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"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and when it has come to rest, drop a plumb line from the point of suspension and mark its direction on the surface. Do the same at any other point, and the centre of gravity will lie where the two line intersect." —Quackenbos 1859

Center of Gravity

"When such a surface is irregular in shape, suspend it at any point, so that it may move freely, and…

"When a line of direction falls within the base, a body stands when not, it falls... On the same principle, a load of stone may pass safely over a hillside, on which a load of hay would be overturned [as shown by the line of direction in this illustration]." —Quackenbos 1859

Line of Direction from the Center of Gravity of an Object

"When a line of direction falls within the base, a body stands when not, it falls... On the same principle,…

"Let any irregularly shpaed body, as a stone or chair, be suspended so as to move freely. Drop a plumb line from the point of the suspendsion, and make it fast or mark its direction. The center of mass will lie in this line. From a second point, not in the line already determined, suspend the body; let it fall a plumb line as before. The center of mass will lie in this line also. But to lie in both lines, it must lie at their intersection." -Avery 1895

Finding the Center of Mass

"Let any irregularly shpaed body, as a stone or chair, be suspended so as to move freely. Drop a plumb…

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Circle With Diameter, Radius, Segment, Line

Illustration showing a circle with a diameter, radius, lines, triangle, and segment drawn.

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference between the sum of the legs and the hypotenuse.

Circle Inscribed in a Right Triangle

Illustration showing the diameter of a circle inscribed in a right triangle is equal to the difference…

Illustrations of a circle with secant AD and line BC tangent to it.

Circle with Secant and Point of Tangency

Illustrations of a circle with secant AD and line BC tangent to it.

Illustration of a circle with a tangent drawn - a straight line perpendicular to a radius at its extremity.

Circle With Tangent Line Drawn

Illustration of a circle with a tangent drawn - a straight line perpendicular to a radius at its extremity.

Illustration showing a circle with an inscribed triangle and radii.

Circle With Inscribed Triangle and Radii

Illustration showing a circle with an inscribed triangle and radii.

Illustration showing a circle with various chords drawn.

Circle With Various Chords

Illustration showing a circle with various chords drawn.

Illustration showing a circle with various chords drawn.

Circle With Various Chords

Illustration showing a circle with various chords drawn.

Illustration showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration showing a circle with various chords and tangents drawn.

Circle With Various Chords And Tangents

Illustration showing a circle with various chords and tangents drawn.

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point where the circumference cuts the hypotenuse bisects the other leg.

Circle With a Right Triangle

Illustration where one leg of a right triangle is the diameter of a circle. The tangent at the point…

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are drawn, the perpendiculars dropped on them from the middle point of the subtended arc are equal.

Circle With a Tangent Line and Chord

Illustration showing that from any point in the circumference of a circle, a chord and a tangent are…

A line of interlocking circles.

Circles

A line of interlocking circles.

Illustration showing various circles and the angles formed by intersecting lines.

Intersecting Lines in Circles

Illustration showing various circles and the angles formed by intersecting lines.

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated by the circumferences. The chords joining the ends of theses lines are parallel.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a line drawn through each point of intersection terminated…

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Two Intersecting Circles With Lines

Illustration showing 2 intersecting circles with a lines drawn that form a triangle.

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact terminated by the circumference. The chords joining the ends of theses lines are parallel.

Tangent Circles With Chords

Illustration showing 2 circles with that touch each other and two lines drawn through the point of contact…

A device consisting of a pair of clamping jaws carrying a ring and a hook. Used for securing or attaching the end of a cord, as a round lathe belt or rail car signal cord.

Rope Clamp

A device consisting of a pair of clamping jaws carrying a ring and a hook. Used for securing or attaching…

An illustration of clothes hanging on a clothes line with shoe sand gloves resting beneath.

Hanging Clothes

An illustration of clothes hanging on a clothes line with shoe sand gloves resting beneath.

A cord on which clothes are hung to dry

Early Use Clothesline

A cord on which clothes are hung to dry

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;…

Illustration of the construction used to bisect a given angle.

Construction of Bisecting a Given Angle

Illustration of the construction used to bisect a given angle.

Illustration of the construction used to bisect a given arc.

Construction of Bisecting a Given Arc

Illustration of the construction used to bisect a given arc.

Illustration of the construction used to bisect a given line.

Construction of Bisecting a Given Line

Illustration of the construction used to bisect a given line.

A line which is divided into seven equal parts, shown by construction.

Construction of Dividing Lines

A line which is divided into seven equal parts, shown by construction.

A line which is divided into equal parts, shown by construction and square.

Construction of Dividing Lines

A line which is divided into equal parts, shown by construction and square.

Illustration used to construct a circle that shall pass through a given point and cut chords of a given length from two parallels.

Construction of a Circle Through a Given Point that Cuts Chords of Given Lengths From Parallels

Illustration used to construct a circle that shall pass through a given point and cut chords of a given…

Illustration to let fall a perpendicular upon a given line from a given external point.

Construction of Perpendicular Upon a Given Line From an External Point

Illustration to let fall a perpendicular upon a given line from a given external point.

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point O on the straight line.

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Construction of Perpendicular From a Given Point on a Straight Line

Illustration of the construction of a perpendicular to a line when given a point B on the straight line.

Illustration of the construction used to draw a tangent to a given circle through a given point.

Construction of Tangent Line Through a Given Point to a Given Circle

Illustration of the construction used to draw a tangent to a given circle through a given point.

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting lines also intersect."

