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Illustration used to prove the theorem "Two parallelograms are equal if two sides and the included angle of one are equal respectively to two sides and the included angle of the other."

2 Equal Parallelograms

Illustration used to prove the theorem "Two parallelograms are equal if two sides and the included angle…

Illustration of a two equal parallelograms. Two parallelograms are equal, if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other.

Equal Parallelograms

Illustration of a two equal parallelograms. Two parallelograms are equal, if two sides and the included…

Diagram used to prove the theorem: "The opposite faces of a parallelopiped are equal and parallel."

Equal and Parallel Opposite Faces of a Parallelopiped

Diagram used to prove the theorem: "The opposite faces of a parallelopiped are equal and parallel."

Diagram used to prove the theorem: "The rectangular parallelopipeds which have two dimensions in common are to each other as their third dimension."

Relationship Between 2 Parallelopipeds With Equal Altitudes

Diagram used to prove the theorem: "The rectangular parallelopipeds which have two dimensions in common…

Diagram used to prove the theorem: "The rectangular parallelopipeds are to each other as the product of their three dimensions."

Relationship Between Dimensions of Parallelopipeds

Diagram used to prove the theorem: "The rectangular parallelopipeds are to each other as the product…

Illustration showing two congruent pentagons.

Congruent Pentagons

Illustration showing two congruent pentagons.

Illustration of a two polygons. Polygons may be mutually equiangular without being mutually equilateral.

Equiangular Polygons

Illustration of a two polygons. Polygons may be mutually equiangular without being mutually equilateral.

Illustration of two polygons. Polygons may be mutually equilateral without being mutually equiangular (except for triangles).

Equilateral Polygons

Illustration of two polygons. Polygons may be mutually equilateral without being mutually equiangular…

"Get a lamp-chimney, preferably cylindrical. With a diamond or a steel glass-cutter, cut a disk of window glass a little larger than the cross-section of the lamp-chimney. Pour some fine emery powder on the disk, and rub one end of the chimney upon it, thus grinding them until they fit accurately...place [the chimney] under the water as shown. the upward pressure of the water will hold the disk in place. Pour water carefully into the tube; the disk will fall as soon as the weight of the water in the chimney plus the weight of th disk, exceeds the upward pressure of the water." -Avery 1895

Water Pressure Experiment

"Get a lamp-chimney, preferably cylindrical. With a diamond or a steel glass-cutter, cut a disk of window…

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…

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one are equal respectively to the three faces about a trihedral of the other, and similarly arranged."

Two Equal Prisms

Diagram used to prove the theorem: "Two prisms are equal when the three faces about a trihedral of one…

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Equivalent Triangular Pyramids

Two triangular pyramids having equivalent bases and equal altitudes are equivalent.

Illustration to show that if the diagonals of a parallelogram are equal, the figure is a rectangle.

Rectangle With Diagonals

Illustration to show that if the diagonals of a parallelogram are equal, the figure is a rectangle.

"Suppose a, b, to be a marble floor, and c, to be an ivory ball, which has be thrown towards the floor in the direction of the line c e; it will rebound in the direction of the line e d, thus making the two angles f and g exactly equal." -Comstock 1850

Reflected Motion

"Suppose a, b, to be a marble floor, and c, to be an ivory ball, which has be thrown towards the floor…

"Angle of incidence equals angle of reflection." —Croft 1917

Reflection of Light

"Angle of incidence equals angle of reflection." —Croft 1917

Five students are learning how to use scales to measure a book. They have balanced the book with some weights.

Children Using Scales

Five students are learning how to use scales to measure a book. They have balanced the book with some…

Illustration of a how to construct a square equivalent to the sum of two given squares.

Square Constructed to be Equal to the Sum of Two Given Squares

Illustration of a how to construct a square equivalent to the sum of two given squares.

Illustration of a how to construct a square equivalent to the difference of two given squares.

Square Constructed to be Equal to the Difference of Two Given Squares

Illustration of a how to construct a square equivalent to the difference of two given squares.

Illustration showing an equiangular triangle (one that has all three angles that are equal).

Equiangular Triangle

Illustration showing an equiangular triangle (one that has all three angles that are equal).

"Having equal sides." — Williams, 1889

Equilateral triangle

"Having equal sides." — Williams, 1889

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three angles of a triangle is equal to two right angles.

Triangle with Exterior Angles Drawn

Illustration showing a triangle with exterior angles. This can be used to show the sum of the three…

An isosceles triangle with angles 60, 60, 60

Isosceles Triangle degrees 60, 60, 60

An isosceles triangle with angles 60, 60, 60

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an isosceles triangle the angles opposite the equal sides are equal.

Isosceles Triangle With Interior Segment Drawn

Illustration showing an isosceles triangle with a segment inside. This can be used to show that in an…

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…

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…

Diagram used to prove the theorem: "The plane passed through two diagonally opposite edges of a parallelopiped divides it into two equivalent triangular prisms."

Parallelopiped Divided Into Triangular Prisms

Diagram used to prove the theorem: "The plane passed through two diagonally opposite edges of a parallelopiped…

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes are equivalent."

Equivalent Triangular Pyramids

Diagram used to prove the theorem: "Two triangular pyramids having equivalent bases and equal altitudes…

"Therefore, the small quantity in the spout balances the large quantity in the pot, or presses with the same force downwards, as that in the body of the pot presses upwards." -Comstock 1850

Water Pressure

"Therefore, the small quantity in the spout balances the large quantity in the pot, or presses with…

"...represents two wave systems of equal periods and amplitudes but of opposite phases." -Avery 1895

Waves with Equal Periods and Opposite Amplitudes

"...represents two wave systems of equal periods and amplitudes but of opposite phases." -Avery 1895