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An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and meet two parallel lines at right angles in the given points A and B. "Join A and B; divide AB into four equal parts erect perpendiculars; then m and n are the centers of the circle arcs of the required talon."

Construction Of A Talon

An illustration showing how to construct a talon, or two circle arcs that will tangent themselves, and…

An illustration showing how to construct a circle arc without recourse to its center, but its chord AB and height h being given. "With the chord as radius, and A and B as centers, draw the dotted circle arcs AC and BD. Through the point O draw the lines AOo and BOo. Make the arcs Co=Ao and Do=Bo. Divide these arcs into any desired number of equal parts, and number them as shown on the illustration. Join A and B with the divisions, and the crossings of equal numbers are points in the circle arc."

Construction Of A Circle Arc

An illustration showing how to construct a circle arc without recourse to its center, but its chord…

An illustration showing how to construct a pentagon on a given line without resort to its center. "From B erect Bo perpendicular to and equal to AB; with C as center and Co as radius, draw the arc Do, then AD is the diagonal of the pentagon. With AD as radius and A as center, draw the arc DE; and with E as center and AB as radius, finish the cross E, and thus complete the pentagon."

Construction Of A Pentagon On A Line

An illustration showing how to construct a pentagon on a given line without resort to its center. "From…

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal to the side of the hexagon."

Construction Of A Hexagon In A Circle

An illustration showing how to construct a hexagon in a given circle. "The radius of the circle is equal…

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the length of the side of the heptagon. Set off AB equal to the radius of the circle; draw a from the center C at right angles to AB; then a is the required side of the heptagon."

Construction Of A Heptagon

An illustration showing how to construct a heptagon, or septagon. "The appotem a in a hexagon is the…

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center and AB as radius, draw the circle AFDEC; from B, draw BI at right angles to AB; divide the angles ABC and DBC each into two equal parts; then BD is one side of the octagon. With A and E as centers, draw the arcs HKE and AKI, which determine the points H and I, and thus complete the octagon as shown in the illustration."

Construction Of An Octagon

An illustration showing how to construct an octagon on a given line. "Prolong AB to C. With B as center…

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose base is equal to the sum of all the sides, and the height a equal to the appotem of the polygon. "The reason of this is that the area of two or more triangles ABC and ADC having a common or equal base b and equal height h are alike."

Area Of Regular Polygon Proof

An illustration showing that the area of a regular polygon is equal to the area of a triangle whose…

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide OA and OB each into three equal parts; draw the quadrant AC. From C, draw the line Cc through the point 1. Through the points 2 draw de at an angle of 45° with the major axis. Then 2 is the center for the ends of the ellipse; e is the center for the arc dc; and C is the center for the arc cf."

Construction Of An Isometric Ellipse

An illustration showing how to construct an isometric ellipse by compass and six circle arcs. "Divide…

"A regular township, according to United States surveys, is 6 miles square and is divided into 36 equal parts or sections, each section containing 640 acres and measuring one mile square...How many acres or land in 4.75 sections? How many more acres in 7.5 sections than there are in 3 sections? How many acres of land in .5 section?, 2.5 sections?, 5 sections? How many more acres in 3.5 sections than in 2 sections?" -Foster, 1921

Land Measurement

"A regular township, according to United States surveys, is 6 miles square and is divided into 36 equal…

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles with diameters equal to the long and short axes of the desired ellipse. Draw from o any number of radii, A, B, etc. Draw a line Bb' parallel to n and bb' parallel to m, then b is a point in the desired ellipse.

Construction Of An Ellipse

An illustration showing how to construct an ellipse. "With a as a center, draw two concentric circles…

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three equal parts, draw the two circles, and where they intersect one another are the centers for the tangent arcs of the ellipses as shown by the figure."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Divide the long axis into three…

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off the short axis from A to b, divide b into three equal parts, set off two of these parts from o towards c and c which are the centers for the ends of the ellipse. Make equilateral triangles on cc, when ee will be the centers for the sides of the ellipse. If the long axis is more than twice the short one, this construction will not make a good ellipse."

Construction Of An Ellipse

An illustration showing how to construct an ellipse using circle arcs. "Given the two axes, set off…

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a semicircle on AB, draw ordinates in the circle at right angle to AB, the corresponding and equal ordinates for the ellipse to be drawn parallel to the lines, and thus the elliptic curve is obtained as shown by the figure."

Construction Of An Ellipse Tangent To Two Parallel Lines

An illustration showing how to construct an ellipse parallel to two parallel lines A and B. "Draw a…

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…

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…

An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch of the spiral, construct a square about the center, with the four sides together equal to the pitch. Prolong the sides in one direction as shown by the figure, the corners are the centers for each arc of the external angles."

