Some problems of diophantus franz lemmermeyer december 21, 2003 it is believed that diophantus worked around 250 ad. His equations are linear or quadratic and are composed of units, roots and squares. What little is known of diophantuss life is circumstantial. In it he introduced algebraic manipulations on equations including a symbol for one unknown probably following other authors in alexandria. Diophantus of alexandria a study in the history of greek. One of his greatest contributions is the book of arithmetica. The earliest surviving texts are from copies in arabic transmitted through the islamic world, before returning to western europe in the 1600s via translations from arabic back into greek or latin. The text used is the edition of tannery 1893, but i have also consulted the translation of ver eecke 1959 and the paraphrase of heath 1910. We may generalize diophantus s solution to solve the problem for any given square, which we will represent algebraically as a 2. The problems he worked on were mostly linear systems of equations with a few quadratics. Books iv to vii of diophantus arithmetica springerlink.
Addition was indicated by placing the numbers side by side, subtraction by placing a dot over the subtrahend, and division by placing the divisor below the dividend, similar to our notation but without the bar. Some of the things i found though were that he studied at the university of alexandria in egypt. One, porisms, is completely lost, and only a fragment remains of another, on polygonal numbers. Diodorus siculus, greek historian of agyrium in sicily, ca.
His writing, the arithmetica, originally in books six survive in greek. Modern historians of mathematics sometimes wrangle over book 2 of euclids elements from. Arithmetica is an ancient greek text on mathematics written by the mathematician diophantus. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations. This edition contains the seminal mathematic work of diaphanous in a more consolidated and applicable form, containing chapters such as. Engage your students during remote learning with video readalouds. Arithmetica originally had thirteen books, out of which we only have six. However six books from thirteen of his most important work, arithmetica, are still in existence through a latin translation of the original greek text by xlander in the. Diophantus of alexandria a study in the history of greek algebra.
Heath briefly goes through the histories of the various translations. Sources in the history of mathematics and physical sciences, vol 3. We know he must have lived after 150 bc since he quotes in his. He is sometimes called the father of algebra, and wrote an influential series of books called the arithmetica, a collection of algebraic problems which greatly influenced the subsequent development of number theory. The history of algebra is very intriguing because of the many cultures that contributed to its origins. For example, to alkhwarizmi a unit was a number, a root was x, and a square was x 2. Diophantus of alexandria, sometimes called the father of algebra, was an alexandrian mathematician and the author of a series of books called arithmetica. Diophantus, often known as the father of algebra, is best known for his. It is a collection of algebraic problems giving numerical solutions of. Diophantus biography, facts and pictures famous scientists. Diophantes was a hellenistic greek mathematician who lived around 200 ad.
From the appellation of alexandria it seems that he worked in the main scientific centre of the ancient greek world. Generalized solution in which the sides of triangle oab form a rational triple if line cb has a rational gradient t. Diophantus, the father of algebra, told this when ask his age. He did numerous things for the world of mathematics. Sep 17, 2014 the history of algebra is very intriguing because of the many cultures that contributed to its origins. It is with this in mind that the author endeavored to make accessible again the teachings contained within this rare tome. The year associated with syncopated algebra is 275 because diophantus was probably the first to take steps toward an algebraic notation. Heath, thomas little, sir, 18611940,euler, leonhard, 17071783.
Diophantus s book text book is wonderful if one wants to learn about greek mathematics by puzzling through and by attempting to follow how he solved a lot of complex, complicated algebra problems. Roughly five centuries after euclids era, he solved hundreds of algebraic equations in his great work arithmetica, and was the first person to use algebraic notation and symbolism today we usually indicate the unknown quantity in algebraic equations with the letter x. In book 3, diophantus solves problems of finding values which make two linear. Diophantus of alexandria arithmetica book i joseph. Diophantus arithmetica consists of books written originally in greek circa in 270 ce. His text the arithmetica was composed of books and 189 problems. What little is known of diophantus s life is circumstantial.
His main work arithmetica consists of 7 books of worked examples on rational solutions of indeterminate equations. Deakin the american mathematical monthly,march 1994, volume 101, number 3, pp. From aristarchus to diophantus dover books on mathematics 9780486240749 by heath, sir thomas and a great selection of similar new, used and collectible books available now at great prices. Is there an english translation of diophantuss arithmetica. The silver age of alexandria, also known as the later alexandrian age, was about 250 350 c. Copy and paste one of these options to share this book elsewhere. I found very little known facts about diophantus s life. In pursuing this question, some modern historians of mathematics have contested the old and broadly accepted view that the work of diophantus belongs to the history of algebra. Diophantine equations i putnam practice october 27, 2004 in his book arithmetica diophantus discussed the problem of. Diophantus, greek mathematician, famous for his work in algebra.
Histoire du livre in france, geschichte des buchwesens in germany, history of books or of the book in englishspeaking countries. The information from these books tell us that diophantus studied from babylonian teachers as his works are inspired from greek and babylonian observes. Diophantus about 200 about 284 mactutor history of mathematics. God granted him to be a boy for the sixth part of his life, and adding a twelfth part to this, he clothed his cheeks with down. Search the history of over 424 billion web pages on the internet. However, his work led to one of the greatest mathematical challenges of all time, fermats last theorem. The information from these books tell us that diophantus studied from babylonian teachers. Go to abbreviations for forms go to rules for manipulations of forms go to prob. These steps were mostly stenographic abbreviations, to help with printing. The first edition of this book, which was the first english diophantus, appeared in 1885 and has long been out of print.
Like the algebra of diophantus, the algebra of brahmagupta was syncopated. Fifth book of the treatise of diophantus the alexandrian on. His claim to fame comes from substituting symbols for numbers and operations in equations, thus creating algebra, but everything else we know about his life comes from a single algebraic riddle. Little is known about the life of the greek mathematician diophantus. Porismata is a collection of lemmas, although the book is entirely lost. Diophantus, often referred to as the father of algebra, is best known for his arithmetica, a unique collection of 189 algebraic equations and their solutions. The first woman mathematician of whom we have reasonably secure and detailed knowledge is hypatia of alexandria. Diophantus was born and lived in alexandria, now in egypt, which was at the time a great center of culture and learning in. Little is known about the life of diophantus and even the exact time when he lived is a matter of debate among historians. Having introduced the natural numbers, alkhwarizmi introduces the main topic of this first section of his book, namely the solution of equations. The change from rhetorical to syncopated to symbolic was a transition. Contribution to mathematics arithmetika a major work of diophantus, is considered to be the most noticeable and influential work done on algebra in greek history. From aristarchus to diophantus dover books on mathematics on free shipping on qualified orders.
Although there were many ancient civilizations that studied algebra, there are two men that are best know for bringing algebra to our modern day. This edition of books iv to vii of diophantus arithmetica, which are extant only in a recently discovered arabic translation, is the outgrowth of a doctoral dissertation submitted to the brown university department of the history of mathematics in may 1975. Diophantus, a greek algebraist of this era, was thought to belong to this time period, but there is some uncertainty to the exact time frame of his life. A history of algebra from antiquity to the early twentieth century on free shipping on qualified orders.