ClipArt ETC
A blank banner with a circle focal point.

Blank Banner

A blank banner with a circle focal point.

A blank banner with a circle focal point.

Blank Banner

A blank banner with a circle focal point.

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped rulers, called irregular curves. A series of points is first determined through which the curved line is to pass. The line is then drawn through these points by using such parts of the irregular curve as will pass through several of the points at once, the curve being shifted from time to time as required." — Hallock, 1905

Irregular Curves

"Curves other than arcs of circles are drawn with the pencil or ruling pen by means of curved or irregular-shaped…

"The pennies of the Saxon and Danish sole monarches of England had a portrait on them. Alfred's earlier coins have a grotesque-looking portrait, and on the reverse a monogram of London; in his later coins the head disappears, and a cross and circle take its place." — Chambers, 1881

English Coin

"The pennies of the Saxon and Danish sole monarches of England had a portrait on them. Alfred's earlier…

"Three principal parts, the card, the needle on its lower suface, and the case. The whole is enclosed in the compass-box, or binnacle. the term compass is said to have been applied to the instrument because the card involves or compasses the whole plane of the horizon, or because the needle indicates the whole circle of possible variations of direction. The surface of the card is divided by radiating lines into 32 parts, each containing 11 degrees." — Encyclopedia Britannica, 1893

Compass Card

"Three principal parts, the card, the needle on its lower suface, and the case. The whole is enclosed…

A cross bound by a circle.

Bound Cross

A cross bound by a circle.

"The coil is of flat, rectangular shape, with a narrow central opening just large enough to allow one of the magnets of the astatic system to swing freely. The other magnet swings over a graduated circle placed on the top of the coil, and serves also as an index. Sometimes a mirror and scale are substituted for the index and graduated circle. The sole on which the coil stands is movable on a fixed piece which can be levelled by means of three screws." &mdash Encyclopedia Britannica, 1893

Astatic Multiplier

"The coil is of flat, rectangular shape, with a narrow central opening just large enough to allow one…

"An altazimuth theodolite of an improved pattern now used on the Ordnance Survey. The horizontal circle of 14 inches diameter is read by three micrometer microscopes; the vertical circle has a diameter of 12 inches, and is read by two microscopes." — Encyclopedia Britannica, 1893

Altazimuth Theodolite

"An altazimuth theodolite of an improved pattern now used on the Ordnance Survey. The horizontal circle…

"The instrument is supported on a strong tripod, fitted with levelling screws; to this tripod is fixed the azimuth circle and a long vertical steel axis. Fitting on this axis is a hollow axis which carries on its uper end a short transverse horizontal axis. This latter carries the telescope, which, supported at the center of its length, is free to rotate in a vertical plane. The telescope is thus mounted excentrically with respect to the vertical axis around which it revolves." — Encyclopedia Britannica, 1893

Zenith Telescope

"The instrument is supported on a strong tripod, fitted with levelling screws; to this tripod is fixed…

"The plate A is 46 inches in diameter, and is composed of gun metal. These were put on by original graduation, mainly on the plan of Edward Troughton. One very great improvement in this engine is that the axis B is tubular, as seen at C. The object of this hollow is to receive the axis of the circle to be divided, so that it can be fixed flat to the plate by the clamps E, without having first to be detached from the axis and other parts to which it has already been carefully fitted. This obviates the necessity for resetting, which can hardly be done without some error. D is the tangent screw, and F the flame carrying it, which turns on carefully polished steel pivots. The screw is pressed against the edge of the plate by a spiral spring acting under the lever G, and by screwing the lever down the screw can be altogether removed from contact with the plate." — Encyclopedia Britannica, 1893

Dividing Engine

"The plate A is 46 inches in diameter, and is composed of gun metal. These were put on by original graduation,…

"Upon a tripod provided with levelling screws stands the pillar P, to which is fixed the graduated azimuthal circle CC. The compass box B, with the vernier V, attached to it, moves on the azimuthal circle by means of a pivot at the pillar P. Two uprights, U, U, are fixed to the side of the compass-box, on the tops of which rests the axis of the telescope T. A graduated are A, is fixed to the bottom of one of the uprights, and the angle of elevation of the telescope is marked by the vernier on the arm E, attached to the axis of the telescope. A level, L, is also hung on the axis of the telescope, for adjusting the instrument. Inside the compass-box is another graduated circle, F, the line joining the zero-points of which is parallel to the axis of the telescope. All the fittings are in brass or copper, iron, of course, being unsuitable." — Chambers' Encyclopedia, 1875

