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Encyclopedia > Arithmetica
Cover of the 1621 edition, translated into Latin by Claude Gaspard Bachet de Méziriac.
Cover of the 1621 edition, translated into Latin by Claude Gaspard Bachet de Méziriac.

Arithmetica is an ancient Greek text on mathematics written by the mathematician Diophantus in the 3rd century CE. It is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. Image File history File links Download high resolution version (668x1081, 368 KB) Summary Work by Diophantus (died in about 280 B.C.), translated from Greek into Latin by Claude Gaspard Bachet de Méziriac. ... Image File history File links Download high resolution version (668x1081, 368 KB) Summary Work by Diophantus (died in about 280 B.C.), translated from Greek into Latin by Claude Gaspard Bachet de Méziriac. ... For other uses, see Latins and Latin (disambiguation). ... Claude Gaspard Bachet de Méziriac (October 9, 1581 - February 26, 1638) was a French mathematician born in Bourg-en-Bresse. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... // Overview Events 212: Constitutio Antoniniana grants citizenship to all free Roman men 212-216: Baths of Caracalla 230-232: Sassanid dynasty of Persia launches a war to reconquer lost lands in the Roman east 235-284: Crisis of the Third Century shakes Roman Empire 250-538: Kofun era, the first... This article is about the branch of mathematics. ... This article is about equations in mathematics. ...


Equations in the book are called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the Arithmetica problems lead to quadratic equations. It was these equations which inspired Pierre de Fermat to propose Fermat's Last Theorem, which states that for the equation xn + yn = zn where x, y, and z are integers not equal to zero, n cannot be an integer greater than 2. In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ... In mathematics, a Diophantine equation is an equation between two polynomials with integer coefficients with any number of unknowns. ... In mathematics, a quadratic equation is a polynomial equation of the second degree. ... Pierre de Fermat Pierre de Fermat IPA: (August 17, 1601 – January 12, 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to modern calculus. ... Pierre de Fermats conjecture written in the margin of his copy of Arithmetica proved to be one of the most intriguing and enigmatic mathematical problems ever devised. ...


In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form 4n + 3 cannot be the sum of 2 squares. Diophantus also appears to know that every number can be written as the sum of 4 squares. If he did know this result it would be truly remarkable for even Fermat, who stated the result, failed to provide a proof of it and it was not settled until Joseph Louis Lagrange proved it using results due to Leonhard Euler. Joseph-Louis, comte de Lagrange (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian-French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. ... Euler redirects here. ...


Arithmetica became known to the Arabs sometime before the tenth century[1] when Abu'l-Wefa translated it into Arabic.[2]


