Liber Mahameleth

ISBN-13: 9783319039398 / Angielski / Twarda / 2014 / 1734 str.

Jacques Sesiano

Opis

The Liber mahameleth is a work in Latin written in the mid-12th century based (mainly) on Arabic sources from Islamic Spain. It is now our principal source on mathematics in Islamic Spain at that time; There are few extant Arabic texts and no one is as complete as the LM. It is also the second largest mathematical work from the Latin Middle Ages (the other is by Fibonacci, some 50 years later).Since the three main manuscripts preserving it are incomplete and there are many scribal errors, a reliable Latin text has been established, which reports (in notes) the various readings of the manuscripts and the errors in them. This is how a so-called critical edition is made. This edition of the Latin text is preceded by General Introduction, describing the various manuscripts, the content of the work and what we know about its author.Part Two of the volume is a translation of the text and ends with a glossary of Latin terms. The glossary will be of great importance for the knowledge of Latin scientific terms from that time, since there is no other mathematical text of this size from the 12th century. Part Three begins with a short introduction and then analyzes all the problems from the text, with a summary of the mathematical methods involved in each chapter. The commentary is a companion to the translation and explains the author's solving methods.

Recenzje

"Sesiano's description of the manuscripts is excellent. Furthermore, his translations are precise and readable, and his mathematical commentary is clear and useful. Overall, the work is a splendid contribution by Sesiano to the field of history of mathematics. The careful, critically edited Latin text will be of interest mainly to specialists, but the English translation and study will be of broader interest." (Toke Lindegaard Knudsen, Mathematical Reviews, March, 2016)

"Sesiano's book is a milestone in the history of medieval mathematics. It not only makes available one of the most important mathematical treatises in an excellent edition with English translation, but also gives a detailed analysis of the different problems and the methods for solving them and presents a comprehensive glossary which is also useful for non-mathematical texts." (Menso Folkerts, Historia Mathematica, Vol. 42, 2015)

Spis treści

Part I.- 1. The rebirth of mathematics in mediaeval Europe.- 2. The Liber mahameleth.- 3. Manuscripts of the Liber mahameleth.- 4. Transmission of the Liber mahameleth.- 5. Mathematics in the Liber mahameleth.- 6. The edited Latin text.- Part II.- Translation.- Beginning of the Book (on) mahameleth.- A-I. on Numbers.- A-II. on the Premisses necessary for practical arithmetic.- A-III. on Multiplication.- A-IV. on Division.- A-V. on the Multiplication of fractions.- A-VI. on the Addition of fractions to fractions.- A-VII. on Subtracting.- A-VIII. on the Division of fractions, with or without integers.- A-IX. on the Determination of roots and on their multiplication, division, subtraction, addition and other related subjects.- Beginning of the Second Part.- B-I. on Buying and selling.- B-II. on Profits.- B-III. on Profit in partnership.- B-IV. on Division according to portions.- B-V. on Masses.- B-VI. on Drapery.- B-VIII. on Linens.- B-VIII. on Grinding.- B-IX. on Boiling must.- B-X. on Borrowing.- B-XI. on Hiring.- B-XII. on the Diversity of workers' wages.- B-XIII on Hiring carriers.- B-XIV. on Hiring stone-cutters.- B-XV. on the Consumption of oil by lamps.- B-XVI. on the Consumption by animals.- B-XVII. on the Consumption of bread by men.- B-XVIII. on the Exchange of morabitini.- B-XIX. on Cisterns.- XX. on Ladders.- B-XXI. on Another topic.- B-XXII. on Messengers.- B-XXIII. on Another topic.- Glossary.- Part III.- Mathematical Commentary.- Book A.- A-I. Numbers.- A-II. Premisses.- A-III. Multiplication of Integers.- A-IV. Division of integers.- A-V. Multiplication of fractions.- A-VI. Addition of fractions.- A-VII. Subtraction of fractions.- A-VIII. Division of fractions.- A-IX. Roots.- Book B.- Introduction.- B-I. Buying and selling.- B-II. Profit.- B-III. Profit in partnership.- B-IV. Sharing out according to prescribed parts.- B-V. Masses.- B-VI. Drapery.- B-VII. Linen cloths.- B-VIII. Grinding.- B-IX. Boiling must.- B-X. Borrowing.- B-XI. Hiring workers.- B-XII. Wages in arithmetical progression.- B-XIII. Hiring a carrier.- B-XIV. Hiring stone-cutters.- B-XV. Consumption of lamp-oil.- B-XVI. Consumption by animals.- B-XVII. Consumption of bread.- B-XVIII. Exchanging moneys.- B-XIX. Cisterns.- B-XX. Ladders.- B-XXI. Bundles.- B-XXII. Messengers.- B-XXIII. Mutual lending.- Bibliography.- Index.