Declinometer

"Upon a tripod provided with levelling screws stands the pillar P, to which is fixed the graduated azimuthal…

"In order to produce, on the catoptric system, a fixed light showing all round the circle, a number of reflectors are fixed round the outside of a stationary chandelier n. As the ordinary paraboloid has about 14 degrees of divergence, twenty-five reflectors were needed to light up continuously (though not equally) the whole horizon." —The Encyclopedia Britannica, 1910

Revolving Light

"In order to produce, on the catoptric system, a fixed light showing all round the circle, a number…

"The whole length of the tube of the wheel barometer, from C to A, is 34 or 35 inches, and it is filled with mercury, as usual. The mercury rises in the short leg to the point a, where there is a small piece of glass floating on its surface, to which there is attached a silk string, passing over the pulley p. To the axis of the pulley is fixed an index, or hand, and behind this is a graduated circle, as seen in the figure. It is obvious, that a very slight variation in the height of the mercury at o, will be indicated by a considerable motion of the index, and thus changes in the weight of the atmosphere, hardly perceptible by the common barometer, will become quite apparent by this." —Comstock, 1850

Wheel Barometer

"The whole length of the tube of the wheel barometer, from C to A, is 34 or 35 inches, and it is filled…

"The following description of a section of Lord Rosse's telescope, though not so perfect as could be desired, is the best we could obtain. it exhibits a view of the inside of the eastern wall, with the tube, and machinery by which it is moved. A is the mason-work on the ground; B the universal joint, which allows the tube to turn in all directions; C the speculum in the tube; E the eye-piece through which the observer looks; F a pulley by which the tube is moved; H a chain attached to the pulley, and to the side of the tube; I, a chain running to K, the counterpoise; L, a lever connecting the chain M with the tube; Z another chain which passes from the upper part of the tube over a pulley at W, (not seen) and crosses to the opposite wall; X a railroad on which the speculum is drawn either to or from the tube. The dotted line H, shows the course of the weight R, as the tube rises or falls. The tube is moved from wall to wall by a ratchet wheel at R, which is turned by the lever O, on the circle N, the ends of which are fixed in the two walls." —Comstock, 1850

Telescope

"The following description of a section of Lord Rosse's telescope, though not so perfect as could be…

"The twelve signs of the zodiac, together with the Sun, and the Earth revolving around him. When the Earth is at A, the Sun will appear to be just entering the sign Aries, because then, when seen from the Earth, he ranges towards certain stars at the beginning of that constellation. When the Earth is at C, the Sun will appear in the opposite part of the heavens, and therefore in the beginning of Libra. The middle line, dividing the circle of the zodiac into equal parts, is the line of the ecliptic." —Comstock, 1850

Zodiac Signs

"The twelve signs of the zodiac, together with the Sun, and the Earth revolving around him. When the…

"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.…

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the days and nights to differ at the same place at different seasons of the year, for on reviewing the positions of the globe at A, it will be observed that the line formed by the enlightened and dark hemispheres, does not coincide with the line of the axis and the pole, but that the line formed by the darkness and the light, extends obliquely across the line of the Earth's axis, so that the north pole is in the light while the south is in the dark. In the position A, therefore, an observer at the north pole would see the sun constantly, while another at the south pole would not see it at all. Hence those living in the north temperate zone, at the season of the year when the earth is at A, or in the Summer, would have long days and short nights, in proportion as they approached the polar circle; while those who live in the south temperate zone, at the same time, and when it would be Winter there, would have long nights and short days in the same proportion." —Comstock, 1850

Earth Axis

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the…

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the days and nights to differ at the same place at different seasons of the year, for on reviewing the positions of the globe at A, it will be observed that the line formed by the enlightened and dark hemispheres, does not coincide with the line of the axis and the pole, but that the line formed by the darkness and the light, extends obliquely across the line of the Earth's axis, so that the north pole is in the light while the south is in the dark. In the position A, therefore, an observer at the north pole would see the sun constantly, while another at the south pole would not see it at all. Hence those living in the north temperate zone, at the season of the year when the earth is at A, or in the Summer, would have long days and short nights, in proportion as they approached the polar circle; while those who live in the south temperate zone, at the same time, and when it would be Winter there, would have long nights and short days in the same proportion." —Comstock, 1850

Earth Axis

"Now it is the inclination of the Earth's axis, as above described, which causes the lengths of the…

"Suppose the Earth to be in her Summer solstice, which takes place on the 21st of June. At this period she will be at a, having her north pole, n, so inclined towards the Sun, that the whole arctic circle will be illuminated, and consequently the Sun's rays will extend 23.25 degrees, the breadth of the polar circle, beyond the north pole." —Comstock, 1850

