"This machine consists essentially of a horizontal piston and cylinder engine fixed upon a platform carried upon four wheels, which are coupled together by side rods, so that on motion being communicated by means of a mitre wheel in the hind axle, it can be moved forward by hand. On the forward end of the frame are two bosses forming the centres for a pair of bell cranks or bent levers places close to the ground, and facing in opposite directions, either one of which can be connected with the piston rod. The outer arm of each lever carries a square socket, into which is fixed the pick, which has two cutting heads, one placed a little in front of the other so as to cut to the whole depth at one operation." — Encyclopedia Britanica, 1893

Coal-cutting Machine

"This machine consists essentially of a horizontal piston and cylinder engine fixed upon a platform…

"The Mimic Beetles seldom exceed one-third of an inch in length, and are of very solid consistence, their elytra being so hard that the pin of the entomologist is with difficulty made to enter. They are somewhat square in form, with the upper surface highly polished, feeding chiefly on putrid substances and found in great abundance in spring on the dung of oxen and horses." — Encyclopedia Britanica, 1893

Mimic Beetle

"The Mimic Beetles seldom exceed one-third of an inch in length, and are of very solid consistence,…

A sovereign crown of Egypt, composed of the tall pointed miter, or white crown, of southern Egypt, combined with te red crown, square in front and rising to a point behind, of northern Egypt.

Pschent

A sovereign crown of Egypt, composed of the tall pointed miter, or white crown, of southern Egypt, combined…

"Muller gives a quaint description not very unlike that used by Hall and Forbes, only the mouth of the dredge was square, a form which, unless used with great caution, gives fatal facilities for "washing out" in the process of hauling in." — Encyclopedia Britannica, 1893

Fredrick Muller's Dredge

"Muller gives a quaint description not very unlike that used by Hall and Forbes, only the mouth of the…

A bolt or arrow having a square or four edged head, especially a crossbow bolt.

Quarrel

A bolt or arrow having a square or four edged head, especially a crossbow bolt.

A plane for plowing a groove along the edge of a board.

Square Rabbet Plane

A plane for plowing a groove along the edge of a board.

A quadrilateral plane figure having four right angles and its opposite sides equal in length. The adjacent sides are unequal.

Rectangle

A quadrilateral plane figure having four right angles and its opposite sides equal in length. The adjacent…

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

A solid bound by six rhombic planes.

Rhombohedron

A solid bound by six rhombic planes.

Special rods used for multiplication, division, and extracting square roots.

Napier's Rods

Special rods used for multiplication, division, and extracting square roots.

"The section and ground plan of one of the older forms of open-mouthed furnaces used at Dowlais (Truran), consisting of a heavy mass of mascury, square at base, strongly braced together with iron tie-rods, rising in the shape of a truncated pyramid to the height of the boshes, and then surmounted with a conical top surrounded at the throat by a gallery for the introduction of the enarging materials. In the square base were four arched recesses or tuyere houses, one on each side, F, F, for the introduction of G also serving for the removal of cinder and the tapping of the furnace for the running of the pig. The lowest portion of the hearth or crucible, A, was constructed of refractory sandstone, grit, or conglomerate, or of difficulty fusible firebrick, the inner portion of the upper part of the furnace being also built of firebrick set in fireclay with an air course between the double lining thus constructed; exteriorly the furnace was built of less expensive and refractory materials, usually of stone, strongly bound round with iron hoops." — The Encyclopedia Britannica, 1893

Furnace

"The section and ground plan of one of the older forms of open-mouthed furnaces used at Dowlais (Truran),…

"A signet ring has a square revolving bezel on which are four serpents interlaced." —The Encyclopedia Britannica, 1910

Signet Ring

"A signet ring has a square revolving bezel on which are four serpents interlaced." —The Encyclopedia…

"Rupture of a Mountain.—There is no doubt, but in the operations of nature, great effects are sometimes produced among mountains, by a small quantity of water finding its way to a reservoir in the crevices of the rocks far beneath. Suppose, in the interior of a mountain, there should be a space of ten yards square, and an inch deep, filled with water, and closed up on all sides; and suppose that, in the course of time, a small fissure, no more than an inch in diameter, should be openeing by the water, from the height of two hundred feet above, down to this little reservoir. The consequence might be, that the side of the mountain would burst asunder, for the pressure, under the circumstances supposed, would be equal to the weight of five thousand tons." —Comstock, 1850

