An Engineer's Scale ruler for plotting and map drawing.

Engineer's Scale Ruler

An Engineer's Scale ruler for plotting and map drawing.

An Architect's Scale ruler for drawing machinery and structures.

Architect's Scale Ruler

An Architect's Scale ruler for drawing machinery and structures.

Different ruler shapes for different scales. The triangle shape, lettered A, is commonly used in Engineer's Scale and Architect's Scale.

Scale Ruler Shapes

Different ruler shapes for different scales. The triangle shape, lettered A, is commonly used in Engineer's…

A homemade section liner device made by slipping a wooden block to hold the triangle to make cross hatching lines.

Section Lining Device

A homemade section liner device made by slipping a wooden block to hold the triangle to make cross hatching…

The Universal Drafting Machine is used in a large drafting room. It combines the functions of T-square, triangle, scale, and protractor to save time in machine drawing and civil engineering work.

Universal Drafting Machine

The Universal Drafting Machine is used in a large drafting room. It combines the functions of T-square,…

The Kelsey triangle is a modified triangle ruler, where the hypotenuse is inwardly bent.

Kelsey Triangles

The Kelsey triangle is a modified triangle ruler, where the hypotenuse is inwardly bent.

The Rondinella triangle is a modified triangle ruler, where the hypotenuse is outwardly bent.

Rondinella Triangle

The Rondinella triangle is a modified triangle ruler, where the hypotenuse is outwardly bent.

The Zange triangle is a modified triangle ruler, where one of the legs is longer making the hypotenuse is elongated.

Zange Triangle

The Zange triangle is a modified triangle ruler, where one of the legs is longer making the hypotenuse…

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 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,…

"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…

"Through the center of the space draw the three construction lines, AB vertical, DE and FG at 30 degrees. Measure CA and CB 1 1/2" long. Draw AE, AF, DB and BG at 30 degrees. Complete hexagon by drawing DF and GE vertical. Set spacers to 3/32". Step off 3/32" on each side of the center lines, and 3/16" from each side of hexagon. Complete figure as shown with triangle against T-square." —French, 1911

Drawing Hexagonal Figure

"Through the center of the space draw the three construction lines, AB vertical, DE and FG at 30 degrees.…

"An exercise in starting and stopping short lines. Draw three-inch square. Draw diagonals with 45-degree triangle. With scale lay off 3/8" spaces along the diagonals, from their intersection. With 45-degree triangle complete figure, finishing one-quarter at a time." —French, 1911

Drawing Street Paving Intersection

"An exercise in starting and stopping short lines. Draw three-inch square. Draw diagonals with 45-degree…

"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…

"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…

A T-square is a technical drawing instrument, primarily a guide for drawing horizontal lines on a drafting table. It is used by draftsmen. It is also used to guide the triangle that draws the vertical lines.

Architects Drafting Square

A T-square is a technical drawing instrument, primarily a guide for drawing horizontal lines on a drafting…

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

Triangle Prism Exercise

An illustration to draw triangle prism's development, or stretched out surfaces, in a 4" by 5" surface.

An illustration to exercise a stretched out, or development, image of the triangular prism using 4" by 5 " surface.

Triangular Prism Development Exercise

An illustration to exercise a stretched out, or development, image of the triangular prism using 4"…

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length of the edges of each triangle.

Development Exercise of Triangular Pyramid

Exercise problem to develop, or rolled out, image of the triangular pyramid by creating an equal length…

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled out image, of the pyramid.

Development Exercise of Pentagonal Pyramid

A pentagonal pyramid problem exercise to complete the top view of the image, and development, or rolled…

A problem exercise creating a stretched out or developed image of the octagonal light shade by using the hexagonal pyramid development method.

Development Exercise of Octagonal Light Shade

A problem exercise creating a stretched out or developed image of the octagonal light shade by using…

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development, or stretched out, of the image by creating edges at equal lengths, and revolving the sides.

Development Exercise of Hexagonal Pyramid

A sample exercise problem in completing the top part of the hexagonal pyramid and to create a development,…

"A conical surface may be shaded by driving a fine needle at the apex and swinging a triangle about it, as in (A). To avoid a blot at the apex of a complete cone the needle may be driven on the extension of the side as in (B), or it may be shaded by parallel line as in (C)." —French, 1911

Different Cone Shading

"A conical surface may be shaded by driving a fine needle at the apex and swinging a triangle about…

An outside view of the spherical triangle from a church. The window has three rounded parts in a shape of a triangle.

Gothic Architecture Spherical Triangle Outside Window

An outside view of the spherical triangle from a church. The window has three rounded parts in a shape…

A fourteenth century spherical triangle viewed inside a church. The window is indented with a bottom part sloped to let sun light in.

Gothic Architecture Spherical Triangle Inside Window

A fourteenth century spherical triangle viewed inside a church. The window is indented with a bottom…

The illustration showing the projection of the triangles from the triangle pyramid as shown on top. This projection helps create the development of the pyramid by connecting each projection together.

Triangle Pyramid Side Projections

The illustration showing the projection of the triangles from the triangle pyramid as shown on top.…

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom of each triangles to guide the straight lines. The triangle ABC is the base of the pyramid. When folded, the pyramid will form from the image.

Development of Triangle Pyramid

A development, or rolled out, triangle pyramid. The image is created by making an arc at the bottom…

A problem exercise using a t square and 45 degree triangle to divide the paper into half inch squares. Then, divide the squares with diagonal lines both sides of the paper.

