History of diophantus biography of abraham lincoln

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All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single entry from a reference work in OR for personal use for details see Privacy Policy and Legal Notice. Personal Profile. Oxford Reference. The book contains easily understood examples of how solving algebraic problems could be handled.

Basically, this book is an opening call to what is to follow in the other books realizing only that six books were known to have remained. As mentioned before about indeterminates more than one solution is possible , Book II and on follow the deeper work. Also Diophantus placed into the books the concept that equations can be reduced to easier expression and that the result will be a rational realization of the problem.

This means the result will extensibly be in the form of a numerical square or even a cube. Remembering that Diophantus did not believe in negative numbers, or zero for that matter; the result must imply a positive, rational numerical entity. Book II begins illustrating general methods. For example, in Book II, three problems give these details:.

History of diophantus biography of abraham lincoln

His book also gives rise to what an integer number is in his view. He did not prescribe to a belief in negative numbers, so integer use had to never give an allusion to negative possibilities. Although he did not prescribe to the concept, he was willing to acknowledge that different methods could exist which obviously would preclude his concept of below zero integers.

The case for number theory. In Books IV through VI, Diophantus gives the case for deeper degrees of equations having simplified methods for their being solved. His desire is that the reader of his books will practice the methods of their own volition to prove his points. So it seems that teaching methods was a big reason for the concept of the books of this collection.

Diophantus was declaring in Arithmetica that understanding and solving algebra equations should not be difficult, but made easier for the reader to practice themselves. Book VI also put into play right-angled triangles. These were looked at falling under certain situations for being handled. Diophantus is described as having written a couple of other works.

Much of their content seems to be aspects of his major work, Arithmetica. This book brings an identifiable identity to a man that seems vaporous in extent to his actual life. However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived. There are a few limits which can be put on the dates of Diophantus's life.

On the one hand Diophantus quotes the definition of a polygonal number from the work of Hypsicles so he must have written this later than BC. On the other hand Theon of Alexandria, the father of Hypatia , quotes one of Diophantus's definitions so this means that Diophantus wrote no later than AD. However this leaves a span of years, so we have not narrowed down Diophantus's dates a great deal by these pieces of information.

There is another piece of information which was accepted for many years as giving fairly accurate dates. Heath [ 3 ] quotes from a letter by Michael Psellus who lived in the last half of the 11 th century. Psellus wrote Heath's translation in [ 3 ] :- Diophantus dealt with [ Egyptian arithmetic ] more accurately, but the very learned Anatolius collected the most essential parts of the doctrine as stated by Diophantus in a different way and in the most succinct form, dedicating his work to Diophantus.

Psellus also describes in this letter the fact that Diophantus gave different names to powers of the unknown to those given by the Egyptians. This letter was first published by Paul Tannery in [ 7 ] and in that work he comments that he believes that Psellus is quoting from a commentary on Diophantus which is now lost and was probably written by Hypatia.

However, the quote given above has been used to date Diophantus using the theory that the Anatolius referred to here is the bishop of Laodicea who was a writer and teacher of mathematics and lived in the third century. From this it was deduced that Diophantus wrote around AD and the dates we have given for him are based on this argument.

Knorr in [ 16 ] criticises this interpretation, however:- But one immediately suspects something is amiss: it seems peculiar that someone would compile an abridgement of another man's work and then dedicate it to him, while the qualification "in a different way", in itself vacuous, ought to be redundant, in view of the terms "most essential" and "most succinct".

Knorr gives a different translation of the same passage showing how difficult the study of Greek mathematics is for anyone who is not an expert in classical Greek which has a remarkably different meaning:- Diophantus dealt with [ Egyptian arithmetic ] more accurately, but the very learned Anatolius, having collected the most essential parts of that man's doctrine, to a different Diophantus most succinctly addressed it.

One of the puzzles is:. This tomb holds Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son.

After consoling his grief by this science of numbers for four years, he reached the end of his life. The translation and solution of this epigram-problem infers that Diophantus' boyhood lasted fourteen years, acquired a beard at 21, and married at age He fathered a son five years later, but that son died at age 42—Diophantus, at this time, was 80 years old.

He tried to distract himself from the grief with the science of numbers, and died 4 years later, at This puzzle reveals that Diophantus lived to be about 84 years old. It is not certain if this puzzle is accurate or not. The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations.

Of the original thirteen books of which Arithmetica consisted, only six have survived, though there are some who believe that four Arab books discovered in are also by Diophantus. Some Diophantine problems from Arithmetica have been found in Arabic sources. After Diophantus's death, the Dark Ages began, spreading a shadow on math and science, and causing knowledge of Diophantus and the Arithmetica to be lost in Europe for roughly years.

Sir Heath stated in his Diophantus of Alexandria, "After the loss of Egypt, the work of Diophantus long remained almost unknown among the Byzantines; perhaps one copy only survived of the Hypatian recension , which was seen by Michael Psellus and possibly by the scholiast to Iamblichus, but of which no trace can be found after the capture of Constantinople in The first Latin translation of Arithmetica was by Bombelli who translated much of the work in , but it was never published.

Bombelli did, however, borrow many of Diophantus's problems for his own book, Algebra. The editio princeps of Arithmetica was published in , by Xylander. The most famous Latin translation of Arithmetica was by Bachet in , which was the first translation of Arithmetica available to the public. The edition of Arithmetica by Bombelli gained fame after Pierre de Fermat wrote his famous "Last Theorem" in the margins of his copy:.

I have a truly marvelous proof of this proposition which this margin is too narrow to contain. Fermat's proof was never found, and the problem of finding a proof for the theorem went unsolved for centuries.