Construction Of A Spiral

An illustration showing how to construct a spiral with compasses and four centers. "Given the pitch…

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw AB at right angle to x, and BP parallel to x, divide AB and BP into an equal number of equal parts. From the vertex A draw lines to the divisions on BP, from the divisions on AB draw the ordinates parallel to x, the corresponding intersections are points in the parabola."

Construction Of A Parabola

An illustration showing how to construct a parabola. "Given the vertex A, axis x, and a point P. Draw…

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…

A balance scale holding 5 pounds on the left and 3 and 2 pound weights on the right showing 3+2=5.

Addition Scale

A balance scale holding 5 pounds on the left and 3 and 2 pound weights on the right showing 3+2=5.

The shaded region represents 5/8 of the rectangle. If II is divided in to thirds, then those pieces are equal to the five in I.

Five Eighths

The shaded region represents 5/8 of the rectangle. If II is divided in to thirds, then those pieces…

"The triangle ABC is divided into 2 right triangles I and II. ABC is seen to be equal to 1/2 of the rectangle ABNO." -Foster, 1921

Area of Triangle

"The triangle ABC is divided into 2 right triangles I and II. ABC is seen to be equal to 1/2 of the…

"The child sees triangle ACB = triangle ADB, and that I + II = CA - DB; and so he sees that the area of triangle=1/2 area of rectangle whose base and altitude are the same as those of the triangles." -Foster, 1921

Area of Triangle

"The child sees triangle ACB = triangle ADB, and that I + II = CA - DB; and so he sees that the area…

"Fig. 3 shows triangle I = triangle II, III = IV, and so triangle ABC = 1/2 of rectangle ABDE. The fact is realized that the area of a triangle equals 1/2 the product of the base and altitude." -Foster, 1921

Area of Triangle

"Fig. 3 shows triangle I = triangle II, III = IV, and so triangle ABC = 1/2 of rectangle ABDE. The fact…

"From Figure 4 he sees a parallelogram equal to a rectangle of the same base and altitude. Cut out and paste in rectangle form." -Foster, 1921

Area of Parallelogram

"From Figure 4 he sees a parallelogram equal to a rectangle of the same base and altitude. Cut out and…

"The student sees the trapezoid is equal in area to a rectangle whose base is the average base of the trapezoid, and whose altitude is the same as that of the trapezoid." -Foster, 1921

Area of Trapezoid

"The student sees the trapezoid is equal in area to a rectangle whose base is the average base of the…

"The student sees the trapezoid is equal in area to a rectangle whose base is the average base of the trapezoid, and whose altitude is the same as that of the trapezoid." -Foster, 1921

Area of Trapezoid

"The student sees the trapezoid is equal in area to a rectangle whose base is the average base of the…

"It is found that the cord covering the curved surface is twice as long as the one covering the flat surface. So the area of the entire curved surface of a sphere is equal to the area of the surface of 4 circles like the one measured." -Foster, 1921

Area of Sphere

"It is found that the cord covering the curved surface is twice as long as the one covering the flat…

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…

In the nervous system of the centipede the ganglions are arranged in pairs of nearly equal size, except the ganglion that answers to the brain, which is larger, along the surface of the alimentary canal.

Diagram of the Nervous System of a Centipede

In the nervous system of the centipede the ganglions are arranged in pairs of nearly equal size, except…

In the embryo the place of fibrous tissues is at first occupied by a mass of roundish cells, derived from the mesoblast. These develop into a network of branched cells or into groups of fusiform cells. Shown is a portion of submucous tissue of a uterus during pregnancy. Labels: a, branched cells, more or less spindel-shaped; b, bundles of connective tissue.

Tissue Growth of the Uterus

In the embryo the place of fibrous tissues is at first occupied by a mass of roundish cells, derived…

Two small infundibula or groups of air cells, a, with air cells, b, and the ultimate bronchial tubes, c, with which the air cells communicates. From a newborn child.

Infundibula

Two small infundibula or groups of air cells, a, with air cells, b, and the ultimate bronchial tubes,…

Diagram of the principle groups of the Lymphatic vessels.

Lymphatic Vessels

Diagram of the principle groups of the Lymphatic vessels.

From a section of the testis of a dog, showing portions of seminal tubes. A, seminal epithelial cells, and numerous small cells loosely arranged; B, the small cells or spermatoblasts converted into spermatozoa; groups of these is a further stage of development.