Seasons

"Suppose the Earth to be in her Summer solstice, which takes place on the 21st of June. At this period…

"Let S be the Sun, E the Earth, and A, B, C, D, F, the Moon in different parts of her orbit. Now when the Moon changes, or is in conjunction with the Sun, as at A, her dark side is turned towards the Earth, and she is invisible, as represented at a. The Sun always shines on one half of the Moon, in every direction, as represented at A and B, on the inner circle; but we at the Earth can see only such portions of the enlightened part as are turned towards us. After her change, when she has moved from A to B, a small part of her illuminated side comes in sight, and she appears horned, as at b, and is then called the new Moon. When she arrives at C, severel days afterwards, one half of her disc is visible, and she appears as at c, her appearance being the same in both circles. At this point she is said to be in her first quarter, because she has passed through a quarter of her orbit, and is 90 degrees from the place of her conjunction with the Sun. At D, she shows us still more of her enlightened side, and is then said to appear gibbous as at d. When she comes to F, her whole enlightened side is turned towards the Earth, and she appears in all the spendor of a full Moon." —Comstock, 1850

Moon Phases

"Let S be the Sun, E the Earth, and A, B, C, D, F, the Moon in different parts of her orbit. Now when…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis the telescope it gives only one image of the object. In a direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the grduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed." —The Encyclopedia Britannica, 1903

Micrometer

"a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to…

A Great Circle is one which would be formed on the earth's surface by a plane passing through the earth's centre, hence dividing it into two equal parts. All great circles, therefore, divide the earth into two hemispheres.

Great Circle

A Great Circle is one which would be formed on the earth's surface by a plane passing through the earth's…

A small circle is one formed by a plane which does not cut the earth into two equal parts. The small circles are the <em>parallels</em>.

Small Circle

A small circle is one formed by a plane which does not cut the earth into two equal parts. The small…

The Meridian of any given place is that half of the meridian circle which passes through that place and both poles. A meridian of any place reaches from that place to both poles, and therefore is equal to one-half of a great circle, and, with the meridian directly opposite to it, forms a great circle called a meridian circle. There are as many meridians as there are places on the equator or on any parallel. Parallels are small circles which pass around the earth parallel to the equator.

Meridians and Parallels

The Meridian of any given place is that half of the meridian circle which passes through that place…

Diagram of flower of Trillium. In this, as in all such diagrams of cross-section of blossoms, the parts of the outer circle represent the calyx; the next, corolla; within, stames (here in two circles of three each, and the cross-section is through the anthers); in the centre, section of three ovaries joined into a compound one of three cells.

Trillium

Diagram of flower of Trillium. In this, as in all such diagrams of cross-section of blossoms, the parts…

Horsetail, view of under side of the shield-shaped body, bearing a circle of spore-cases.

Horsetail

Horsetail, view of under side of the shield-shaped body, bearing a circle of spore-cases.

If every diameter is perpendicular to its conjugate, the conic is a circle.

Circle Diameters

If every diameter is perpendicular to its conjugate, the conic is a circle.

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the curve vertices of the conic.

Conic Axes

Conjugate diameters perpendicular to each other are called, axes, and the points where they cut the…

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…

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.

Intersection of lines between a circle and its polar point.

Circle Polar Point

Intersection of lines between a circle and its polar point.

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.

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.

Generating a hyperbola from two equal and parallel circular disks.

Generate Hyperbola

Generating a hyperbola from two equal and parallel circular disks.

The goniometer is an instrument for measuring the angles of crystals. Nicolaus Stena in 1669 determined the interfacial angles of quartz crystals by cutting sections perpendicular to the edges, he plane angles of the sections being then the angles between faces which are perpendicular to the sections.

Horizontal-Circle Goniometer

The goniometer is an instrument for measuring the angles of crystals. Nicolaus Stena in 1669 determined…

The goniometer is an instrument for measuring the angles of crystals. Nicolaus Stena in 1669 determined the interfacial angles of quartz crystals by cutting sections perpendicular to the edges, he plane angles of the sections being then the angles between faces which are perpendicular to the sections.

Vertical Circle Goniometer

The goniometer is an instrument for measuring the angles of crystals. Nicolaus Stena in 1669 determined…

The magic circle of circles, first developed by Benjamin Franklin, consists of eight annular rings and a central circle, each ring being divided into eight cells by radii drawn from the centre; there are therefore 65 cells. The number 12 is placed in he center and the consecutive numbers 13 to 75 are placed in the other cells. The properties are: 1) sum of eight numbers in any ring with 2 equals 360, 2) sum of eight numbers in any set of radial rings with 12 is 360, 3) sum of numbers in any four adjoining cells is 180.

