Roman Mathematics: Boethius and Cassiodorus
For those who are interested in tracing developments in theoretical mathematics, the Roman period is singularly barren of interest. However excellent the Romans may have been in the arts, literature, and law, they showed no disposition to master the Greek sciences, let alone to add to them. As the early Church emerged from the catacombs, people argued less about mathematics and more about salvation. Learning of any kind was deemed useful as it was necessary for the proper understanding of the Scriptures and the writings of the Church fathers. The trivium of liberal arts became the accepted format of Christian education; and within the trivium, the study of grammar and rhetoric received far more attention than what was devoted to logic. Contributing to this lack of interest in theoretical studies was the fact that a knowledge of the Greek language, in which much of the scientific learning of antiquity remained, gradually faded in the Latin-speaking West.
Perhaps the best known Roman commentator to interest himself in the Greek works then available was Anicius Boethius (circa 475-524). Memorably characterized as “the last of the Romans and the first of the Scholastics,” Boethius provided a bridge between Antiquity and the Middle Ages. Born into one of the wealthy and illustrious families of senatorial rank, he received the best education to be had in those troubled times. Scholars disagree over where Boethius was educated, some favoring Athens and others Alexandria. As a young man Boethius entered the Roman administrative system. The Ostrogothic king Theodoric, who had ruled Italy since 493, needed the experience of the old Roman aristocracy in his task of governing. Holding a number of trusted positions, Boethius reached the height of his political power in 522 when he became Master of the Offices, a post in which he functioned virtually as the king’s prime minister. Soon afterward, Boethius fell out of Theodoric’s favor and was accused of treasonable conduct. The official charge – widely accepted now as unjust – was that he corresponded with the Byzantine Emperor Justinian in a conspiracy to overthrow Theodoric. In prison awaiting execution, Boethius wrote the Consolation of Philosophy, one of the classics of Western thought.
Boethius, realizing the sad state of the sciences and aware of his own command of Greek, had previously embarked on the ambitious program of providing the scholars of his day with textbooks on all four subjects of the quadrivium (arithmetic, geometry, music, and astronomy). His geometry consisted of nothing more than definitions and statements of theorems – with no proofs – from Books I, III, and IV of the Elements, along with various practical applications. Boethius’s popular work, De Institutione Arithmetica, is actually a paraphrase, bordering on a translation, of the Introduction Arithmeticae of Nicomachus. Although occasionally adding material and condensing portions of the original, Boethius contributed nothing really new. He was not an expert mathematician, and in his departures from Nicomachus he was trying to exhibit his own talents, after the fashion of Latin commentators. Yet such was the poverty of mathematical learning of the time that it is mainly through Boethius that the Middle Ages came to know the principles of formal arithmetic. His Arithmetica remained for over a thousand years the authoritative text on the subject in monastic schools (that the Church proclaimed him a martyr no doubt helped too). Indeed, the last known edition of Boethius’s Arithmetica was published in Paris in 1521. In the East, meanwhile, the Greek masterpieces were being zealously preserved, studied, and recopied by each generation. After the original texts were rediscovered by the Latin West in the fifteenth century, Boethius sank into an obscurity that became as great as his reputation once was.
Magnus Aurelius Cassiodorus (circa 480-575), a younger friend of Boethius and not so great a scholar, yet made a more substantial contribution to the preservation of the classical heritage. Like Boethius, he was a Roman aristocrat who rose to high position in the government of Theodoric. Upon retiring from public life to his estate at Vivarium, Cassiodorus founded a large monastery with the conscious aim of making it a center of Christian learning and scholarship – the first education – oriented monastic house. This involved the creation of a scriptorium for the translation into Latin of the classical texts to be studied; copies were made for their own library and to be sent to monasteries that were less well equipped. For the education of his monks and to facilitate their teaching of others, Cassiodorus composed the Introduction to Divine and Human Writings. Most of it was devoted to holy scripture and the works of the church fathers, but he did offer a brief discussion of each of the seven liberal arts. This primitive textbook served as the basis of the curriculum of the church schools in the early Middle Ages.
