Illustration to show that an angle bisector of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that an angle bisector of a triangle divides the opposite side into segments which…

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Exterior Angle Bisector of Triangle Dividing Opposite Side Into Proportionate Segments

Illustration to show that a bisector of a an exterior angle of a triangle divides the opposite side…

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts are proportional.

Parallel Lines Cut by Parallels, Corresponding Intercepts Proportional

Illustration to show that if parallel lines are cut by any number of parallels, the corresponding intercepts…

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side, it divides those sides proportionally.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line is drawn through two sides of a triangle parallel to the third side,…

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to the third side.

Triangle Divided by Parallel Lines to Form Proportionate Triangles

Illustration to show that if a line divides two sides of a triangle proportionally, it is parallel to…

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Pentagonal Pyramids

Illustration of 2 right pentagonal pyramids with hidden edges shown. The pentagonal bases are congruent,…

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent, but the height of the smaller pyramid is one half that of the larger.

2 Right Rectangular Pyramids

Illustration of 2 right rectangular pyramids with hidden edges shown. The rectangular bases are congruent,…

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid and length of the side of the pentagon (base) on the smaller pentagonal pyramid are one half that of the larger.

Similar Pentagonal Pyramids

Illustration of 2 similar right pentagonal pyramids with hidden edges shown. The height of the pyramid…

At birth the head measures about 4 times into height. At 5 years the head measures about 6 times into height. In the adult about 7 1/2 times into height.

Relation of Head to Height by Age

At birth the head measures about 4 times into height. At 5 years the head measures about 6 times into…

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.

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

Illustration used to construct a square that shall be in proportion to a given square.

Construction of Proportional Square

Illustration used to construct a square that shall be in proportion to a given square.

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to each other as the products of the including edges."

Two Proportional Tetrahedrons

Diagram used to prove the theorem: "Two tetrahedrons having a trihedral angle in each equal, are to…

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to form a right triangle.

Leaning Tower

Illustration of a leaning tower with a perpendicular drawn from the top of the tower to the ground to…

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as is the ground. This drawing could be used for shadow, proportion, trigonometric, or Pythagorean Theorem problems.

Palm Tree Perpendicular to Ground

Illustration of a palm tree that is perpendicular to the ground. The tree is perfectly straight, as…

Triangle diagram for measuring heights of trees using proportions.

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions.

Triangle diagram for measuring heights of trees using proportions

Using Proportions To Find Heights of Trees

Triangle diagram for measuring heights of trees using proportions

Inclined plane using right triangle and proportions

Inclined Plane Triangle

Inclined plane using right triangle and proportions

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in the circumference to the diameter of a circle is the mean proportional between the segments of the diameter.

Right Triangle Inscribed in Semicircle Shows Mean Proportional

Right triangle inscribed in semicircle. Illustration shows that the perpendicular from any point in…

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a river.

Oblique Triangle for Distance Across a River

Illustration of oblique triangle used to find distance across a river.

Illustration of oblique triangle used to find distance across a lake.

Oblique Triangle for Distance Across Lake

Illustration of oblique triangle used to find distance across a lake.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Similar triangles with corresponding sides labeled.

Similar Triangles

Similar triangles with corresponding sides labeled.

Illustration that shows two mutually equiangular triangles are similar.

Mutually Equiangular Similar Triangles

Illustration that shows two mutually equiangular triangles are similar.

Illustration that shows that two triangles which have their sides respectively parallel, or respectively perpendicular, are similar.

Similar Triangles With Respective Sides Parallel or Perpendicular

Illustration that shows that two triangles which have their sides respectively parallel, or respectively…

Illustration of 2 similar triangles with altitudes drawn.

Similar triangles

Illustration of 2 similar triangles with altitudes drawn.

Illustration of similar triangles used to find distance across a lake.

Similar Triangles for Distance Across Lake

Illustration of similar triangles used to find distance across a lake.

Illustration of similar triangles used to find distance across a stream

Similar Triangles for Distance Across Stream

Illustration of similar triangles used to find distance across a stream

Illustration of similar triangles used to find height of smokestack.

Similar Triangles for Height of Smokestack

Illustration of similar triangles used to find height of smokestack.

Illustration that shows two similar triangles with altitudes drawn.

Similar Triangles With Altitudes Drawn

Illustration that shows two similar triangles with altitudes drawn.

"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…