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Although he did not explicitly seek the office of commander and even claimed that he was not equal to it, there was no serious competition. Congress created the Continental Army on June 14, 1775; the next day, on the nomination of John Adams of Massachusetts, Washington was appointed Major General and elected by Congress to be Commander-in-chief.

Washington Taking Command of the Army

Although he did not explicitly seek the office of commander and even claimed that he was not equal to…

The Great Seal of the State of Wyoming. The seal shows two men symbolizing livestock and mining next to a draped statue with the banner "Equal Rights." The ribbon around the columns reads "Oil, Mines, Livestock, Grain."

Seal of Wyoming

The Great Seal of the State of Wyoming. The seal shows two men symbolizing livestock and mining next…

At the end of the lengthy series of entrance ways leading into the interior is the structure's main chamber, the King's Chamber. This chamber was originally 10 × 20 × 11.2 cubits, or about 5.25 m × 10.5 m × 6 m, comprising a double 10 × 10 cubit square, and a height equal to half the double square's diagonal.

Section of the King's Chamber

At the end of the lengthy series of entrance ways leading into the interior is the structure's main…

The chief advantages of the horizontal sundial are that it is easy to read, and the sun lights the face throughout the year. All the hour-lines intersect at the point where the gnomon's style crosses the horizontal plane. Since the style is aligned with the Earth's rotational axis, the style points true North and its angle with the horizontal equals the sundial's geographical latitude λ. A sundial designed for one latitude can be used in another latitude, provided that the sundial is tilted upwards or downwards by an angle equal to the difference in latitude. For example, a sundial designed for a latitude of 40° can be used at a latitude of 45°, if the sundial plane is tilted upwards by 5°, thus aligning the style with the Earth's rotational axis.

Horizontal Dial

The chief advantages of the horizontal sundial are that it is easy to read, and the sun lights the face…

A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal sundial, the sun casts a shadow from its style (a thin rod or a sharp, straight edge) onto a flat surface marked with lines indicating the hours of the day. As the sun moves across the sky, the shadow-edge progressively aligns with different hour-lines on the plate. Such designs rely on the style being aligned with the axis of the Earth's rotation. Hence, if such a sundial is to tell the correct time, the style must point towards true North (not the north or south magnetic pole) and the style's angle with horizontal must equal the sundial's geographical latitude.

Sundial

A sundial is a device that measures time by the position of the Sun. In common designs such as the horizontal…

Remains of the circular walls round towns and palaces, which are known under the name Cyclopean, exist at the present day. These are found both in Greece itself and in many of the Greek colonies, as in Italy and Sardinia. Such walls consist of gigantic polygonal blocks of stone, the corners of which fit accurately into one another. Other structures of this kind consist of regular blocks of equal height. Both kinds are constructed entirely without mortar.

Cyclopean Masonry

Remains of the circular walls round towns and palaces, which are known under the name Cyclopean, exist…

Remains of the circular walls round towns and palaces, which are known under the name Cyclopean, exist at the present day. These are found both in Greece itself and in many of the Greek colonies, as in Italy and Sardinia. Such walls consist of gigantic polygonal blocks of stone, the corners of which fit accurately into one another. Other structures of this kind consist of regular blocks of equal height. Both kinds are constructed entirely without mortar. The Lion Gate served as the gateway to the city of Mycenæ.

The Lion Gate at Mycenæ

Remains of the circular walls round towns and palaces, which are known under the name Cyclopean, exist…

The frieze of the Doric order is not taken up with sculpture in uninterrupted succession, but it occurs in groups at regular intervals, separated by features called triglyphs (a). The spaces formed between the triglyphs are called metopes (b).

Doric Order Frieze in the Parthenon at Athens

The frieze of the Doric order is not taken up with sculpture in uninterrupted succession, but it occurs…

The Roman square panels is an 1879 bas-relief design found near the Tiber river in Rome, Italy. This panel is divided into eight equal spaces that are decorated with a repeated design.

Roman Square Panel

The Roman square panels is an 1879 bas-relief design found near the Tiber river in Rome, Italy. This…

The Assyrian pavement square panel is a divided into eight equal spaces that are decorated with a repeated design.

Assyrian Pavement Square Panel

The Assyrian pavement square panel is a divided into eight equal spaces that are decorated with a repeated…

The Greek square panel is found on the coffer of the Propylaea ceiling, the entrance to the Acropolis in Athens. This panel is divided into eight equal spaces that are decorated with a repeated design.