Intersecting Lines Corollary

Illustration used to prove the corollary that "Two lines perpendicular respectively to two intersecting…

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular to the line."

Perpendicular to Line Corollary

Illustration used to prove the corollary that "From a point outside a line there exists only one perpendicular…

"Cross Quarterly is a Cross cut by a partition line, and the tinctures reversed or counter-changed."—Aveling, 1891

Cross Quarterly

"Cross Quarterly is a Cross cut by a partition line, and the tinctures reversed or counter-changed."—Aveling,…

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing as much of an arc as will practically coincide with the curve, then changing the center and radius for the next portion, remembering always that if arcs are to be tangent, their centers must lie on the common normal at the point of tangency." —French 1911

Curve Inked with Circle Arcs

"Any noncircular curve may be approximated by tangent circle arcs, selecting a center by trial, drawing…

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn by the series of perpendicular lines parallel to the axis.

Drawing Irregular Isometric Curves of Solid

The illustration of an irregular curves for solid. The isometric projection of the curve can be drawn…

A round, laterally flattened wooden block, encircled by a rope or an iron band, and pierced with three holes to recieve the lanyard, used to extend the shrouds and stays, and for other purposes.

Deadeye

A round, laterally flattened wooden block, encircled by a rope or an iron band, and pierced with three…

A round, laterally flattened wooden block, encircled by a rope or an iron band, and pierced with three holes to recieve the lanyard, used to extend the shrouds and stays, and for other purposes.

Deadeye

A round, laterally flattened wooden block, encircled by a rope or an iron band, and pierced with three…

Illustration 1 of the Dedekind axiom.

Dedekind Property 1

Illustration 1 of the Dedekind axiom.

Illustration 2 of the Dedekind axiom.

Dedekind Property 2

Illustration 2 of the Dedekind axiom.

Illustration 3 of the Dedekind axiom.

Dedekind Property 3

Illustration 3 of the Dedekind axiom.

Illustration 4 of the Dedekind axiom.

Dedekind Property 4

Illustration 4 of the Dedekind axiom.

Illustration showing an angle of depression from a horizontal line to a line of sight.

Angle of Depression

Illustration showing an angle of depression from a horizontal line to a line of sight.

"The diving dress envelops the whole body of the diver, the upper portion a being the "helmet," the intermediate portion b the "breast-plate," and the lower portion c the "dress." The hose by which the air is supplied is shown at d, and e is the "life" or "signal" line, which is attached to the diver's waist, and by which he makes signals and is hauled to the surface. The water-proof material of which the dress is made is very generally sheet india-rubber covered on both sides with tanned twill to protect the india-rubber from injury." — Encyclopedia Britannica, 1893

Diving Dress

"The diving dress envelops the whole body of the diver, the upper portion a being the "helmet," the…

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel to the one given, place a triangle against the T-square and move them together until the hypotenuse of the triangle matches the line. Hold the T-square firmly and slide the triangle in the direction of the arrow until the desired position of the parallel line is reached.

Drawing Parallel Lines Exercise

Parallel lines are drawn by using a triangle in combination with a T-square. To draw a line parallel…

Parallel lines are drawn by holding the triangle against the T-square at an angle, or another triangle, then slip the first triangle onto the required position.

Drawing Parallel Lines Using T-square and Triangle

Parallel lines are drawn by holding the triangle against the T-square at an angle, or another triangle,…

Perpendicular lines are drawn by fitting the hypothenuse of the triangle to the T-square at an angle, or another triangle. Then, turn the triangle so that the hypothenuse is perpendicular to the line.

Drawing Perpendicular Lines Using T-square and Triangle

Perpendicular lines are drawn by fitting the hypothenuse of the triangle to the T-square at an angle,…

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Angle of Elevation

Illustration showing an angle of elevation from a horizontal line to a line of sight.

Illustration used to show how to divide a given straight line into any number of equal parts.

Line Divided Into Equal Parts

Illustration used to show how to divide a given straight line into any number of equal parts.

Finding the polar equation of a straight line.

Polar Equation

Finding the polar equation of a straight line.

An exercise for mechanical drawing to construct a series of horizontal lines. The solid lines are drawn without using a T square, while the dashed lines are produced using a T square.

Horizontal Solid and Dashed Line Drawing Exercise

An exercise for mechanical drawing to construct a series of horizontal lines. The solid lines are drawn…

An exercise problem drawing a series of horizontal lines using a straight edge or triangle without using a T square.

Horizontal Solid Line Drawing Exercise

An exercise problem drawing a series of horizontal lines using a straight edge or triangle without using…

"Argent, a fess gules, embattled grady. EMBATTLED GRADY. Where the battlements gradually rise one above another." -Hall, 1862

Fess Embattled Grady

"Argent, a fess gules, embattled grady. EMBATTLED GRADY. Where the battlements gradually rise one above…

A flashcard featuring an illustration of a Line

Flashcard of a Line

A flashcard featuring an illustration of a Line

A flashcard featuring an illustration of a Line Segment

Flashcard of a Line Segment

A flashcard featuring an illustration of a Line Segment

A flashcard featuring an illustration of a Parallel Lines

Flashcard of a Parallel Lines

A flashcard featuring an illustration of a Parallel Lines

A flashcard featuring an illustration of a Ray

Flashcard of a Ray

A flashcard featuring an illustration of a Ray

A flashcard featuring an illustration of a Straight angle

Flashcard of a Straight angle

A flashcard featuring an illustration of a Straight angle