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Equal circles inside and tangent to the outside circle, also tangent to each other

Circle to Circle Tangents

Equal circles inside and tangent to the outside circle, also tangent to each other

Illustration of 2 right circular cones that are similar.

2 Similar Right Circular Cones

Illustration of 2 right circular cones that are similar.

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles OAB and OAC thus formed are similar, and have all their sides positive except AC, which is negative.

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles From Positive and Negative Theta, Θ

Angle XOP=Θ and angle XOQ=- Θ. From a point in the terminal side of each a perpendicular line is drawn…

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is drawn to the x-axis. The right triangles AOB and OCD thus formed are similar, and have all their sides positive except OC

Coordinate Axis With Perpendiculars Drawn To Form Similar Right Triangles

Angle XOP=Θ and angle XOQ=90+Θ. From a point in the terminal side of each a perpendicular line is…

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters. Both cylinders (discs) are resting on a side/edge.

2 Narrow Cylinders on Their Sides

Illustration of 2 narrow right circular cylinders with equal heights (thickness) and different diameters.…

Illustration of 2 right circular cylinders in which one cylinder is twice the height of the other.

2 Right Circular Cylinders

Illustration of 2 right circular cylinders in which one cylinder is twice the height of the other.

Illustration of 2 right circular cylinders in which one cylinder is twice the height and twice the diameter of the other.

2 Right Circular Cylinders

Illustration of 2 right circular cylinders in which one cylinder is twice the height and twice the diameter…

Illustration of 2 similar cylinders. The height and diameter of the smaller cylinder is half that of the larger one.

2 Similar Cylinders

Illustration of 2 similar cylinders. The height and diameter of the smaller cylinder is half that of…

Illustration of 2 soup cans that are similar cylinders. The diameter and height of the smaller can is one half that of the larger.

2 Soup Can Cylinders

Illustration of 2 soup cans that are similar cylinders. The diameter and height of the smaller can is…

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is 1/2 that of the previous one.

3 Similar Cylinders

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is…

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is one half that of the previous one.

3 Similar Cylinders

Illustration of 3 similar cylinders. The height and diameter in each successively smaller cylinder is…

Illustration of 2 regular concentric decagons.

2 Concentric Decagons

Illustration of 2 regular concentric decagons.

Illustration of 2 regular concentric decagons.

2 Concentric Decagons

Illustration of 2 regular concentric decagons.

Illustration of 3 regular concentric decagons that are equally spaced.

3 Concentric Decagons

Illustration of 3 regular concentric decagons that are equally spaced.

Illustration of 4 regular concentric evenly spaced decagons.

4 Concentric Decagons

Illustration of 4 regular concentric evenly spaced decagons.

Illustration of a how to construct a triangle equivalent to a given hexagon/polygon.

Hexagon Used to Construct Equivalent Triangle

Illustration of a how to construct a triangle equivalent to a given hexagon/polygon.

Illustration of a how to construct a square equivalent to a given parallelogram.

Parallelogram Used to Construct Equivalent Square

Illustration of a how to construct a square equivalent to a given parallelogram.

Illustration of a how to construct a pentagon similar to two given pentagons.

Pentagon Constructed to be Similar to Given Pentagons

Illustration of a how to construct a pentagon similar to two given pentagons.

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are divided proportionally, and the section is a polygon similar to the base."

Pyramid Cut By Plane

Diagram used to prove the theorem: "If a pyramid is cut by a plane parallel to the base, the edges are…

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each, and similarly placed.

Similar Polyhedrons

Two similar polyhedrons may be decomposed into the same number of tetrahedrons similar, each to each,…

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of tetrahedrons, similar each to each , and similarly placed."

Two Similar Polyhedrons

Diagram used to prove the theorem: "Two similar polyhedrons may be decomposed into the same number of…

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of the smaller prism is one half that of the larger.

2 Octagonal Prisms

Illustration of 2 right octagonal prisms with congruent bases, but different heights. The height of…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger. Hidden edges are shown.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism is one half that of the larger.

2 Rectangular Prisms

Illustration of 2 right rectangular prisms. The bases are congruent, but the height of the smaller prism…

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller prism are one half that of the larger.

2 Similar Octagonal Prisms

Illustration of 2 Similar right octagonal prisms. The height and length of the edges of the smaller…

Illustration of 4 congruent rectangular prisms placed in the shape of a square. They are arranged to look like they are 3-dimensional rectangular solids coming out of the page.

4 Congruent Rectangular Prisms

Illustration of 4 congruent rectangular prisms placed in the shape of a square. They are arranged to…

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

4 Hexagonal Prisms

A cluster of 4 right hexagonal prisms with congruent bases, but varying heights.

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,…

The volumes of two similar tetrahedrons are to each other as the cubes of their homologous (corresponding) edges.

Similar Tetrahedrons

The volumes of two similar tetrahedrons are to each other as the cubes of their homologous (corresponding)…

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…