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Much of the early Greek arithmetic and geometry can be traced back to the Pythagoreans. He worked on the problems of squaring the circle and duplicating the cube. Among his accomplishments was to bring the ordinary citizen into the Athenian democracy.

While working on the problem of squaring the circle, he was able to find the areas of lunes. E.) Hippocrates of Cos is known to us as the Father of Western Medicine and he is credited with originating the Hippocratic Oath that all doctors take upon completing their studies. He was a gifted orator as was documented by the historian Thycidides.

It appears that rather than contradict each other, the tale of Aeneas adds to that of Romulus and Remus. This agrees very closely to the established legend that Rome was founded on 21 April 753 B. He is also credited by some historians with being the “Father of deductive geometry.” Thales is usually credited with five theorems of elementary geometry: A circle is bisected by any diameter. The mathematikoi lived permanently with the Society, had no personal possessions and were vegetarians.

Archaeological evidence shows that early settlement of the Palatine Hill dates back to about 750 B. The base angles of an isosceles triangle are equal. They were taught by Pythagoras himself and obeyed strict rules set down by Pythagoras. E.) Zeno was an Eleatic philosopher and was a favorite disciple of Parmenides.

All of what we know of Pythagoras and his followers come from commentators who lived a hundred years of more later, since it appears that all knowledge and information was passed on orally. This empire lasted for over two centuries until it was divided by the successors of Alexander the Great. Four of the paradoxes were to have a significant impact on the development of mathematics. E) Under the leadership of the statesman Pericles, Greece reached the height of its glory in the 5th century BCE.

What has become evident is that Pythagoras and his followers were considered to be, among other things, pure mathematicians. An interesting discussion of these can be found at Hippocrates of Chios (470 – 410 B. E.) Hippocrates of Chios was an excellent geometer who taught in Athens. Pericles was born to a family of wealth and position.

THE PLAGUE IN ATHENS DURING THE PELOPONNESIAN WAR The plague in Athens was caused by the war strategy of Pericles. The curve may be used for dividing an angle into any number of equal parts.

His strategy was to bring all citizens from the surrounding area into Athens and let the Spartans have control of the outlying area. It appears that this was the first curve in in mathematics that was not either a straight line or part of a circle.

With arrangements of these two symbols they could represnt numbers of any size.

Numbers between 1 and 59 were the symbols for 1 and 10 tightly grouped together.

When these "digits" were to multiply powers of 60, they were separated by more space.

The angles between two intersecting straight lines are equal. All knowledge and discoveries were attributed to Pythagoras. E.), the Persians, under the leadership of King Cyrus, took Babylon, the ancient capital of a middle eastern empire covering modern Iraq, Syria, Lebanon, and Israel, and thus became masters of Western Asia. E.) Parmenides was Greek philosopher who was a follower of Pythagoras. Philosophers of his time considered his philosophy to be quite negative.

Two triangles are congruent if they have two angles and one side equal. The rule that probably had the most impact on the history of mathematics was that all members of the brotherhood should observe strict loyalty to Pythagoras and the brotherhood and maintain secrecy. A remarkable aspect of the capture of Babylon is the fact that Cyrus allowed the Jews (who were exiled in Babylonia) to return home. He was an early believer of a cosmology that consisted of a spherical earth and a finite, motionless, spherical universe. Zeno wrote a book that reportedly contained forty paradoxes concerning the continuum.

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The axle rotated against the bed of the vehicle and this probably helped round the axles.

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