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He made his observations with very simple instruments, using an ordinary plumb-line to measure the angles of elevation of the stars. He also introduced a mathematical innovation by using Hindu-Arabic numerals in his sine tables, the first transition from the duodecimal to the decimal system.
He made his observations with very simple instruments, using an ordinary plumb-line to measure the angles of elevation of the stars. He also introduced a mathematical innovation by using Hindu-Arabic numerals in his sine tables, the first transition from the duodecimal to the decimal system.
Such was the accuracy of Purbach's set tables that they were still in use almost two hundred years later. He also compiled a table of sines, using Arabic numerals, and was one of the first to popularize their use instead of chords in trigonometry. From: Purbach, Georg von in A Dictionary of Scientists. Peuerbach's life remains relatively unknown until he enrolled at the University of Vienna in 1446.[3] He was born in the Austrian town of Peuerbach in upper Austria. A horoscope published eighty-nine years after his death places his date of birth specifically on May 30, 1423, though other evidence only indicates that he was born sometime after 1421.[4] He received his Bachelor of Arts in 1448.
Georg's intellect was discovered by a priest of his hometown, Dr. Heinrich Barucher. Dr. Barucher recognized Peuerbach's academic abilities from a young age and put him in contact with the Augustinian provost of Klosterneuburg Monastery, Georg Muestinger.[5] Georg Muestinge taught a course at the University of Vienna entitled Theoricae Planetarum. These lectures was the first that George von Peuerbach attended at the University of Vienna and inspired him to enroll.
During his time at University of Vienna, Georg received a master of philosophy in 1446 and a second master's degree in 1448, studying mathematics under the guidelines of Johann von Gmünden.[6] His curriculum was composed primarily of humanities courses, as was usual at the time.[7] His knowledge of astronomy derived from independent study, possibly from studying under followers of John von Gmünden.[4] During his enrollment, there were no professors of astronomy at the University of Vienna.[7] However, under his tutelage astronomic studies emerged at the University of Vienna throughout the 15th and 16th centuries.
Peuerbach observed the occultation of Jupiter by the Moon in 1451, signifying the beginning of his personal astronomy career. After this point Peuerbach essentially devoted his life to astronomy, he developed tools and theories, and collaborated with his pupil Regiomontanus (Johannes Müller von Königsberg) to make Astrology more digestible to common people.[8] Majority of Georg's astrological discoveries were made in the last ten years of his life.[9]
Georg Peuerbach traveled through central and southern Europe, most notably in Italy, giving lectures on astronomy. His lectures led to offers of professorships at several universities, including those at Bologna and Padua. During this time he also met Italian astronomer Giovanni Bianchini of Ferrara, perhaps the leading astronomer at the time, and the Cardinal Nicholas of Cusa.[7] He returned to the University of Vienna in 1453, earned his Masters of Arts, and began lecturing on Latin poetry.[3] He is often credited as a leader in reviving classical Greek and Roman literature in arts and sciences.[4]
Peuerbach attended many university lectures that focused on Roman poets, which led to him playing one of the leading roles in the revitalization of classical learning introduced by Aenaes Silvius Piccolomini.[4] Peuerbach eventually followed the advice of the court astrologer to Emperor Friedrich III in Wiener-Nestadt, Johann Nihil, and took the position of court astrologer to the king of Hungary. After being court astrologer for a few years, Peuerbach eventually went on to become imperial astrologer.[4]
While at Vienna in 1454, Peuerbach taught planetary motion to students at the university. Peuerbach's lectures were based on Ptolemaic teachings and became so famous that from 1472 they were printed under the title ‘Theoricae Novae Planetarum‘.[10]
In 1454 Peuerbach was appointed court astrologer to King Ladislas V of Bohemia and Hungary. It was in this capacity that Peuerbach first met Ladislas' cousin Frederick who was then serving as guardian to the 14-year-old king and who would later become Frederick III, Holy Roman Emperor. Ladislas resided primarily in Prague and Vienna, allowing Peuerbach to maintain his position at the University of Vienna. During this time Peuerbach met Regiomontanus, who was then a student at the university. After Regiomontanus graduated in 1452 at the age of 15, he began collaborating extensively with Peuerbach in his astronomical work.[7] In 1457, following the assassination of two notable political figures, Ladislas fled Vienna and died in 1458. Peurbach did not receive an appointment from either of Ladislas' two successors.[7] However he was asked to be the Astronomus caesaris for Emperor Frederick III, which is the position he held until his death.[5]
Georg von Peuerbach passed away on April 8, 1461. His work set the path for future scholars, scientists, and astronomers for years to come; Peurbach’s early death was a serious loss to the progress of astronomy, [11] although Regiomontanus, his successor, was able to continue his work.
Georg von Purbach was a 15th century Austrian mathematician and astronomer who made several contributions to trigonometry. He wrote a book called "Theoricae Novae Planetarum" which contains the first systematic treatment of trigonometry in the modern sense.
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He also introduced the concept of the sine and
He also introduced the concept of the sine and cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.
cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.
cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.
cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.
cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.cosine functions, which are now fundamental to trigonometry and other branches of mathematics. Purbach also made significant contributions to the field of astronomy, including the calculation of the solar and lunar tables.
Georg von Peurbach (1423-1461), also known as Georg Peurbach or Georgius Purbachius, was an Austrian mathematician and astronomer who made significant contributions to the development of trigonometry during the Renaissance period.
Here are some of his key contributions:
Improved trigonometric tables: Von Peurbach was one of the first mathematicians to recognize the importance of accurate trigonometric tables in astronomy and other fields. He collaborated with his student Regiomontanus to produce more accurate and comprehensive tables of sines, cosines, and tangents.
Developed the theory of spherical trigonometry: Von Peurbach extended the principles of planar trigonometry to the study of spherical triangles, which are triangles that are formed on the surface of a sphere. His work on spherical trigonometry was particularly important for navigators and astronomers, who used it to calculate positions and distances in the sky and on the Earth.
Influenced other mathematicians: Von Peurbach's work on trigonometry was influential in the development of mathematics in the 15th and 16th centuries. His books, including "Theoricae novae planetarum" and "Epitome in almagestum Ptolomei," were widely read and studied by other mathematicians, including Johannes Kepler and Nicolaus Copernicus.
Overall, Georg von Peurbach's contributions to trigonometry helped to lay the foundation for the development of modern mathematics and astronomy. His work on trigonometric tables and spherical trigonometry was particularly important for practical applications in navigation and astronomy, and his influence can still be seen in mathematics and science today.
His most important contribution was the production of tables of the sine function.
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