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Geometric pattern for translation and rotation exercises.

Geometric Block Pattern 76

Geometric pattern for translation and rotation exercises.

War token buiders square and compass obverse and shield and "UNITED STATES MEDAL" reverse. These little mementoes of the War of the Rebellion represent the small currency chiefly in use during that period. They were all privately issued, and the Government did not interfere. Merchants displayed their cards on them (often with appropriate characteristic devices), and freely used them in their business. Others partook of the general type, were supplied in suitable quantities to the purchaser, and were "current everywhere." They continued in circulation until about 1867 when their use was prohibited by law.

War Token, 1863

War token buiders square and compass obverse and shield and "UNITED STATES MEDAL" reverse. These little…

Compasses are used for drawing circles and arcs of circles.

Compasses and Attachments

Compasses are used for drawing circles and arcs of circles.

In some instruments joints are held in position by lock nuts allowing ample movement of the legs, yet gives proper stiffness

Compass

In some instruments joints are held in position by lock nuts allowing ample movement of the legs, yet…

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Pencil

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Pen

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

Bow Divider

Bow compasses should be used on all arcs and circles having a radius of less than 3/4 inch.

For drawing straight lines and curves that are not arcs of circles, the ruling pen is used. The distance between the pen points, which regulates the width of line to be drawn, is adjusted by the thumb screw, and the blades are given a slight curvature so that there will be a cavity for ink when the points are close together.

Ruling Pen

For drawing straight lines and curves that are not arcs of circles, the ruling pen is used. The distance…

For larger circles beam compasses are used. The two parts called channels which carry the pen and the needle point are clamped to a wooden beam at a distance equal to the radius of the circle. The thumb nut underneath one of the channel pieces makes accurate adjustment possible.

Beam Compasses

For larger circles beam compasses are used. The two parts called channels which carry the pen and the…

Adjusting the needle point so that it is slightly longer than that of the pencil.

The Tip of the Compass

Adjusting the needle point so that it is slightly longer than that of the pencil.

In changing the compass from a small to large radius, hold the legs together with one hand and spin the nut with the other, in order to save wear on the threads.

Adjusting the Compass

In changing the compass from a small to large radius, hold the legs together with one hand and spin…

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the handle between the thumb and finger.

Inking a Circle

Always draw a circle in one stroke, inclining the compass in the direction of the line and rolling the…

"If a compass is not available, a watch can be used. Hold the watch flat in the hand and with the hour hand pointing in the direction of the sun; a direction halfway between the hour hand and 12 is south." -Finch, 1920

Watch Compass

"If a compass is not available, a watch can be used. Hold the watch flat in the hand and with the hour…

The Mariner's Compass shows all of the points.

Mariner's Compass

The Mariner's Compass shows all of the points.

Compass used by surveyors.

Surveyor's Compass

Compass used by surveyors.

"Direction by Azimuth Method." -Finch, 1920

Azimuth Compass

"Direction by Azimuth Method." -Finch, 1920

The diagram shows the relationship between true, magnetic, and grid azimuths and bearings.

Azimuths

The diagram shows the relationship between true, magnetic, and grid azimuths and bearings.

The diagram shows how to determine North using a watch and the location of the sun.

Watch Compass

The diagram shows how to determine North using a watch and the location of the sun.

Illustration of a compass with one leg at point A on the line segment and the other at Point B.

Compass and Line

Illustration of a compass with one leg at point A on the line segment and the other at Point B.

Illustration of a compass with one leg at point O on the line segment and the other at Point M.

Compass and Line

Illustration of a compass with one leg at point O on the line segment and the other at Point M.

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where the circle intersects the line at D and B, place pins. These pins represent the foci of the ellipse. Use a cord and a pencil to draw the ellipse as shown in figure 60. This illustrates the definition of an ellipse.

Construction Of An Ellipse

Illustrations used to construct an ellipse. Fig. 59 shows a compass at C used to strike a circle. Where…

"Leaves standing nearly vertical in compass-plant. (Silphium laciniatum). A, view from east or west; B, from north or south." -Bergen, 1896

Compass Plant

"Leaves standing nearly vertical in compass-plant. (Silphium laciniatum). A, view from east or west;…

"The mariner's compass is used on board ship; it consists of several magnetic needles arranged parallel to one another and attached to a card, which is mounted at its center upon the end of an upright steel pivot." -Foster, 1921

Mariner's Compass

"The mariner's compass is used on board ship; it consists of several magnetic needles arranged parallel…

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…

In changing the compass from a small to large radius, hold the legs together with one hand and spin the nut with the other, in order to save wear on the threads.

