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Ancient Greek Science
Thales of Mitetus was one of the first ancient Greek scientists who along with others tried to look at things from a logic and mathematical sense, and tried to study the nature of the world including the sun, sky and weather and indeed our relationship with other planets including the moon.
From about 600 BC, Greek scientists spent time observing the planets and the sun and trying to figure out how astronomy worked. They followed the observations of the Babylonians, who were very good at astronomy because of their obvious interest in it.
By the 400's BC, Pythagoras studied rules in mathematics and music, and invented the idea of a mathematical proof. In the 300's BC, the ancient Greek scientists studied Botany and agriculture, which lead to the the process of looking at plants as a whole and what benefit they could be to us in the form of food and medicine.
Aristotle and other philosophers at the Lyceum and the Academy in Athens worked on the observation of botanics and all living things including humans and animals, as a way of creating order out of chaos.
Theophrastus was a student of Aristotle and he was one of the first to name plants and animals. This was how the study of Botany was invented after Aristotle, using his ideas and also ideas from Egypt and the Persians and Indians, Hippocrates and other Greek doctors wrote important medical texts that were used for hundreds of years.
Eudemus wrote the history of Greek mathematics and astronomy. Unfortunately very little of this have survived, included in the works of later authors.
Earth Science became the study of the location of metal and mineral deposits and the study of fossils. Furthermore, the information about evolution and the Earth's other fossil fuel such as oil, became important and helped scientists, throughout the generations since.

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