Illustration to show that the difference of the distances from any point in the base produced of an isosceles triangle to the equal sides of the triangle is constant.

Point in Base of Isosceles Triangle

Illustration to show that the difference of the distances from any point in the base produced of an…

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Trigonometric Reference Triangles/Angles (60 degrees) Drawn in Quadrants

Trigonometric reference triangles/angles drawn for 60 degree reference angel in quadrants I and II.

Illustration showing a right triangle (one that has one right angle).

Right Triangle

Illustration showing a right triangle (one that has one right angle).

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth horizontal plane.

Inclined Plane Forming Right Triangle

Inclined plane forming right triangle showing the velocity of a body sliding a distance,s, down a smooth…

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right Triangle With Sides .7 and 1 and Angle of 35 degrees

Right triangle OQP with angle of 35 degrees, height of .70 inches, and leg of 1 inch.

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right Triangle With Sides .64 and 1 and Angle of 40 degrees

Right triangle OQP with angle of 40 degrees, height of .64 inches, and hypotenuse of 1 inch.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right Triangle ABC With Angle 67 degrees 42.8 minutes and Hypotenuse 23.47 ft.

Right triangle ABC with a base angle of 67 degrees 4208 minutes and a hypotenuse of 23.47 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

Right Triangle ABC With Leg 23.85 ft. and Hypotenuse 35.62 ft.

Right triangle ABC with a leg of 23.85 feet and a hypotenuse of 35.62 feet.

Illustration of a right triangle with one angle the double of the other.

Right Triangle With One Angle Double the Other

Illustration of a right triangle with one angle the double of the other.

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can be shown to show adjacent angles ACB and ACD as well.

Triangle With Segment Extended for Exterior Angle

Illustration showing a triangle with an exterior segment drawn to show and exterior angle. This can…

Illustration showing a triangle with an interior segment drawn

Triangle With Interior Segment

Illustration showing a triangle with an interior segment drawn

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 30, 60, 90 degrees

Special right triangle with angles 30 degrees, 60 degrees, and 90 degrees with side measures/relationships…

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships shown.

Special Right Triangle with Angles 45, 45, 90 degrees

Special right triangle with angles 45 degrees, 45 degrees, and 90 degrees with side measures/relationships…

Illustration showing a triangle with a segment inside.

Triangle With Interior Segment Drawn

Illustration showing a triangle with a segment inside.

Illustration showing two equal triangles.

Equal Triangles

Illustration showing two equal triangles.

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other.

Equal Triangles by Side Side Side

Illustration showing two equal triangles. This can be used to show that two triangles are equal if the…

Illustration to show if two triangles have two sides of the one equal, respectively, to two sides of the other, and the angles opposite two equal sides equal, the angles opposite the other two equal sides are equal or supplementary, and if equal the triangles are equal.

Proof of Equal Triangles Drawing

Illustration to show if two triangles have two sides of the one equal, respectively, to two sides of…

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration could be used to find trig ratios.

Trigonometric Reference Triangles/Angles Drawn in Quadrants

Trigonometric reference triangles/angles drawn for reference angel in quadrants I and II. This illustration…

Illustration showing two equal right triangles. This can be used to show that two right triangles are equal if a leg and the hypotenuse of the one are equal, respectively, to a leg and the hypotenuse of the other.

Equal Right Triangles by Hypotenuse Leg

Illustration showing two equal right triangles. This can be used to show that two right triangles are…

Illustration showing three triangles. This is used to show the following theorem: If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Three Triangles Used to Compare Sides

Illustration showing three triangles. This is used to show the following theorem: If two triangles have…

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking off streets at 100 foot intervals.

Triangular City Block With Angles and Lengths

Illustration showing an angle of 23 degrees 40 minutes making a triangle in a city block and marking…

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their vertexes at the center O of the circle, one side of the angle lying to the right of O, and coinciding with the horizontal diameter, as OB."

Arcs and Angles of a Trigonometric Circle

"In trigonometry, the arcs of circles are used to measure angles. All angles are supposed to have their…

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent" to O. OA is the hypotenuse. Sine is defined as the ratio of the opposite side to the hypotenuse (AC/OA). Cosine is defined as the ratio of the adjacent side to the hypotenuse (OC/OA), and Tangent is defined as the ratio of the opposite side to the adjacent side (DB/OB).

Trigonometry Triangle to Show Sine, Cosine, and Tangent

Right triangle OCA, inside of Circle O is used to show that side AC is "opposite" O and side OC is "adjacent"…

"Direction of the needle when placed at a right angle to the uniting wire." -Comstock 1850

Wire at Right Angle to the Uniting Wire

"Direction of the needle when placed at a right angle to the uniting wire." -Comstock 1850

OP is a line representing a vector (directed quantity)

Vector

OP is a line representing a vector (directed quantity)

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

Vector Showing Force at Angle of 20 degrees

OP is a vector (directed quantity) showing the force by a weight acting on it at an angle of 20 degrees.

"Suppose the object a, appears to the naked eye of the length repreesnted in the drawing. Now, as the rays coming from each end of the object, form by their convergence at the eye, the visual angle, or the angle under which the object is seem, and we call objects large or small in proportion as this angle is obtuse or acute, if, therefore, the object a be withdrawn futher from the eye, it is apparent that the rays o, o, proceeding from its extremities, will enter the eye under a more acute angle, and therefore that the object will appear diminished in proportion." -Comstock 1850

Visual Angle

"Suppose the object a, appears to the naked eye of the length repreesnted in the drawing. Now, as the…

"1, Screw-wrench; 2, Tap-wrench; 3, Angle-wrench; 4, Tube-wrench; 5, Monkey-wrench for hexagonal and square nuts." — Williams, 1889

Wrenches

"1, Screw-wrench; 2, Tap-wrench; 3, Angle-wrench; 4, Tube-wrench; 5, Monkey-wrench for hexagonal and…