Testis of a Dog, Section of the

From a section of the testis of a dog, showing portions of seminal tubes. A, seminal epithelial cells,…

"Diagram illustrating the gradual filling up of lakes by the encroachment of vegetation, and also the stages in the origin of peat and marl deposits in lakes. The several plant associations of the Bog series, displacing one another, belong to the following major groups: (I) O. W., open water succession; (2) M., marginal succession; (3) S., shore succession; (4) B., bog succession, comprising the bog-meadow (Bm), bog-shrub (Bs) and bog-forest (Bf); and (5) M. F., mesophytic forest succession." -Gager, 1916

Lake and Vegetation

"Diagram illustrating the gradual filling up of lakes by the encroachment of vegetation, and also the…

Drawing equal parts, one of three.

Dividers

Drawing equal parts, one of three.

Drawing equal parts, two of three.

Dividers

Drawing equal parts, two of three.

Drawing equal parts, three out of three.

Dividers

Drawing equal parts, three out of three.

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly lengthwise of the cylinder at the some time. The hypotenuse of a right triangle will form one turn of a helix if it is wrapped around a cylinder. The base of the triangle is equal to the circumference of the cylinder and the altitude is the pitch of the helix.

Helix

A cylindrical helix is a curve generated by a point moving uniformly around a cylinder and uniformly…

"It lives in groups on cabbages in gardens, and similar vegetables. It is so voracious that it consumes in a day more than double its own weight."

Caterpillar and Chrysalis of Pieris Brassicae

"It lives in groups on cabbages in gardens, and similar vegetables. It is so voracious that it consumes…

Adipose tissue from omentum. The fat cells are arranged as groups between the bundles of connective tissue.

Adipose Tissue from Omentum

Adipose tissue from omentum. The fat cells are arranged as groups between the bundles of connective…

Peripheral part of transverse section of spinal cord, showing nerve fibers subdivided into groups by ingrowth of subpial layer of neuroglia.

Transverse Section of Spinal Cord

Peripheral part of transverse section of spinal cord, showing nerve fibers subdivided into groups by…

This figure has six pulleys and one cord passes round them all. Each pulley is stretched with the same amount of force, which is equal to the power creating a mechanical advantage of 6.

Pulley System

This figure has six pulleys and one cord passes round them all. Each pulley is stretched with the same…

One group will take the spherical form and produce a shell in the shape of the nautilus. Some are more or less oblong, each new segment being nearly equal to the entire length of the shell.

Spiroloculina Depressa

One group will take the spherical form and produce a shell in the shape of the nautilus. Some are more…

One group will take the spherical form and produce a shell in the shape of the nautilus. Some are more or less oblong, each new segment being nearly equal to the entire length of the shell.

Rotalia

One group will take the spherical form and produce a shell in the shape of the nautilus. Some are more…

This experiment illustrates the law of action and reaction, which asserts that momentum cannot be imparted to any body without equal and opposite momentum being imparted to some other body.

Backward Movement of Discharging Vessel

This experiment illustrates the law of action and reaction, which asserts that momentum cannot be imparted…

This experiment showed that every surface exposed to the atmosphere sustains a normal pressure equal to the weight of a column of mercury whose base is this surface and whose height is 30 inches.

Torricellian Experiment

This experiment showed that every surface exposed to the atmosphere sustains a normal pressure equal…

If the barometric tube is suspended from one of the scales of a balance, there will be required to balance it in the other scale a weight equal to the weight of the tube minus the upward pressure in the cistern.

Counterpoised Barometer

If the barometric tube is suspended from one of the scales of a balance, there will be required to balance…

The four types of cecum. Type I is the infantile form which persists throughout life, in about 2 percent of cases. In Type II the conical cecum had become quadrate by the growing out of a saccule on either side of the anterior longitudinal band. The saccules are of equal side, and the appendix arises from between them instead of from the apex of a cone. This type is found in 3 percent of cases. Type III is the normal type of man. Here the two saccules, which in the second type were uniform, have grown at unequal rates, the right with greater rapidity than the left. This type occurs in about 90 percent of cases. Type IV is merely an exaggerated condition of the third; the right saccule is still larger, and at the same time the left saccule had been atrophied, so that the original apex of the cecum, with the appendix, is close to the ileocecal junction, and the anterior band courses inward to the same situation. This type is present in about 4 percent of cases.

Four Types of Cecum

The four types of cecum. Type I is the infantile form which persists throughout life, in about 2 percent…

The maturation of the ovum. A, An ovum at the commencement process. B, After the formation of the spindle. The chromosomes are gathered at the equator of the spindle in groups of four, i.e. in tetrads, each which consists of two dyads. C, One apex of the spindle has projected into a bud on the surface, and the dyads have passed to the poles. D, The separation of the first polar body. E, The commencement of the second polar body; F, The completion of the second polar body.

Maturation of the Ovum

The maturation of the ovum. A, An ovum at the commencement process. B, After the formation of the spindle.…

Vincent Colyer (1825 - July 12, 1888) was a successful American artist noted for the images he created of the American West and a humanitarian who worked with philanthropic and Christian groups and the U.S. government to try to help freed black slaves and Native Americans.