References

  1. ^ Boyer, Carl B. (1991). "The Arabic Hegemony", A History of Mathematics, Second Edition, John Wiley & Sons, Inc., 234. ISBN 0471543977. “Note the omission of Diophantus and Pappus, authors who evidently were not at first known in Arabia, although the Diophantine Arithmetica became familiar before the end of the tenth century.” 
  2. ^ Boyer, Carl B. (1991). "The Arabic Hegemony", A History of Mathematics, Second Edition, John Wiley & Sons, Inc., 239. ISBN 0471543977. “Abu'l-Wefa was a capable algebraist as well as a trigonometer. He commented on al-Khwarizmi's Algebra and translated from Greek one of the last great classics - The Arithmetica of Diophantus.” 
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Carl Benjamin Boyer (November 3, 1906 - April 26, 1976) was a historian of mathematics. ... Carl Benjamin Boyer (November 3, 1906 - April 26, 1976) was a historian of mathematics. ... Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... Anaxagoras Anaxagoras (Greek: Αναξαγόρας, c. ... Anthemius of Tralles (c. ... Aratus (Greek Aratos) (ca. ... Archytas Archytas (428 BC - 347 BC) was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... Aristaeus the Elder (370 BCE-300 BCE) Aristaeus the Elder was a Greek mathematician who worked on conic sections. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Apollonius of Perga [Pergaeus] (ca. ... For other uses, see Archimedes (disambiguation). ... Autolycus of Pitane (c. ... For other people of the same name, see Boethius (disambiguation). ... Bryson of Heraclea (ca. ... Calippus of Syracuse Callippus (or Calippus) (ca. ... Chrysippus of Soli (279-207 BC) was Cleanthess pupil and eventual successor to the head of the stoic philosophy (232-204 BC). ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... Ctesibius or Ktesibios or Tesibius (Greek Κτησίβιος) (flourished 285–222 BC) was a Greek[1] inventor and mathematician in Alexandria. ... ‎ Democritus (Greek: ) was a pre-Socratic Greek materialist philosopher (born at Abdera in Thrace ca. ... Dicaearchus (also Dicearchos, Dicearchus or Dikæarchus, Greek Δικαιαρχος; circa 350 BC – circa 285 BC) was a Greek philosopher, cartographer, geographer, mathematician and author. ... Diocles was a Greek mathematician and geometer, who probably flourished sometime around the end of the second century and the beginning of the first century BC. He was probably the first to prove the focal property of a parabola. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... Dinostratus (b. ... Dionysodorus of Caunus (ca. ... Domninus of Larissa (ca. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Eudemus (350-290 BC) was the second major companion of Aristotle besides Theophrastus. ... For other uses, see Euclid (disambiguation). ... Not to be confused with Eudoxus of Cyzicus. ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Hero (or Heron) of Alexandria (Greek: Ήρων ο Αλεξανδρεύς) (c. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... Hippasus of Metapontum, born circa 500 B.C. in Magna Graecia, was a Greek philosopher. ... Hippias can also refer to a son of Pisistratus and a tyrant of Athens. ... Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. ... Hypatia, as depicted in Raphaels The School of Athens. ... This article is about Hypsicles of Alexandria. ... Marinus (Μαρίνος ο Νεαπολίτης) was neo-Platonist philosopher born in Neapolis (modern Nablus), Palestine in the mid 5th century CE. He was probably a Samaritan, or possibly a Jew. ... Greek mathematician and geometer said to have been the tutor of Alexander the Great. ... Menelaus of Alexandria (c. ... Nicomachus (Gr. ... Oenopides of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived around 450 BCE. He was born shortly after 500 BC on the island of Chios, but mostly worked in Athens. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... Perseus (c. ... Philolaus (circa 480 BC – circa 405 BC) was a Greek mathematician and philosopher. ... Philon, Athenian architect of the 4th century BC, is known as the planner of two important works: the portico of the great Hall of the Mysteries at Eleusis and an arsenal at Athens. ... Porphyry of Tyre (Greek: , c. ... The bust of Posidonius as an older man depicts his character as a Stoic philosopher. ... This article is about Proclus Diadochus, the Neoplatonist philosopher. ... This article is about the geographer, mathematician and astronomer Ptolemy. ... Pythagoras of Samos (Greek: ; born between 580 and 572 BC, died between 500 and 490 BC) was an Ionian Greek mathematician[1] and founder of the religious movement called Pythagoreanism. ... Pytheas (Πυθέας), ca. ... Serenus of Antinouplis (ca. ... Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ... Sosigenes of Alexandria was named by Pliny the Elder as the astronomer consulted by Julius Caesar for the design of the Julian calendar. ... Sporus of Nicaea was a Greek mathematician and astronomer, born: circa 240, probably Nicaea (Greek Nikaia), ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: circa 300. ... For the Defense and Security Company, see Thales Group. ... Theaetetus (ca. ... Theano was one of the few women in ancient mathematics. ... This article is about Theodorus the mathematician from Cyrene. ... Theodosius of Bithynia (ca. ... Theon (c. ... Theon of Smyrna (ca. ... Thymaridas of Paros (ca. ... Xenocrates of Chalcedon (396 - 314 BC) was a Greek philosopher and scholarch or rector of the Academy from 339 to 314 BC. Removing to Athens in early youth, he became the pupil of the Socratic Aeschines, but presently joined himself to Plato, whom he attended to Sicily in 361. ... Zeno of Elea (pronounced , Greek: Ζήνων ὁ Ἐλεάτης) (ca. ... Zeno of Sidon, Epicurean philosopher of the 1st century BC and contemporary of Cicero. ... Zenodorus (ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... Apollonius of Perga [Pergaeus] (ca. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Aristarchuss 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century CE Greek copy On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa... On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... Autolycus of Pitane (c. ... For other uses, see Academy (disambiguation). ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... Cyrene (Greek Κυρήνη, Kurene) was an ancient Greek colony in present-day Libya, the oldest and most important of the five Greek cities in the region. ... Babylonian clay tablet YBC 7289 with annotations. ... This article or section is in need of attention from an expert on the subject. ... For a timeline of events in mathematics, see timeline of mathematics. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... This article is under construction. ...

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