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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.

This illustrates how to determine the force required to turn a connecting rod of a steam engine.

Connecting Rod of a Steam Engine

This illustrates how to determine the force required to turn a connecting rod of a steam engine.

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,…

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

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

The Human Skeleton. Labels: a, parietal bone; b, frontal; c, cervical vertebrae; d, sternum; e, lumbar vertebrae; f, ulna; g, radius; h, wrist or carpal bones; i, metacarpal bones; k, phalanges; l, tibia; m, fibula; n, tarsal bones; o, metatarsal; p, phalanges; , patella; r, femur; s, haunch (hip) bone; t, humerus; u, clavicle.

The Human Skeleton

The Human Skeleton. Labels: a, parietal bone; b, frontal; c, cervical vertebrae; d, sternum; e, lumbar…

The Ulna and Radius. Labels: 1, radius; 2, ulna; o, olecranon process, on the anterior surface of which are seen the large (gs) and the small (ls) cavities for the reception of the lower end of the humerus and of the head of the radius, respectively; h, head of radius.

The Human Ulna and Radius

The Ulna and Radius. Labels: 1, radius; 2, ulna; o, olecranon process, on the anterior surface of which…

"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…

A section across the forearm a short distance below the elbow-joint. R and U, its two supporting bones, the radius and ulna; e, the epidermis, an d, the dermis, of the skin; the latter is continuous below with bands of connective tissue, s, which penetrate between and invest the muscles (I, 2, 3, 4, etc.); n, n, nerves and vessels.

Section Across the Forearm

A section across the forearm a short distance below the elbow-joint. R and U, its two supporting bones,…

The skeleton of the arm and leg. Labels: H, the humerus; Cd, its articular head which fits into the glenoid fossa of the scapula; U, the ulna; R, the radius; O, the olecranon; Fe, the femur; P, the patella; Fi, the fibula; T, the tibia.

Arm and Leg Skeleton

The skeleton of the arm and leg. Labels: H, the humerus; Cd, its articular head which fits into the…

"Considered as a lever, the fulcrum is at the common axis, while the arms of the lever are the radii of the wheel and of the axle. The usual arrangement is to take ac, the radius of the wheel, as the power arm, and bc , the radius of the axle, as the weight arm." -Avery 1895

Wheel and Axle

"Considered as a lever, the fulcrum is at the common axis, while the arms of the lever are the radii…

"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.…

Demonstration of the movement of a pivot joint. Labels: A, arm in supination (palm uppermost); B, arm in pronation (back of hand upward). H, humerus; R, radius; U, ulna.

Arm Bones

Demonstration of the movement of a pivot joint. Labels: A, arm in supination (palm uppermost); B, arm…

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

Cone

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

"If a body be fastened to a string and whirled, so as to give it a circular motion, there will be a pull on the string that will be greater or less according as the velocity increases or decreases... If the string were cut, the pulling force that drew it away from the straight line would be removed, and the body would then fly off at a tangent; that is, it would move in a straight line tangent to the circle, as shown in Fig. 9." —Hallock 1905

Centrifugal Force

"If a body be fastened to a string and whirled, so as to give it a circular motion, there will be a…

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick impulse to the ball. It will be found to move in a circle, ABCD, because the cord keeps it within a certain distance of the centre (sic). Were it not for this, it would move in a straight line." —Quackenbos 1859

Centrifugal Force

"Attach a ball, for instance, to a cord; and , fastening the end of the cord at a point, O, give a quick…

"The instant one of the strings is let go, the centrifugal force carries off the stone in a tangent to the circle it was describing." —Quackenbos 1859

Centrifugal Force

"The instant one of the strings is let go, the centrifugal force carries off the stone in a tangent…

2 circles that are similar figures

Similar Figures

2 circles that are similar figures

Circle with diameter, radius, arc, chord, and arc.

Circle With Parts

Circle with diameter, radius, arc, chord, and arc.

Illustration of concentric circles.

Concentric Circles

Illustration of concentric circles.

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Polygon Inscribed in Circle

Illustration of polygon inscribed in circle. Or, circle circumscribed about the polygon.

Illustration of point of tangency (line and circle).

Point of Tangency

Illustration of point of tangency (line and circle).

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Polygon Circumscribed About Circle

Illustration of polygon circumscribed about circle. Or, circle inscribed in the polygon.

Illustration of circle with inscribed angle and central angle.

Inscribed and Central Angles

Illustration of circle with inscribed angle and central angle.

Illustration of circle with arc and chord.

Arc and Chord in Circle

Illustration of circle with arc and chord.

Illustration of circle with inscribed angle 30 and central angle 60.

Inscribed and Central Angles 30 60

Illustration of circle with inscribed angle 30 and central angle 60.

Illustration of radius drawn to point of contact of a tangent.

Point of Tangency

Illustration of radius drawn to point of contact of a tangent.

Illustration of circle with segments labeled and arch.

Segments of Circle and Arch

Illustration of circle with segments labeled and arch.

Illustration of circle with parts drawn to show area.

Area of a Circle by parts

Illustration of circle with parts drawn to show area.

Illustration of concentric circles used to find area between two circles (ring).

Concentric Circles (Ring) Area

Illustration of concentric circles used to find area between two circles (ring).

Illustration of circles used to find area between two circles (ring).

Area of Circles and Rings

Illustration of circles used to find area between two circles (ring).