Vincent Colyer

Vincent Colyer (1825 - July 12, 1888) was a successful American artist noted for the images he created…

A Puritan of 16th and 17th century England was an associate of any number of religious groups advocating for more "purity" of worship and doctrine, as well as personal and group piety. Puritans felt that the English Reformation had not gone far enough, and that the Church of England was tolerant of practices which they associated with the Church of Rome. The word "Puritan" was originally an alternate term for "Cathar" and was a pejorative used to characterize them as extremists similar to the Cathari of France. The Puritans sometimes cooperated with presbyterians, who put forth a number of proposals for "further reformation" in order to keep the Church of England more closely in line with the Reformed Churches on the Continent.

Puritan Costumes

A Puritan of 16th and 17th century England was an associate of any number of religious groups advocating…

A Puritan of 16th and 17th century England was an associate of any number of religious groups advocating for more "purity" of worship and doctrine, as well as personal and group piety. In addition to arming the Puritans to fight against later developments of the Roman Catholic tradition, these studies also led to the rediscovery of some ancient scruples.

A Puritan Soldier

A Puritan of 16th and 17th century England was an associate of any number of religious groups advocating…

An illustration of Bowery Theater, a playhouse in the Bowery neighborhood of New York City. Although it was founded by rich families to compete with the upscale Park Theater, the Bowery saw its most successful period under the populist, pro-American management of Thomas Hamblin in the 1830s and 1840s. By the 1850s, the theater came to cater to immigrant groups such as the Irish, Germans, and Chinese. It burnt down 5 times in 17 years, a fire in 1929 destroying it for good. Although the theater's name changed several times (Thalia Theater, Fay's Bowery Theater, etc.), it was generally referred to as the "Bowery Theater".

Bowery Theater

An illustration of Bowery Theater, a playhouse in the Bowery neighborhood of New York City. Although…

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines.

Glacier Contours

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height)…

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines.

Glacier Form Lines

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height)…

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines.

Contour System

In cartography, a contour line (often just called a "contour") joins points of equal elevation (height)…

The guanaco (Lama guanicoe) is a camelid animal native to South America that stands between 107 and 122 centimeters (3.5 and 4 feet) at the shoulder and weighs about 90 kg (200 lb). The colour varies very little, ranging from a light brown to dark cinnamon and shading to white underneath. Guanacos have grey faces and small straight ears. They are extremely striking with their large, alert brown eyes, streamlined form, and energetic pace. They are particularly ideal for keeping in large groups in open parklands.

Guanaco

The guanaco (Lama guanicoe) is a camelid animal native to South America that stands between 107 and…

Cloves (Syzygium aromaticum, syn. Eugenia aromaticum or Eugenia caryophyllata) are the aromatic dried flower buds of a tree in the family Myrtaceae. Cloves are native to Indonesia and used as a spice in cuisine all over the world. The name derives from French clou, a nail, as the buds vaguely resemble small irregular nails in shape. Cloves are harvested primarily in Indonesia, Madagascar, and Zanzibar, ; it is also grown in India called Lavang , Pakistan, and Sri Lanka. The clove tree is an evergreen which grows to a height ranging from 10-20 m, having large oval leaves and crimson flowers in numerous groups of terminal clusters. The flower buds are at first of a pale color and gradually become green, after which they develop into a bright red, when they are ready for collecting. Cloves are harvested when 1.5-2 cm long, and consist of a long calyx, terminating in four spreading sepals, and four unopened petals which form a small ball in the centre.

Clove Plant and Seed

Cloves (Syzygium aromaticum, syn. Eugenia aromaticum or Eugenia caryophyllata) are the aromatic dried…

Curassows are one of the three major groups of cracid birds. Three of the four genera are restricted to tropical South America; a single species of Crax ranges north to Mexico. They form a distinct clade which is usually classified as the subfamily Cracinae.

Curassow

Curassows are one of the three major groups of cracid birds. Three of the four genera are restricted…

An illustration of the fruit of a date palm, a date. The fruit is a drupe known as a date. They are oval-cylindrical, 3–7 cm long, and 2–3 cm diameter, and when unripe, range from bright red to bright yellow in colour, depending on variety. Dates contain a single seed about 2–2.5 cm long and 6–8 mm thick. Three main cultivar groups of date exist; soft (e.g. 'Barhee', 'Halawy', 'Khadrawy', 'Medjool'), semi-dry (e.g. 'Dayri', 'Deglet Noor', 'Zahidi'), and dry (e.g. 'Thoory'). The type of fruit depends on the glucose, fructose and sucrose content.

Dates

An illustration of the fruit of a date palm, a date. The fruit is a drupe known as a date. They are…