Squares Diagonal Lines Repeating Patterns

A problem exercise using a t square and 45 degree triangle to divide the paper into half inch squares.…

"Use the T square and 45 degree triangle to divide the square as indicated, the size of the small squares being ½". This is an excellent test of precision in measurement and lining. Care must be observed in the inking of this figure to allow each line to dry before inking the next one." —Anthony, 1904

Drawing Diagonal Lines with T Squares and Triangle

"Use the T square and 45 degree triangle to divide the square as indicated, the size of the small squares…

A diagonal line pattern drawing exercise in for T square and triangle. The image is constructed by dividing the paper into squares with the T square, and the diagonal lines are drawn using a 45 degree triangle.

Drawing Exercise for Drawing Diagonal Line Pattern using T Square and Triangle

A diagonal line pattern drawing exercise in for T square and triangle. The image is constructed by dividing…

The construction of a star with square overlapping each other using a triangle and T square. This image is drawn by dividing the paper with dashed lines using T square. Using the 45 degree triangle, draw diagonal lines to create the star and the star.

Constructing Star and Box Overlap Pattern using T Square and Triangle

The construction of a star with square overlapping each other using a triangle and T square. This image…

A problem exercise to construct a star overlapping square using a triangle and T square. The image is drawn by dividing the paper with dashed lines using T square. Using the 45 degree triangle, draw diagonal lines to create the star and the star.

Constructing 4 Point Star Overlapping Box Pattern using T Square and Triangle

A problem exercise to construct a star overlapping square using a triangle and T square. The image is…

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…

"With a 45 degree triangle draw lines AC and BD through the center and construct three squares. Set the bow—pencil to a radius of 3∕8' and describe a circular arc in the corner of each square just touching, but not intersecting, the sides of the square. Ink the circular arcs first." —Anthony, 1904

Mechanical Drawing Exercise Three Inscribed Squares with Rounded Corners using Triangle and Bow

"With a 45 degree triangle draw lines AC and BD through the center and construct three squares. Set…

An illustration of the position and the size of the image viewed by the eye. The eye approximates the the height of the image. The image's height is the hypotenuse of the triangle, creating an angle with the eye. This image is then reflected upside down in the eye.

Position and Size of Image for Eye Optics

An illustration of the position and the size of the image viewed by the eye. The eye approximates the…

A pulley system used to reduce motion between the piston and the indicator of the steam engine. The indicator is attached by a string on the curved bottom triangle. As the piston moves, the string is pulled to record the pressure of the steam.

Reducing Motion of Piston and Indicator using Brumbo Pulley

A pulley system used to reduce motion between the piston and the indicator of the steam engine. The…

Asplenium radicans fronds are shaped like a triangle. The fronds are between three and five feet long. This fern grows in the tropical regions of north and south America.

Asplenium Radicans

Asplenium radicans fronds are shaped like a triangle. The fronds are between three and five feet long.…

The center of gravity of a triangle is the point of intersection O of the midpoint lines.

Center of Gravity

The center of gravity of a triangle is the point of intersection O of the midpoint lines.

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into a triangle, parallelogram, circle, etc., based on the shape of the figure. Find the area of each part and combine the centers of gravity found for each.

Center of Gravity

Finding the center of gravity of an irregular plane figure. Divide one of the parallel surfaces into…

This form is bounded by forty-eight similar scalene triangles. Its solid angles are of three kinds: six octahedral, at the extremities of the principal axes; eight hexahedral, at the extremities of the trigonal axes; and twelve tetrahedral, at the extremities of the digonal axes. Naumann's symbol for this form is m 0 n; Dana's, m-n.

Hexoctahedron

This form is bounded by forty-eight similar scalene triangles. Its solid angles are of three kinds:…

Tambourine, drum, bells, and a triangle.

Musical instruments

Tambourine, drum, bells, and a triangle.

Showing distance between two points on a coordinate plane.

Distance

Showing distance between two points on a coordinate plane.

A right triangle on a coordinate plane.

Right Triangle

A right triangle on a coordinate plane.

A scalene triangle.

Scalene Triangle

A scalene triangle.

Finding the area of a triangle in terms of polar coordinates of its three vertices.

Triangle Area

Finding the area of a triangle in terms of polar coordinates of its three vertices.

A positive slope line making a 60 degree angle with the x-axis.

Straight Line

A positive slope line making a 60 degree angle with the x-axis.

Finding the equation of a circle with the origin as its center.

Circle Equation

Finding the equation of a circle with the origin as its center.

An inscribed triangle in a circle.

Particular Cases

An inscribed triangle in a circle.

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

Coordinate Plane

A circle with part of a triangle inscribed in it. They are lying on a coordinate plane.

A circle and triangle situated on coordinate planes.

Circle

A circle and triangle situated on coordinate planes.

Mechanical drawing triangle.

Drawing Triangle

Mechanical drawing triangle.

Mechanical drawing triangle.

Drawing Triangle

Mechanical drawing triangle.

"So David and all the house of Israel brought up the ark of Jehovah with shouting, and with the sound of the trumpet." 2 Samuel 6:15 ASV
<p>Illustration of King David marching before the ark, playing his harp. The priests and people march behind him, carrying the ark and playing trumpets and tambourines. A young boy marches and plays a triangle.

King David Takes the Ark of the Covenant to Mount Zion

"So David and all the house of Israel brought up the ark of Jehovah with shouting, and with the sound…

"A draftsman's instrument for ruling parallel lines. It consists of a triangle so attached to a straight-edge that it can be moved back and forth on it a distance predetermined by the adjustment of a set-screw. a, a straight-edge; b, triangle moving on <i>a</i> for a distance determined by the set of the micrometer scale <i>c</i>; d, spring for releasing triangle and keeping it in the end of its slot." -Whitney, 1889

Section Liner, A Draftsman's Tool

"A draftsman's instrument for ruling parallel lines. It consists of a triangle so attached to a straight-edge…