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Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints. The endpoints are marked A and B.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.…

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints. The endpoints are A and B.

Segment, Vertical Line

Illustration of a vertical line segment. A line segment is a section of a line with definite endpoints.…

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints. The endpoints are marked A and B.

Segment, Slanted Line

Illustration of a slanted line segment. A line segment is a section of a line with definite endpoints.…

Illustration of line segment AB, which is made up of line segments AC and CB. C is considered the midpoint of segment AB.

Segment, 3 Points on a Line

Illustration of line segment AB, which is made up of line segments AC and CB. C is considered the midpoint…

2 line segments, AB and CD. AB is half the length of CD.

Segments, 2 Line

2 line segments, AB and CD. AB is half the length of CD.

6 parallel horizontal line segments.

Segments, 6 Parallel Line

6 parallel horizontal line segments.

5 parallel horizontal line segments.

Segments, 5 Parallel Line

5 parallel horizontal line segments.

4 parallel horizontal line segments.

Segments, 4 Parallel Line

4 parallel horizontal line segments.

3 parallel horizontal line segments.

Segments, 3 Parallel Line

3 parallel horizontal line segments.

2 parallel horizontal line segments.

Segments, 2 Parallel Line

2 parallel horizontal line segments.

6 slanted parallel line segments.

Segments, 6 Parallel Line

6 slanted parallel line segments.

6 slanted parallel line segments.

Segments, 6 Parallel Line

6 slanted parallel line segments.

2 slanted parallel line segments.

Segments, 2 Parallel Line

2 slanted parallel line segments.

2 slanted parallel line segments.

Segments, 2 Parallel Line

2 slanted parallel line segments.

Square with dotted vertical, horizontal, and diagonal lines that are lines of symmetry.

Lines of Symmetry, Square With

Square with dotted vertical, horizontal, and diagonal lines that are lines of symmetry.

2 lines that are intersected by a third line known as a transversal.

Transversal, 2 Lines Intersected By A

2 lines that are intersected by a third line known as a transversal.

Tree that has no symmetry.

Symmetry, Tree With No

Tree that has no symmetry.

Tree with dotted vertical line that shows symmetry.

Line of Symmetry, Tree With

Tree with dotted vertical line that shows symmetry.

Square with dotted lines that are lines of symmetry.

Lines of Symmetry, Triangle With

Square with dotted lines that are lines of symmetry.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A zig zag line known as a broken line in mathematics.

Line, Broken

A zig zag line known as a broken line in mathematics.

A test to ensure the triangle is accurate by drawing a perpendicular line from a T-square.

Triangle Accuracy Test using T-square

A test to ensure the triangle is accurate by drawing a perpendicular line from a T-square.

When drawing vertical lines, the blade of the T-square is held with the thumb while the fingers adjusting the triangle.

Drawing Vertical Lines Using a T-square and a Triangle

When drawing vertical lines, the blade of the T-square is held with the thumb while the fingers adjusting…

The arrows shows the motion direction of drawing a 30-degrees, 45-degrees, or a-60 degrees angle using a 60-degree triangle.

Drawing Lines using Triangle, 30-, 45-, 60-Degrees

The arrows shows the motion direction of drawing a 30-degrees, 45-degrees, or a-60 degrees angle using…

The line can be divided by using the divider and estimating the leg distance by the eye.

Bisecting Line Using Divider

The line can be divided by using the divider and estimating the leg distance by the eye.

The 45-degree triangle can be used to make a line at a multiple of 15 degrees.

Drawing Lines using Triangle at Angles in Multiples of 15 degrees

The 45-degree triangle can be used to make a line at a multiple of 15 degrees.

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,…

To draw a straight line, the pen must be perpendicular with the straight edge ruler, as shown in A. A one sided ragged line will result if the pen is positioned at C. If the pen is positioned at B, the ink will run under the edge and form a blot.

Positioning Pen with the Straight Edge

To draw a straight line, the pen must be perpendicular with the straight edge ruler, as shown in A.…

Alphabet of lines are lines needed to cover the lines with labeling symbols within the diagram.

Alphabet of Lines

Alphabet of lines are lines needed to cover the lines with labeling symbols within the diagram.

A French Curve is used by connecting sufficient points to sketch a curve. The sketch should be line lightly with pencil, without losing points, until the a smooth line is drawn.

Using French Curve

A French Curve is used by connecting sufficient points to sketch a curve. The sketch should be line…

"Through the center of the space draw a horizontal and a vertical line, measuring on these lines as diameters lay off a three-inch square. Along the lower side and the upper half of the left side measure 3/8' spaces with the scale. Draw all horizontal lines with the T-square and all vertical lines with the T-square and triangle." —French, 1911

Drawing Exercise for T-square, Triangle, and Scale

"Through the center of the space draw a horizontal and a vertical line, measuring on these lines as…

"Draw three-inch square. Draw lines AB, BC, DE and EF at 30 degrees. Divide lower side into seven equal parts with the dividers. Draw the vertical lines, and mark divisions on AC with pencil as each line is drawn. Through the division points on top and bottom draw the converging lines using the triangle alone as a straight-edge." —French, 1911

Drawing Converging Lines

"Draw three-inch square. Draw lines AB, BC, DE and EF at 30 degrees. Divide lower side into seven equal…

"Draw three-inch square and one-inch square. From the corners of inner square draw lines to outer square at 15 degrees and 75 degrees, with the two triangles in combination. Mark points with spacers 3/16" inside of each line of this outside cross, and complete figure with triangles in combination." —French, 1911

Drawing Maltese Cross using T-square, Spacers, and Triangles

"Draw three-inch square and one-inch square. From the corners of inner square draw lines to outer square…

"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,…

"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…

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center C and radius CB draw an arc intersecting AB at E, then AE will be equal in length be to the arc AB." —French, 1911

Approximating Length of Circle Arc using Straight Line

"At A draw the tangent AD and Chord AB produced. Lay off AC equal to half the chord AB. With center…

Make a perpendicular lines at point B and C, and join by a straight line. Create a desired curve by referencing the lines as a center and tangent.