Greek Square Panel

The Greek square panel is found on the coffer of the Propylaea ceiling, the entrance to the Acropolis…

The Greek square panel is found on the coffer of the Propylaea ceiling, the entrance to the Acropolis in Athens. This panel is divided into eight equal spaces that are decorated with a repeated design.

Greek Square Panel

The Greek square panel is found on the coffer of the Propylaea ceiling, the entrance to the Acropolis…

The Greek square panel is found in Athens. This panel is divided into eight equal spaces that are decorated with a repeated design.

Greek Square Panel

The Greek square panel is found in Athens. This panel is divided into eight equal spaces that are decorated…

The Greek square panel is found on the coffer of the Parhtenon ceiling, a Greek Temple. This panel is divided into eight equal spaces that are decorated with a repeated design.

Greek Square Panel

The Greek square panel is found on the coffer of the Parhtenon ceiling, a Greek Temple. This panel is…

This decorated square panel is found on a 10th century book. This panel is divided into eight equal spaces that are decorated with a repeated design.

Decorated Square Panel

This decorated square panel is found on a 10th century book. This panel is divided into eight equal…

The Scandinavian square panel is a bas-relief design found on a Celtic stone cross. This panel is divided into eight equal spaces that are decorated with a repeated design.

Scandinavian Square Panel

The Scandinavian square panel is a bas-relief design found on a Celtic stone cross. This panel is divided…

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with a repeated design.

Medieval Square Panel

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with…

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with a repeated design.

Medieval Square Panel

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with…

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with a repeated design.

Medieval Square Panel

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with…

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with a repeated design.

Medieval Square Panel

The Medieval square panel is a tile that is divided into eight equal spaces that are decorated with…

"The galvanometer consists of two distinct coils of wire, each having the same resistance, and having equal magnetic effects upon the needle. These coils C and C' are wound in opposite directions, as shown, and one end of each is joined to the same terminal on the frame of the galvanometer; the other ends are joined to separate terminals also situated on the frame." (Britannica, 1891)

Differential Galvanometer

"The galvanometer consists of two distinct coils of wire, each having the same resistance, and having…

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of two rolling bodies is not a constant, the pitch lines take, the conditions of pure rolling contact should be fulfilled, namely, the point of contact must be on the line of centres, and the rolling arcs must be of equal length.

Rolling of Non-cylindrical Surfaces

Illustration showing that the rolling of non-cylindrical surfaces. "If the angular velocity ratio of…

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

Rolling of Logarithmic Spirals

Illustration showing the rolling of two logarithmic spirals of equal obliquity.

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that the distance between the axes O<SUB>1</SUB> and O<SUB>2</SUB> is equal to the major axis of the ellipses, we shall find that they will be in contact on the line of centres and that the rolling arcs are of equal length."

Rolling of Equal Ellipses

"If two equal ellipses, each turning about one of its foci, are placed in contact in such a way that…

Illustration of the rolling of equal parabolas. "The two parabolas may be considered as two ellipses with one focus of each removed to infinity."

Rolling of Equal Parabolas

Illustration of the rolling of equal parabolas. "The two parabolas may be considered as two ellipses…

Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances between their foci O<SUB>1</SUB> and O<SUB>2</SUB>, and d and e, are each equal to fg=hk, they will make contact at some point c.

Rolling of Equal Hyperbolas

Illustration of the rolling of equal hyperbolas. If two equal hyperbolas are placed so that the distances…

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the Law of Sines. In this case, side a is equal to the height (bsin&alpha;).

Ambiguous Case

Illustration of one possible outcome (1 triangle occurs) when discussing the ambiguous case using the…

Illustration showing complex numbers with a modulus equal to unity. The lines representing these numbers terminate in points lying on the circumference of a circle whose radius is unity.

Geometric Inspection of Complex Numbers

Illustration showing complex numbers with a modulus equal to unity. The lines representing these numbers…

A funnel-shaped piece of brass is placed over the ends of a galvanometer when the resistance is equal to that of the pile. This acts as a preservative for the junctions from the heat radiated by the surrounding objects.

Funnel-shaped Brass

A funnel-shaped piece of brass is placed over the ends of a galvanometer when the resistance is equal…

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

Illustration used to show how to divide a given straight line into required number of equal parts.

Construction Of Dividing A Line

Illustration used to show how to divide a given straight line into required number of equal parts.

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal in length to a given straight line."

Construction Of Arc

Illustration used to show how to "find an arc of a circle having a known radius, which shall be equal…

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Construction Of Line Equal To Arc

Illustration used to show how to find a straight line of the same length as a given arc of a circle.

Illustration of the intersection of 2 cylinders of equal diameter.