Mountain Rupture

"Rupture of a Mountain.—There is no doubt, but in the operations of nature, great effects are…

"A plate of glass about 2.5 inches square is ruled with twenty-one lines in one direction .1 inch apart, and two lines in the other direction 2 inches apart. The extreme lines of the set therefore form a perfect square of 2 inches. These lines are ruled with exceeding accuracy and care, but provision is left for ascertaining any errors that remain either as to distance or want of perfect squareness." —The Encyclopedia Britannica, 1903

Micrometer

"A plate of glass about 2.5 inches square is ruled with twenty-one lines in one direction .1 inch apart,…

"In this the four lateral planes are rectangular and equal; they may be either oblong or square; in the latter case the form is the cube." —The Encyclopedia Britannica, 1903

Primitive Crystal

"In this the four lateral planes are rectangular and equal; they may be either oblong or square; in…

"If the base is a square and the prism stands erect—that is, if its sides or lateral planes, as they are called, are perpendicular to the base—the form is termed a right square prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"If the base is a square and the prism stands erect—that is, if its sides or lateral planes, as…

"When the base is a rectangle instead of a square, the form is a right rectangular prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rectangle instead of a square, the form is a right rectangular prism." —The…

"When the base is a rhombus, and the prism stands erect, the form is a right rhombic prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rhombus, and the prism stands erect, the form is a right rhombic prism." —The…

"When the base is a rhomboid, and the prism stands erect, it is only the opposite laeral faces that can be equal. The form is called a right rhomboidal prism." —The Encyclopedia Britannica, 1903

Primitive Crystal

"When the base is a rhomboid, and the prism stands erect, it is only the opposite laeral faces that…

The perspective shown in this plate is parallel perspective; and the subject here intended to be represented is a flat and perfectly square surface, such as the floor of a room, a chess board, or any other such object.  1) The front edge of the given square; 2) One side of it receding to the vanishing point, which also is the point of sight; 3) The other side receding to the same point; 4) A line taken from one corner of the front edge, to the point of measuremen on the opposite side, and giving the perspective width or depth of the square at the intersection of the line 3; 5) A line drawn at the above intersection, and parallel to the front edge; this will give the back of the square. The lines 1, 2, 3, and 5 may then be strongly marked, and the figure will be thus completed. 6) This line is taken from the corner of the front edge to the opposite point of the measurement, showing how exactly either this line, o that marked 4, will give the perspective width of the square. It serves also to find the centre.

Parallel Perspective

The perspective shown in this plate is parallel perspective; and the subject here intended to be represented…

A three masted vessel, with the foremast square rigged, and the mainmast and mizzemast fore and aft rigged.

Barkantine

A three masted vessel, with the foremast square rigged, and the mainmast and mizzemast fore and aft…

The perspective in this plate is "angular perspective," and the figure it represents is a flat square surface; its dimensions are supposed to be either twenty feet or twenty inches. 1) Two lines drawn from the nearest corner of theboard, to the horizontal line, and at a distance from each other equal to the thickness of the board; this fixes the vanishing point at 1. 2) A line drawn from the above vanishing point to the point of station. 3) A line taken at right angles to 2, from the point of station, and fixing on the horizontal line the position of the vanishing point 3. 4) Two lines drawn from the nearest corner of the board to the vanishing point 3, similarly to the previously drawn lines 1. 5) One point of measurement, obtained in the usual way, by the distance of 3 from the point of station. 6) The point of measurement. 7) The line of the geometrical scale, being a line drawn across the base of the nearest corner, and marked according to scale, twenty feet or twenty inches. 8,8) Lines taken from either end of the geometrical scale towards the point of measurement, but extending no farther than where they meet the lines 1,1, and 4,4. 9,10) Small perpendicular lines drawn at the above intersections, by which the width of the board is ascertained. 11) The side of the board opposite and really parallel to that marked 4, and therefore tending to the same vanishing point. 12) The back of the board, opposite and parallel to the front marked 1, and consequently tending to the same vanishing point. The lines 1,1; 4,4; 11 and 12, being strongly marked, the figure will be completed.

