Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal respectively to three face angles of the other , are either equal or symmetrical."

Symmetrical or Equal Trihedral Angles

Diagram used to prove the theorem: "Two trihedral angles, which have three face angles of the one equal…

A design created by inscribing 4 congruent tangent arcs in a circle.

Arcs Inscribed In A Circle

A design created by inscribing 4 congruent tangent arcs in a circle.

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. The arcs are inverted.

Reflected Arcs Of A Circle

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 2 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated and rotated 45° and the overlapping curves are removed to create the star-like illustration.

Reflected Arcs Of 2 Circles

A design created by dividing a circle into 4 equal arcs and reflecting each arc toward the center of…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of four times) and rotated 22.5° to create the star-like illustration.

Reflected Arcs Of 4 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration in scribed in the circle.

Reflected Arcs Of 8 Circles In A Circle

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward the center of the circle. (The arcs are inverted.) The design is then repeated (a total of eight times) and rotated 11.25° to create the star-like illustration.

Reflected Arcs Of 8 Circles

A design created by dividing a circle into 4 equal arcs and creating a reflection of each arc toward…

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal to the length of the major axis of the ellipse. The ellipse is externally tangent to the circle.

Ellipse Inscribed In A Circle

Illustration of an ellipse, whose major axis is vertical, inscribed in a circle whose diameter is equal…

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

16 Rotated Concentric Ellipses

Illustration of 16 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments, are externally tangent to the circle. The illustration could be used as a 3-dimensional drawing of a sphere.

2 Ellipses Inscribed In A Circle

Illustration of 2 concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses are externally tangent to the circle in which they are inscribed.

2 Rotated Concentric Ellipses

Illustration of 2 concentric congruent ellipses that are rotated about the center at 90°. The ellipses…

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals of 45°. The ellipses are externally tangent to the circle in which they are inscribed.

4 Rotated Concentric Ellipses

Illustration of 4 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals of 22.5°. The ellipses are externally tangent to the circle in which they are inscribed.

8 Rotated Concentric Ellipses

Illustration of 8 concentric congruent ellipses that are rotated about the center at equal intervals…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter is equal to the length of the major axes of the ellipses. The ellipses, which decrease in width in equal increments until the smallest one is a line, are externally tangent to the circle. The illustration could be described as a circle rotated about the poles of the vertical axis. It could also be used as a 3-dimensional drawing of a sphere.

Ellipses Inscribed In A Circle

Illustration of concentric ellipses, whose major axes are vertical, inscribed in a circle whose diameter…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it. The outer vertices are connected with a smoother curve to form a circle. Hence, the circle is circumscribed about the triangles.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been rotated 12° in relation to the one next to it.

10 Congruent Rotated Equilateral Triangles

Illustration of 10 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been rotated 6° in relation to the one next to it.

20 Congruent Rotated Equilateral Triangles

Illustration of 20 congruent equilateral triangles that have the same center. Each triangle has been…

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been rotated 24° in relation to the one next to it.

5 Congruent Rotated Equilateral Triangles

Illustration of 5 congruent equilateral triangles that have the same center. Each triangle has been…

Diagram showing 2 superimposed symmetrical spherical triangles.

Superimposed Symmetrical Spherical Triangles

Diagram showing 2 superimposed symmetrical spherical triangles.

Diagram showing 2 symmetrical spherical triangles.

Symmetrical Spherical Triangles

Diagram showing 2 symmetrical spherical triangles.

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.

Square with dotted lines that are lines of symmetry.

Lines of Symmetry, Triangle With

Square with dotted lines that are lines of symmetry.

Illustration of symmetrical spherical triangles.

Symmetric Spherical Triangles

Illustration of symmetrical spherical triangles.

Illustration of symmetrical spherical triangles.

Symmetric Spherical Triangles

Illustration of symmetrical spherical triangles.

Illustration of symmetrical spherical triangles.

Symmetric Spherical Triangles

Illustration of symmetrical spherical triangles.

Diagram showing a 2 symmetrical spherical triangles.

Two Symmetrical Spherical Triangles

Diagram showing a 2 symmetrical spherical triangles.