Draw Reverse or Ogee Curve

Make a perpendicular lines at point B and C, and join by a straight line. Create a desired curve by…

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces small enough as practically to coincide with the arc, and to step off the same number on the right line." —French, 1911

Rectifying Arc Using Dividers

"In ordinary work the usual way of rectifying an arc is to step around it with the dividers, in spaces…

"When the minor axis is at least two-thirds the major, the following method ma be used: Make CF and CG equal to AB-DE. Make CH and CI equal to 3/4 CF F, G, H, I will be centers for arcs E, D, B, and A." —French 1911

Approximate Ellipse using Lines

"When the minor axis is at least two-thirds the major, the following method ma be used: Make CF and…

"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…

"A cycloid is the curve generated by the motion of a point on the circumference of a circle rolled along a straight line." —French, 1911

Cycloid

"A cycloid is the curve generated by the motion of a point on the circumference of a circle rolled along…

There were minor variations from one manufacturer to another, but most typewriters followed the concept that each key was attached to a type bar that had the corresponding letter molded. To have letters typed in exact location, the type bar was guided all its way till the ribbon by segment. When a key was struck briskly and firmly, the type bar hit an inked fabric stretched in front of a cylindrical platen that moved back and forth. The paper was rolled around by the typewriter's platen, which was then rotated by the "carriage return" lever into position for each new line of text

Type Writing Machine

There were minor variations from one manufacturer to another, but most typewriters followed the concept…

A Pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the movement of one specified point is an amplified version of the movement of another point. If a line drawing is traced by the first point, an enlarged copy will be drawn by a pen fixed to the other.

Pantograph Machine

A Pantograph is a mechanical linkage connected in a special manner based on parallelograms so that the…

Cut the sleeve protectors from the pattern. Beginning at the center of the bottom and holding the wrong side of the cloth next to you, baste the edge of the sleeve protector to the line running through the middle of the tape. Make a tiny pleat in the tape at each corner so that when doubled over it will round the corners smoothly. Join the ends of the tape by folding back both ends and overhanging them together on the wrong side. Hem the tape down on the right side.

Sleeve Protector

Cut the sleeve protectors from the pattern. Beginning at the center of the bottom and holding the wrong…

A Linotype machine is a line casting machine used in printing. The machine revolutionized printing and especially newspaper publishing, making it possible for a relatively small number of operators to set type for many pages on a daily basis. The Linotype machine operator enters text on a 90-character keyboard. The machine assembles matrices, which are molds for the letter forms, into a line. The assembled line is then cast as a single piece, called a slug, of type metal in a process known as hot metal typesetting. The matrices are then returned to the type magazine from which they came. The name of the machine comes from the fact that it produces an entire line of metal type at once, hence a line-o-type. This allows much faster typesetting and composition than original hand composition in which operators place down one pre cast metal letter, punctuation mark or space at a time.

Linotype Machine

A Linotype machine is a line casting machine used in printing. The machine revolutionized printing and…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Perpendicular to V

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may be copied in the new position distance from the ground line to any point in the top view be unchanged, hence the new top view may be found by projecting up from the front view and across from the original top view" —French, 1911

Revolution About Axis Forward or Back

"The pyramid be revolved about an axis perpendicular to V, the front view will be unchanged and may…

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars from AB to the plane. These perpendiculars form what is known as the projecting plane. If this projecting plane to be revolved about its H trace, which is the H projection of the line, until it coincides with H, the line will be seen in its true length." —French, 1911

Revolutions into the Plane of Geometric Shapes

"The H projection of the line AB in the space is a line connecting the feet of all the perpendiculars…

"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...…

An illustration of a hexagonal prism rolled out, or "stretched out" in the straight line AB.

Development of Hexagonal Prism

An illustration of a hexagonal prism rolled out, or "stretched out" in the straight line AB.

By about 1910, the mechanical typewriter had reached a somewhat standardized design. There were minor variations from one manufacturer to another, but most type writers followed the concept that each key was attached to a type bar that had the corresponding letter molded, in reverse, into its striking head. To have letters typed in exact location, the type bar was guided all its way till the ribbon by segment. When a key was struck briskly and firmly, the type bar hit a ribbon stretched in front of a cylindrical platen that moved back and forth. The paper was rolled around by the type writers platen, which was then rotated by the carriage return lever into position for each new line of text.

Type Writing Machine

By about 1910, the mechanical typewriter had reached a somewhat standardized design. There were minor…

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose stretchout would be a straight line. If the cutting planes were taken at uniform distances apart, or at random, the elements would not be spaced uniformly on the stretchout but would be found as they project on the turned section of S—S." —French, 1911

Two Cylinders with Axes Not Intersecting

"If the cylinder A were to be developed a right section as at S—S would have to be taken, whose…