Adjusting the Compass

In changing the compass from a small to large radius, hold the legs together with one hand and spin…

To properly change the compass from one size to another, make sure to place legs together while turning the nut slowly.

Compass Adjustment

To properly change the compass from one size to another, make sure to place legs together while turning…

A compass is a navigational instrument for determining direction relative to the poles.

Turning the Compass

A compass is a navigational instrument for determining direction relative to the poles.

The bow pencil is used to draw small circles and arcs.

The Bow Pencil

The bow pencil is used to draw small circles and arcs.

This bow pencil is used to make small curves.

Bow Pencil

This bow pencil is used to make small curves.

Depicted is a hand reaching out for a bow pencil.

Bow Pencil

Depicted is a hand reaching out for a bow pencil.

Galileo Galilei (15 February 1564 - 8 January 1642) was a Tuscan (Italian) physicist, mathematician, astronomer, and philosopher who played a major role in the scientific revolution. His achievements include improvements to the telescope and consequent astronomical observations, and support for Copernicanism. Galileo has been called the "father of modern observational astronomy," the "father of modern physics," the "father of science," and "the Father of Modern Science." The motion of uniformly accelerated objects, taught in nearly all high school and introductory college physics courses, was studied by Galileo as the subject of kinematics. His contributions to observational astronomy include the telescopic confirmation of the phases of Venus, the discovery of the four largest satellites of Jupiter, named the Galilean moons in his honor, and the observation and analysis of sunspots. Galileo also worked in applied science and technology, improving compass design.

Galileo Galilei

Galileo Galilei (15 February 1564 - 8 January 1642) was a Tuscan (Italian) physicist, mathematician,…

The four cardinal directions or cardinal points are north, south, east, and west.

Cardinal Directions

The four cardinal directions or cardinal points are north, south, east, and west.

The North Star (Polaris) varies so slightly from the true north that we may, for practical purposes, consider it true north. The North Star is easily identified by the pointers of the "Big Dipper."

Astronomical Compass

The North Star (Polaris) varies so slightly from the true north that we may, for practical purposes,…

The sector is a hinged rule with scales used for various mathematical calculations.

Sector

The sector is a hinged rule with scales used for various mathematical calculations.

An illustration of a compass rose.

Compass Rose

An illustration of a compass rose.

An illustration of a liquid compass. "A, Bowl, partly in section; B, Expansion chamber; D, The glass; G, Gimbal ring; L, Nut to expand chamber when filling bowl; M, Screw connector; N, Hole for filling; O, Magnetic needle; P, Buoyant chamber; Q, Iridium pivot; R, Sapphire cap; S, Mica card." -Britannica, 1910

Liquid Compass

An illustration of a liquid compass. "A, Bowl, partly in section; B, Expansion chamber; D, The glass;…

"A slender length of brass resting in a small brass button and designed to stand vertically on the center of a compass glass. From the shadow cast by it the sun's bearing is determined. It may also be used to take compass bearings of other objects." -Whitney, 1911

Shadow Pin

"A slender length of brass resting in a small brass button and designed to stand vertically on the center…

This small compass was carried by Mohammedans (Muslims) in Indian when traveling. It is made out of bronze and inlaid with silver. The compass has an inscription and is in the shape of a flying bird. The head of the bird is pointed towards Mecca, where a Muslim should pray towards.

Small Compass

This small compass was carried by Mohammedans (Muslims) in Indian when traveling. It is made out of…

A test to check if the compass is aligned by bending the knuckle joints together and bringing the points together.

Compass Alignment

A test to check if the compass is aligned by bending the knuckle joints together and bringing the points…

The modern regular compass is used depending on personal preference.

Regular Compass

The modern regular compass is used depending on personal preference.

The modern cylindrical compass is used depending on personal preference.

Cylindrical Compass

The modern cylindrical compass is used depending on personal preference.

The modern Richter compass is used depending on personal preference.

Richter Compass

The modern Richter compass is used depending on personal preference.

A center screw bow to draw circles. The adjustable screw is in the middle of the bow.

Center Screw Bow

A center screw bow to draw circles. The adjustable screw is in the middle of the bow.

Compass beam is used for large circles a compass or a lengthening bar cannot draw.

Beam Compass

Compass beam is used for large circles a compass or a lengthening bar cannot draw.

The little finger on the left hand can guide the needle point of the compass to the center.