Magic Circle of Circles

The magic circle of circles, first developed by Benjamin Franklin, consists of eight annular rings and…

Three suspended concentric circles free to move independently of each other at right angles.

Gyroscope

Three suspended concentric circles free to move independently of each other at right angles.

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

Pulley

Pair of circular pulleys connected b a cord, showing the range of motion as arcs

Theory of static equilibrium of mechanism, illustrated b Sir A.B.W. Kennedy.

Wheel Mechanism

Theory of static equilibrium of mechanism, illustrated b Sir A.B.W. Kennedy.

Different compasses used in mechanical drawing.

Compasses

Different compasses used in mechanical drawing.

The use of a compass in drawing perfect circles

Compass Use

The use of a compass in drawing perfect circles

Circles should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

Drawing Lines 4

Circles should be unshaded or shaded evenly with thick and thin lines, changing at about 45 degrees.

Draftsman's method to draw a tangent, AB, to a circle

Tangent To A Circle

Draftsman's method to draw a tangent, AB, to a circle

Six equal circles tangent to each other and to the sides of the triangle

Circle Triangle Tangents

Six equal circles tangent to each other and to the sides of the triangle

Equal circles inside and tangent to the outside circle, also tangent to each other

Circle to Circle Tangents

Equal circles inside and tangent to the outside circle, also tangent to each other

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,…

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"&mdash;Finley, 1917

Shaft lining

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"—Finley,…

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"&mdash;Finley, 1917

Shaft lining

"Until hard rock is reached the sides of the excavation are supported temporarily by a lining"—Finley,…

A spiral of Archimedes.

Archimedes spiral

A spiral of Archimedes.

"Suppose a cannon ball, tied with a string to the centre of a slab of smooth marble, and suppose an attempt be made to push this ball with the hand in the direction of b; it is obvious that the string would prevent its going to that point; but would keep it in thei circle. n this case, the string is the centripedal force." -Comstock 1850

Centrifugal Force

"Suppose a cannon ball, tied with a string to the centre of a slab of smooth marble, and suppose an…

"In a circle, sound is reflected from every plane surface placed around it, and hence, if the sound is emitted from the centre of a circle, this centre will be the point at which the echo will be most distinct." -Comstock 1850

Sound Reflection in a Circle

"In a circle, sound is reflected from every plane surface placed around it, and hence, if the sound…

"If the whole circle be considered the circumfrence of a sphere, of which the plano-convex lens b, a, is a section, then the focus of parallel rays, or the principal focus, will be at the opposite side of the sphere, or at c." -Comstock 1850

Plano Convex Lens

"If the whole circle be considered the circumfrence of a sphere, of which the plano-convex lens b, a,…

"Were the Earth's orbit a perfect circle, and her axis perpendicular to the plane of this orbit, the days would be of a uniform length, and there would be no difference between the clock and the Sun." -Comstock 1850

Suns in the Equator and Ecliptic

"Were the Earth's orbit a perfect circle, and her axis perpendicular to the plane of this orbit, the…

"If we take for example, a slip of zinc, and another of copper, and place the in a cup of diluted sulphuric acid, their upper ends in tontact, and above the water, and their lower ends separated, then there will be constituted a galvanic circle, of the simplest form, consisting of three elements, zinc, acid, copper." -Comstock 1850

Galvanic Battery

"If we take for example, a slip of zinc, and another of copper, and place the in a cup of diluted sulphuric…

"The instant this is done and the galvanic circle completed, the needle will deviate from its north and south position, turning towards the east or west, according to the direction in which the galvanic circle flows." -Comstock 1850

Uniting Wire above the Needle

"The instant this is done and the galvanic circle completed, the needle will deviate from its north…

"The power is generally applied by a wheel or a lever, and moves through the circumfrence of a circle. The distance between the two consecutive turns of any on continuous thread, measured in the direction of the axis of the screw, is called the pitch of the screw." -Avery 1895

Screw with Lever Arm

"The power is generally applied by a wheel or a lever, and moves through the circumfrence of a circle.…

"A cone is a solid whose base is a circle and whose convex surface tapers uniformly to a point." &mdash;Hallock 1905

Cone

"A cone is a solid whose base is a circle and whose convex surface tapers uniformly to a point." —Hallock…