Titlebook: Ancient Mathematics; History of Mathemati Dietmar Herrmann Book 20221st edition The Editor(s) (if applicable) and The Author(s), under excl

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Introduction,Chapter . describes the emergence of a new Greek culture, which leads to a new beginning of Greek civilization, which later becomes predominant in all of Europe. With the emergence of the sciences, mathematics also develops.

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Athens and the Academy,The origin of the name . (ancient Greek Αθήναι, today Αθήνα) is not yet clarified, as the etymological roots of the term are unclear. It is assumed that the name derives from the city’s protective goddess, Athena, but it is also possible that the goddess was named after the city.

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Euclid of Alexandria,Euclid, actually called Euclides (Ευκλείδης), was probably born in Alexandria around 360 BC. Since Book XII and parts of Book V of his . originate from Eudoxus, many authors believe Euclid having studied in Athens at the Academy; this is by no means secure. He was appointed to Alexandria by Ptolemy I Soter (ruled 305–285 BC).

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The Classical Problems of Greek Mathematics,The fact that the ratio of the diagonal to the side in a square is not commensurable was a great disappointment to the early Pythagoreans, who believed that . all ratios are commensurable, i.e. representable by a ratio of whole numbers.

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Eratosthenes of Cyrene,Eratosthenes (Fig. 13.1) (΄Ερατοσϑένης ὁ Κυρηναῖος) from Kyrene (today Shahat/Libya) lived from 273-192 BC and was a contemporary and correspondent of Archimedes for the Alexandrian mathematicians.

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Apollonius of Perga,Very little is known about the life of Apollonius (Aπολλώνιος) of Perga/Perge. As his origin suggests, he was born in Perga (today Murtina/Turkey) during the reign of Ptolemaios III Euergertes.

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Beginnings of Trigonometry,The beginnings of trigonometry are found in the astronomy of the Greeks. The most important contributions to its beginning were made by . and .. The results of the latter two are taken over by C. Ptolemy in his ., omitting the share of Menelaos.