Guiding Needle Point of Compass to Little Finger

The little finger on the left hand can guide the needle point of the compass to the center.

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise motion.

Drawing a Circle Using Compass

When drawing the circle, the compass is turned by the handle with the thumb and forefinger in a clockwise…

The illustration shows the finger position of the compass after the revolution. — French, 1911

Compass Finger Position

The illustration shows the finger position of the compass after the revolution. — French, 1911

"Circles up to perhaps three inches in diameter may be drawn with the legs straight but for larger sizes both the needle-point and the pencil leg should be at the knuckle joints so as to be perpendicular to the paper." — French, 1911

Drawing Large Circles with Compass

"Circles up to perhaps three inches in diameter may be drawn with the legs straight but for larger sizes…

Lengthening bar is used to draw circles bigger than 10 inches.

Use of Lengthening Bar

Lengthening bar is used to draw circles bigger than 10 inches.

Bow instruments can be used for drawing small circles. Hold the the left hand and spin the nut in or out with the finger to avoid wear and stripping the thread. "Small adjustments should be made with one hand, with needle point in position on the paper." — French, 1911

Drawing Small Circles with Bow Instrument

Bow instruments can be used for drawing small circles. Hold the the left hand and spin the nut in or…

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4" apart. In drawing concentric circles always draw the smallest first. The dotted circles are drawn in in pencil with long dashes, and inked as shown." —French, 1911

Drawing Concentric Circles with Compass

"Draw Horizontal line throuch center of space. On it mark off radii for six concentric circles 1/4"…

"On horizontal center line mark off eleven points 1/4" apart, beginning at left side of space. Draw horizontal limiting lines (in pencil only) 1 1/2" above and below center line." —French, 1911

Drawing Concentric Arcs with Compass

"On horizontal center line mark off eleven points 1/4" apart, beginning at left side of space. Draw…

"On horizontal center line mark off eight points 3/8" apart, beginning at right side of space." —French, 1911

Drawing Concentric Arcs with Compass and Lengthening Bar

"On horizontal center line mark off eight points 3/8" apart, beginning at right side of space." —French,…

"Draw a circle three inches in diameter. Divide the circumference into five equal parts by trial with dividers. From these points draw radial lines and divide each into four equal parts with spacers. With these points as centers draw the semicircles as shown The radial lines are not to be inked." —French, 1911

Drawing Tangent Arcs with Compass and Dividers

"Draw a circle three inches in diameter. Divide the circumference into five equal parts by trial with…

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the angles with the 30-degree angle, extending the bisectors to the opposite sides. With these middle points of the sides as centers and radius equal to 1/2 the side, draw arcs cutting the bisectors. These intersection will be centers for the inscribed circles. With centers on the intersection of these circles and the bisectors, round off the points of the triangle as shown." —French, 1911

Drawing Tangent Circles and Lines with Compass and Triangles

"On base AB, 3 1/2" long construct an equilateral triangle, using the 60-degree triangle. Bisect the…

"Draw one and one-half inch square about center of space. Divide AE into four 3/16" spaces, with scale. With bow pencil and centers A, B, C, D draw four semicircles with 3/8" radius and so on. Complete the figure by drawing the horizontal and vertical tangents as shown." —French, 1911

Drawing Tangent to Circle Arcs with Bow Compass

"Draw one and one-half inch square about center of space. Divide AE into four 3/16" spaces, with scale.…

"A circle may be shaded by shifting the center on a 45-degree line toward the lower right hand corner... by keeping the needle in the center after drawing the circle and springing the compass out and gradually pressing with the middle finger in the position as shown." —French, 1911

Shading a Circle Using Compass

"A circle may be shaded by shifting the center on a 45-degree line toward the lower right hand corner...…

A development, or rolled out, cone where the point A is the meeting point for the sides. The development is drawn by drawing the arc by using a compass.

Development of Cone

A development, or rolled out, cone where the point A is the meeting point for the sides. The development…

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal line into half inches. Using a compass, draw the large circle then the smaller circle tangent to the bigger circle using a bow instrument.

Drawing Exercise of Inscribed Circle Pattern Tangent to Left Side

An inscribed circle pattern exercise for mechanical drawing. The pattern is drawn by dividing the horizontal…

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the right angles, then rounded off with a compass. Using a pen, the sides of the shapes are darkened to show points where no light is hitting the image.

Mechanical Drawing Exercise Shading Sides of Inscribed Squares and Circle with Ink

Mechanical drawing exercise of shading squares and circle in ink. The squares are first drawn with the…