration showing two points a and b to be in the same plane and parallel.

Motions Of 2 Points In Same Plane And Parallel

Illustration showing two points a and b to be in the same plane and parallel.

Illustration showing three points a, b, and c in motion. The magnitude and direction of a and b are used to find the l.v. of c.

Motions Of 3 Points

Illustration showing three points a, b, and c in motion. The magnitude and direction of a and b are…

Illustration used "If three component motions ab, ac, and ad are combined, their resultant af will be the diagonal of the parallelopiped of which they are the edges."

Parallelopiped of Motions

Illustration used "If three component motions ab, ac, and ad are combined, their resultant af will be…

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.

Illustration showing a Cassinian Oval.

Cassinian Oval

Illustration showing a Cassinian Oval.

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.

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…

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…