Angular Perspective

The perspective in this plate is "angular perspective," and the figure it represents is a flat square…

This object is a cube, having therefore all its faces of equal dimensions; and as both sides recede, "angular perspective" is employed. The point of sight, horizontal line, and point of station, having been fixed upon, the line A is first to be drawn, touching the bottom of the nearest corner, and is for the geometrical scale or height of the cube, which, in this instance, will be called twelve feet; that is, twelve feet must be marked on the scale from the corner on either side. 1) The ground line of the square, taken from the centre of the geometrical scale line to the horizontal line; by its junction with which is determined the vanishing point or that side. 2) A line drawn from the above vanishing point to the point of station. 3) A line drawn at right angles at the point of station to the line 2, as far as the horizontal line, its intersection with which will give the correct vanishing point to the other side. 4) The ground line of the cube running to the last vanishing point. 5) The nearest corner of the cube, twelve feet in height, being equal to the width. The points of measurement are next to be ascertained, and to be marked in the usual way; and the lines B drawn from the ends of the geometrical scale towards the point of measurement give the perspective width or depth of both sides. This is found at their cutting of the ground lines 1 and 4. The line 6 represents the top line of one side of the cube, and runs from the nearest corner to the vanishing point. 7) The other top line; and it is drawn to the other vanishing point. 8) The far corner line raised vertically from the crossing of the lines B and 1. 9) The other corner line raised vertically from the intersection of the lines B and 4. The lines 1, 4, 5, 6, 7, 8, 9, being strengthened, the figure is complete.

Angular Perspective

This object is a cube, having therefore all its faces of equal dimensions; and as both sides recede,…

The White Tower, the square building with turrets on each corner that gave it its name, is actually in the middle of a complex of several buildings along the River Thames in London, which have served as fortresses, armories, treasuries, zoos/menageries, mints, palaces, places of execution, public records offices, observatories, shelters, and prisons.

Towers of London

The White Tower, the square building with turrets on each corner that gave it its name, is actually…

This doodad has floral and vinelike shapes inside a square shape.

Doodad

This doodad has floral and vinelike shapes inside a square shape.

The Sahara is the world's largest hot desert, 9,000,000 square kilometers, almost as large as the United States.

Desert of Sahara

The Sahara is the world's largest hot desert, 9,000,000 square kilometers, almost as large as the United…

Australia's 7,686,850 square kilometers landmass is on the Indo-Australian Plate. Surrounded by Indian, Southern and Pacific oceans, Australia is separated from Asia by the Arafura and Timor seas. Australia has a total 25,760 kilometers of coastline.

Australian Scenery

Australia's 7,686,850 square kilometers landmass is on the Indo-Australian Plate. Surrounded by Indian,…

The Mississippi Valley lies between the predominant and secondary mountain-systems. It is over 300,000 square miles in area, and includes some of the most fertile land in the country.

Scene of Mississippi

The Mississippi Valley lies between the predominant and secondary mountain-systems. It is over 300,000…

Or Barque, a three-masted vessel of which the foremast and mainmast are square-rigged, but the mizzenmast has fore-and-aft sails only.

Bark

Or Barque, a three-masted vessel of which the foremast and mainmast are square-rigged, but the mizzenmast…

Pediculus Pubis. The crab-louse is gray-black and is a much broader square form than the other two species of louse, that has been a great scourge to soliders in time of war. This insect has been named the crab-louse from its broad crab-like appearance. It is of grayish color; the head is small, and appears to be united with the broad body without any thorax; it inhabits the hairy part of the body, under the arms or shoulders, in the beard, etc., but appears to avoid the head. These insects pierce deeply into the skin of mankind, and produce an intolerable itching.

Crab Louse

Pediculus Pubis. The crab-louse is gray-black and is a much broader square form than the other two species…

A square divided into equal squares, like a chessboard, in each of which is placed one of a series of consecutive numbers from 1 up to the square of the number of cells in a side, in such a manner that the sum of the numbers in each row or column and in each diagonal is constant.

Magic Square

A square divided into equal squares, like a chessboard, in each of which is placed one of a series of…

Squares that have many more summations than just rows, columns, and diagonals. Frost extended this idea to cubes, where various sections have the same singular properties.

Nasik Cube

Squares that have many more summations than just rows, columns, and diagonals. Frost extended this idea…

Dotted lines can indicate a relationship among figures, such as one inside another.

Drawing Lines 1

Dotted lines can indicate a relationship among figures, such as one inside another.

Shading of the right and lower sides gives dimension to drawings.

Drawing Lines 2

Shading of the right and lower sides gives dimension to drawings.

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

Angle of degree 90

Angle Degrees 90

Angle of degree 90

A Roman scutum shield.

Roman scutum

A Roman scutum shield.

