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The Egyptian Solar Calendar came into fruition and was a far more reliable tool for determining the dates and seasons than the Mesopotamian lunar calendar.
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The Egyptians introduced the first base 10 numeration system, and used Hieroglyphs to represent numbers.
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The Old Kingdom of Egypt is established a while after Menes from the upper region of Egypt had conquered the lower region. This is the period in which many recognizable aspects of ancient Egyptian culture begin to appear. The creation of Pyramids and the establishment of Pharaohs are some of many examples of this.
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Sargon the Great becomes the first ruler of the Akkadian Empire. He was well-known for conquering the Sumerian city-states in the 24th - 23rd century BCE.
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The sixth Babylonian king known as Hammurabi created one of the first forms of law which was known as the Code of Hammurabi. It is the longest surviving text from the period of Old Babylon, and is also one of the oldest examples of a written law.
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The Rhind Papyrus is an early example of Egyptian Mathematics. It worked as a sort of instruction manual for arithmetic and geometry. It demonstrated the ways in which multiplication and division were utilized during that time period.
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The Babylonian army led by Nebuchadnezzar II fought with the Egyptians and Assyrians who were unfortunately destroyed. After the battle, Assyria no longer existed as an independent nation and Egypt's influence in the Ancient Near East was reduced to nothing.
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The Persians had conquered Egypt for a period of time, and although they weren't exactly welcomed with open arms by the Egyptians, they were certainly regarded as more merciful and peaceful than previous conquerors of Egypt.
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The Battle of Pelusium was a battle that involved the Achaemenid Empire (also the First Persian Empire) and Egypt. It was fought in a city east of the Nile Delta known as Pelusia. The Egyptians had lost a total of 50,000 troops, while the Persians had lost a comparatively smaller amount of 7,000 troops.