Intersecting Cylinders

Illustration of the intersection of 2 cylinders of equal diameter.

Illustration of the intersection of 2 cylinders of equal diameter.

Intersecting Cylinders

Illustration of the intersection of 2 cylinders of equal diameter.

Illustration of the intersection of 3 cylinders of equal diameter.

Intersecting Cylinders

Illustration of the intersection of 3 cylinders of equal diameter.

Illustration of the intersection of 2 cylinders of equal diameter.

Intersecting Cylinders

Illustration of the intersection of 2 cylinders of equal diameter.

Illustration of an irregular solid form made up of triangular surfaces unfolded on a flat surface. A is the center and the radius is equal to AB.

Irregular Solid With Triangular Surfaces

Illustration of an irregular solid form made up of triangular surfaces unfolded on a flat surface. A…

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction, they are equal and their planes are parallel."

Angles In Parallel Planes

"If two angles not in the same plane have their sides respectively parallel and lying in the same direction,…

An illustration of a oyster shell. The common name oyster is used for a number of different groups of bivalve mollusks, most of which live in marine habitats or brackish water. The shell consists of two usually highly calcified valves which surround a soft body. Gills filter plankton from the water, and strong adductor muscles are used to hold the shell closed.

Oyster Shell

An illustration of a oyster shell. The common name oyster is used for a number of different groups of…

An illustration of a oyster shell. The common name oyster is used for a number of different groups of bivalve mollusks, most of which live in marine habitats or brackish water. The shell consists of two usually highly calcified valves which surround a soft body. Gills filter plankton from the water, and strong adductor muscles are used to hold the shell closed.

Oyster Shell

An illustration of a oyster shell. The common name oyster is used for a number of different groups of…

An illustration of a oyster shell. The common name oyster is used for a number of different groups of bivalve mollusks, most of which live in marine habitats or brackish water. The shell consists of two usually highly calcified valves which surround a soft body. Gills filter plankton from the water, and strong adductor muscles are used to hold the shell closed.

Oyster Shell

An illustration of a oyster shell. The common name oyster is used for a number of different groups of…

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches. Being added are 3 equal portions 20x20x5, equaling 2000 cubic inches. The sum of these are 6000. You can find the second portion of the problem <a href="../62392/62392_cube_add2.htm">here</a>.

Cube with Additions 1

A cube (A) has sides of 20 inches in length each, making its solid contents equal 8000 cubic inches.…

The obverse and reverse sides of the farthing depicting Charles II. The farthing was an English coin equal to one quarter of a penny.

Obverse and Reverse Sides of Farthing of Charles II

The obverse and reverse sides of the farthing depicting Charles II. The farthing was an English coin…

"Bisecting gage, a gage formed by a bar carrying two heads or cheeks connected by two arms of equal length, forming a toggle-joint, at which a pencil or scribe-awl is placed. The pencil or awl is thus at equal distances from the cheeks at whatever gage they may be set." -Whitney, 1911

Bisecting Gauge

"Bisecting gage, a gage formed by a bar carrying two heads or cheeks connected by two arms of equal…

Illustration of a regular nonagon. A nonagon is a closed geometric figure with 9 sides. A regular nonagon has 9 equal sides and 9 equal angles.

Regular Nonagon

Illustration of a regular nonagon. A nonagon is a closed geometric figure with 9 sides. A regular nonagon…

An illustration of children of various ethnic groups playing.

Children Playing

An illustration of children of various ethnic groups playing.

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…

Diagram used to prove the theorem: "The lateral area of a prism is equal to the product of a lateral edge by the perimeter of a right section."

Lateral Area of A Prism

Diagram used to prove the theorem: "The lateral area of a prism is equal to the product of a lateral…

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…

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 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: "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…

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product of its three dimensions."

Volume of Rectangular Parallelopiped

Diagram used to prove the theorem: "The volume of a rectangular parallelopiped is equal to the product…

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its base and its altitude."

Volume of Parallelopiped

Diagram used to prove the theorem: "The volume of a any parallelopiped is equal to the product of its…

Diagram used to prove the theorem: "The volume of a triangular prism is equal to the product of its base and its altitude."

Volume of Triangular Prism

Diagram used to prove the theorem: "The volume of a triangular prism is equal to the product of its…

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…

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular prism of the same base and altitude."

Volume of Triangular Pyramid

Diagram used to prove the theorem: "The volume of a triangular pyramid is equal to one third of a triangular…

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth the altitude into the sum of the two bases and four times the mid-section."

Volume of Prismatoid

Diagram used to prove the theorem: "The volume of a prismatoid is equal to the product of one-sixth…