โรมันคณิตศาสตร์: Boethius และ Cassiodorus ระยะเวลาโรมันจะไม่แห้งแล้ง singularly ที่น่าสนใจสำหรับผู้ที่สนใจในการติดตามพัฒนาในทฤษฎีคณิตศาสตร์ แต่แห่งโรมอาจมีในศิลปะ วรรณคดี และกฏหมาย พวกเขาพบไม่ครอบครองหลักศาสตร์กรีก นับประสาเพิ่มไป เป็นคริสตจักรก่อนเกิดจากสุสาน คนโต้เถียงน้อยเกี่ยวกับคณิตศาสตร์เกี่ยวกับความรอด เรียนรู้ใด ๆ ถือว่ามีประโยชน์ก็จำเป็นสำหรับความเข้าใจพระคัมภีร์ที่เหมาะสมและงานเขียนของบรรพบุรุษคริสตจักร Trivium ของศิลปศาสตร์กลายเป็น รูปแบบยอมรับของคริสเตียนศึกษา และภายใน trivium วิชาไวยากรณ์และสำนวนได้รับความสนใจมากกว่าไกลกว่าสิ่งที่ทุ่มเทให้กับตรรกะ เอื้อต่อการนี้ขาดความสนใจในการศึกษาทฤษฎีเป็นความจริงที่ว่าความรู้ของภาษากรีก ที่มากของการเรียนรู้วิทยาศาสตร์ของยังคง สีจางลงทิศตะวันตกติพูดค่อย ๆ บางทีวิจารณ์โรมันรู้จักกันดีไปสนใจตัวเอง ในงานกรีก แล้วว่างถูก Anicius Boethius (เซอร์กา 475-524) ลักษณะเป็น "สุดท้ายของโรมและแรกของเดอะ Scholastics" น่าจดจำ Boethius ให้สะพานระหว่างโบราณและยุคกลาง เกิดในครอบครัวที่มั่งคั่ง และนานของ senatorial อันดับหนึ่ง เขาได้รับการศึกษาดีที่สุดที่จะได้ในผู้ที่ปัญหาเรื่องเวลา นักวิชาการไม่เห็นด้วยที่มีศึกษา Boethius เอเธนส์บาง favoring และอื่น ๆ ซานเดรีย เป็นชายหนุ่ม Boethius ป้อนระบบปกครองโรมัน พระ Ostrogothic Theodoric ที่มีปกครองอิตาลีตั้งแต่ 493 ประสบการณ์ของขุนนางโรมันเก่าที่จำเป็นในงานของเขาควบคุม กดหมายเลขของตำแหน่งที่เชื่อถือได้ Boethius แล้วความสูงของอำนาจทางการเมืองใน 522 กลายเป็นต้นแบบของสำนักงาน โพสต์ที่เขาแยกแทบเป็นกษัตริย์นายกรัฐมนตรี เร็ว ๆ นี้หลังจากนั้น Boethius ตกตกกระป๋องของ Theodoric และได้ถูกกล่าวหาว่าประพฤติข้อ ค่าธรรมเนียมราชการ – ยอมรับอย่างกว้างขวางนี้เป็นฝ่ายอธรรม – ถูกว่า เขา corresponded กับ Justinian จักรพรรดิไบแซนไทน์ในโค่น Theodoric จำคุกที่รอการดำเนินการ Boethius เขียนปลอบโยนของปรัชญา คลาสสิกของตะวันตกที่คิดอย่างใดอย่างหนึ่ง Boethius, realizing the sad state of the sciences and aware of his own command of Greek, had previously embarked on the ambitious program of providing the scholars of his day with textbooks on all four subjects of the quadrivium (arithmetic, geometry, music, and astronomy). His geometry consisted of nothing more than definitions and statements of theorems – with no proofs – from Books I, III, and IV of the Elements, along with various practical applications. Boethius’s popular work, De Institutione Arithmetica, is actually a paraphrase, bordering on a translation, of the Introduction Arithmeticae of Nicomachus. Although occasionally adding material and condensing portions of the original, Boethius contributed nothing really new. He was not an expert mathematician, and in his departures from Nicomachus he was trying to exhibit his own talents, after the fashion of Latin commentators. Yet such was the poverty of mathematical learning of the time that it is mainly through Boethius that the Middle Ages came to know the principles of formal arithmetic. His Arithmetica remained for over a thousand years the authoritative text on the subject in monastic schools (that the Church proclaimed him a martyr no doubt helped too). Indeed, the last known edition of Boethius’s Arithmetica was published in Paris in 1521. In the East, meanwhile, the Greek masterpieces were being zealously preserved, studied, and recopied by each generation. After the original texts were rediscovered by the Latin West in the fifteenth century, Boethius sank into an obscurity that became as great as his reputation once was. Magnus Aurelius Cassiodorus (circa 480-575), a younger friend of Boethius and not so great a scholar, yet made a more substantial contribution to the preservation of the classical heritage. Like Boethius, he was a Roman aristocrat who rose to high position in the government of Theodoric. Upon retiring from public life to his estate at Vivarium, Cassiodorus founded a large monastery with the conscious aim of making it a center of Christian learning and scholarship – the first education – oriented monastic house. This involved the creation of a scriptorium for the translation into Latin of the classical texts to be studied; copies were made for their own library and to be sent to monasteries that were less well equipped. For the education of his monks and to facilitate their teaching of others, Cassiodorus composed the Introduction to Divine and Human Writings. Most of it was devoted to holy scripture and the works of the church fathers, but he did offer a brief discussion of each of the seven liberal arts. This primitive textbook served as the basis of the curriculum of the church schools in the early Middle Ages.
การแปล กรุณารอสักครู่..