Fragments of striped (striated) muscle fibers, showing a cleavage in opposite directions, magnified 300 diameters. Striped muscle is nearly always under the control of the will, and is often spoken of as voluntary muscle. Labels: A, longitudinal cleavage; c, fibrillae separated from one another at the broken end of the fiber; c'c", single fibrils more highly magnified, in c; the elementary structures are square, in c" round; B, transverse cleavage; a, b, partially detached disks; b' detached disk, more highly magnified, showing the sarcous elements.

Fragments of Striped (Striated) Muscle Fibers

Fragments of striped (striated) muscle fibers, showing a cleavage in opposite directions, magnified…

"It consists of a number of square pieces of board, or of thin iron, connected together through their centres by iron rods, so that they can have no lateral motion..The ascending side of this chain passes through a square box, to which these pieces or buckets are closely fitted..." -Comstock 1850

Chain Pump

"It consists of a number of square pieces of board, or of thin iron, connected together through their…

"Support, as shown, a glass or brass plate, square or round, and strew it evenly with fine sand. Place the finger at any point of the edge of the plate, so as to form a node there, and draw a violin bow at a point properly chosen. The sand immediately begins to dance on the plate and arrange itself along nodal lines. By changing the nodal points and bowing properly, other sand-figures may be produced, one of which is shown." -Avery 1895

Vibrating Plates

"Support, as shown, a glass or brass plate, square or round, and strew it evenly with fine sand. Place…

"An electric motor that uses a square nut to engage the electromagnet which drive the motor." -Avery 1895

Electric Motor

"An electric motor that uses a square nut to engage the electromagnet which drive the motor." -Avery…

"Let the are of the piston a be 20 square inches; of b, 7 sq. in.; of c, 1 sq. in.; of d, 6 sq. in.; of e, 8 sq. in; and of f, 4 sq. in. If... a force of five pounds be applied at c, a pressure of five pounds per square inch will be transmitted in all directions, and in order that there shall be no movement, the required pressure must be applied by all the other pistons in proportion." —Hallock 1905

Water Pressure Demonstration

"Let the are of the piston a be 20 square inches; of b, 7 sq. in.; of c, 1 sq. in.; of d, 6 sq. in.;…

"...let the area of the piston a be 1 square inch; of b, 40 square inches. According to Pascal's law, 1 pound placed on a will balance 40 pounds placed on b." —Hallock 1905

Pascal's Law and Water Pressure

"...let the area of the piston a be 1 square inch; of b, 40 square inches. According to Pascal's law,…

"The radiation of light, or the intensity of light is inversely proportional to the square of the distance from the light source." —Croft 1917

Light Intensity

"The radiation of light, or the intensity of light is inversely proportional to the square of the distance…

"Another illustration of how luminous density varies inversely as the square of the distance." —Croft 1917

Light Intensity Versus Distance

"Another illustration of how luminous density varies inversely as the square of the distance." —Croft…

"The ball C is placed on a square frame between two upright wires, on each of which a ball slides so as to strike C when it descends. Let the ball A drop, and it will drive C to D... Let the ball B drop, and it will drive C to E; this is simple motion. Let A and B drop at the same instant, and they will drive C to F; this is resultant motion." —Quackenbos 1859

Resultant Motion with Ball

"The ball C is placed on a square frame between two upright wires, on each of which a ball slides so…

2 squares that are similar figures

Similar Figures

2 squares that are similar figures

Right angle with square at perpendicular lines

Right Angle

Right angle with square at perpendicular lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Perpendicular Lines

Right angle at perpendicular lines demonstrated by string on plumb line.

Right triangle with square

Right Triangle

Right triangle with square

Square with angles labeled. A rectangle with four equal sides.

Square

Square with angles labeled. A rectangle with four equal sides.

Rectangle with squares to show area.

Rectangle With Area Squares

Rectangle with squares to show area.

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

Parallelogram and Rectangle Relationship

Parallelogram with dimensions drawn to show relationship to the area of a rectangle.

Parallelogram illustration to show where the area of a triangle formula comes from.

Area of Triangle

Parallelogram illustration to show where the area of a triangle formula comes from.

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

Rectangle With Dimensions

Rectangle with dimensions labeled. Rectangle can be used to calculate area.

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram With Dimensions

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Parallelogram With Dimensions

Parallelogram with dimensions labeled. Parallelogram can be used to calculate area.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle with dimensions labeled. Triangle can be used to calculate area.

Triangle With Dimensions

Triangle with dimensions labeled. Triangle can be used to calculate area.