The historical development of algebraic equations from the Ancient Babylonias to Ars Magna -1545 Α.C (Girolamo Cardano)

Postgraduate Thesis uoadl:2895926 192 Read counter

Unit:
Κατεύθυνση Διδακτική και Μεθοδολογία των Μαθηματικών
Library of the School of Science
Deposit date:
2020-01-25
Year:
2020
Author:
Φουσέκη Παναγιώτα
Supervisors info:
Σταύρος Γ, Παπασταυρίδης , Ομότιμος Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Η ιστορική εξέλιξη των αλγεβρικών εξισώσεων από την αρχαία Βαβυλώνα έως το Ars Magna - 1545 μ.Χ. (Girolamo Cardano)
Languages:
Greek
Translated title:
The historical development of algebraic equations from the Ancient Babylonias to Ars Magna -1545 Α.C (Girolamo Cardano)
Summary:
The purpose of this thesis is to monitor how the second- and third-degree equations evolved from antiquity to Ars Magna. The equations made their appearance in mathematics from antiquity even more specifically from the period of Egyptian civilization. The Greek civilization is the one that differed in relation to the others as it introduced the concept of proof. In the beginning they developed mainly through geometry and the effort to solve them, became geometric. The non-existence of symbols made them difficult to manage and it became easier only after the introduction of the Indian numbering system. The non-existence and non - acceptance of negative numbers and complex numbers (which were discovered very late in the 16th century approx.) was another obstacle to their development. The Arabs were the first to start having a more algebraic approach, yet their influences from ancient Greece and the need for geometric proof led them-limited to the non-use of negative numbers. In Europe, the scientific renaissance began in Italy. The development of trade led many Italian traders to travel and become acquainted mainly with the Arab culture, which at that time was descending. The Italian Fibonnaci in his travels met the algebra of the Arabs and the Indian-Arabic numbering system. This numbering system greatly facilitated the calculations and soon became widely acceptable. Liber Abbaci was very influential to the forthcoming mathematicians. The translation of Arabic texts into Latin helped to the further development of algebra and gradually led to the resolution of the cubic equations from Cardano in his work Ars Magna. In Ars Magna we are also given the solution of a form of quartic equations, by Ludovico Ferrari pupil and servant of Cardano. At that time, it still seems to be a link between equations and geometry as Cardano in Ars Magna gives a geometric approach in addition to algebraic
Main subject category:
Science
Keywords:
Quadratic equations, cubic equations, Ars Magna
Index:
Yes
Number of index pages:
2
Contains images:
Yes
Number of references:
35
Number of pages:
254
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