Editing Euclid (section)

==Life==
===Traditional narrative===
[[File:0 Chambre de Raphaël - École d'Athènes - Musées du Vatican.JPG|thumb|upright=1.4|Detail of [[Raphael]]'s impression of Euclid, teaching students in ''[[The School of Athens]]'' (1509–1511)]]

The English name 'Euclid' is the anglicized version of the [[Ancient Greek]] name {{Transliteration|grc|Eukleídes}} ({{lang|grc|Εὐκλείδης}}).{{sfn|Sialaros|2021|loc=§ "Life"}}{{efn|In modern English, 'Euclid' is pronounced as {{IPAc-en|ˈ|j|uː|k|l|ɪ|d}}.{{sfn|''OED''a}}}} It is derived from '[[Wikt:eu-#English|eu-]]' ([[Wikt:εὖ#Ancient Greek|εὖ]]; 'well') and 'klês' ([[Wikt:#-κλῆς|-κλῆς]]; 'fame'), meaning "renowned, glorious".{{sfn|''OED''b}} In English, by [[metonymy]], 'Euclid' can mean his most well-known work, [[Euclid's Elements|Euclid's ''Elements'']], or a copy thereof,{{sfn|''OED''a}} and is sometimes synonymous with 'geometry'.{{sfn|Bruno|2003|p=[https://archive.org/details/mathmathematicia00brun/page/125 125]}}

As with many [[ancient Greek mathematicians]], the details of Euclid's life are mostly unknown.{{sfn|Heath|1981|p=354}} He is accepted as the author of four mostly extant treatises—the ''Elements'', ''[[Euclid's Optics|Optics]]'', ''[[Euclid's Data|Data]]'', ''[[Euclid's Phaenomena|Phaenomena]]''—but besides this, there is nothing known for certain of him.{{sfn|Asper|2010|loc=§ para. 1}}{{efn|Euclid's ''oeuvre'' also includes the treatise ''On Divisions'', which survives fragmented in a later Arabic source.{{sfn|Sialaros|2021|loc=§ "Works"}} He authored numerous [[#Lost works|lost works]] as well.{{sfn|Sialaros|2021|loc=§ "Works"}}}} The traditional narrative mainly follows the 5th century AD account by [[Proclus]] in his ''Commentary on the First Book of Euclid's Elements'', as well as a few anecdotes from [[Pappus of Alexandria]] in the early 4th century.{{sfn|Sialaros|2021|loc=§ "Life"}}{{efn|Some of the information from [[Pappus of Alexandria]] on Euclid is now lost and was preserved in [[Proclus]]'s ''Commentary on the First Book of Euclid's Elements''.{{sfn|Heath|1911|p=741}}}}

<!--Early life-->
According to Proclus, Euclid lived shortly after several of [[Plato]]'s ({{Died in|347}} BC) followers and before the mathematician [[Archimedes]] ({{circa|287|212}} BC);{{efn|Proclus was likely working from (now-lost) 4th-century BC histories of mathematics written by [[Theophrastus]] and [[Eudemus of Rhodes]]. [[Proclus#Commentary on Euclid's Elements|Proclus explicitly mentions]] Amyclas of Heracleia, [[Menaechmus]] and his brother [[Dinostratus]], [[Theudius|Theudius of Magnesia]], [[Athenaeus of Cyzicus]], [[Hermotimus of Colophon]], and [[Philip of Opus|Philippus of Mende]], and says that Euclid came "not long after" these men.}} specifically, Proclus placed Euclid during the rule of [[Ptolemy I Soter|Ptolemy I]] ({{reign|305/304|282}} BC).{{sfn|Heath|1981|p=354}}{{sfn|Asper|2010|loc=§ para. 1}}{{efn|See {{harvnb|Heath|1981|p=354}} for an English translation on Proclus's account of Euclid's life.}} Euclid's birthdate is unknown; some scholars estimate around 330{{sfn|Ball|1960|p=[https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up 52]}}{{sfn|Sialaros|2020|p=141}} or 325 BC,{{sfn|Bruno|2003|p=[https://archive.org/details/mathmathematicia00brun/page/125 125]}}{{sfn|Goulding|2010|p=125}} but others refrain from speculating.{{sfn|Smorynski|2008|p=2}} It is presumed that he was of Greek descent,{{sfn|Ball|1960|p=[https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up 52]}} but his birthplace is unknown.{{sfn|Boyer|1991|p=[https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater 100]}}{{efn|Later Arab sources state he was a Greek born in modern-day [[Tyre, Lebanon]], though these accounts are considered dubious and speculative.{{sfn|Asper|2010|loc=§ para. 1}}{{sfn|Sialaros|2021|loc=§ "Life"}} See {{harvnb|Heath|1981|p=355}} for an English translation of the Arab account. He was long held to have been born in Megara, but by the [[Renaissance]] it was concluded that he had been confused with the philosopher [[Euclid of Megara]],{{sfn|Goulding|2010|p=118}} see [[#Identity and historicity|§Identity and historicity]]}} Proclus held that Euclid followed the [[Platonism|Platonic tradition]], but there is no definitive confirmation for this.{{sfn|Heath|1981|p=355}} It is unlikely he was a contemporary of Plato, so it is often presumed that he was educated by Plato's disciples at the [[Platonic Academy]] in Athens.{{sfn|Goulding|2010|p=126}} Historian [[Thomas Heath (classicist)|Thomas Heath]] supported this theory, noting that most capable geometers lived in Athens, including many of those whose work Euclid built on;{{sfn|Heath|1908|p=[https://archive.org/details/bub_gb_UhgPAAAAIAAJ/page/n13/mode/2up 2]}} historian Michalis Sialaros considers this a mere conjecture.{{sfn|Sialaros|2021|loc=§ "Life"}}{{sfn|Sialaros|2020|pp=147–148}} In any event, the contents of Euclid's work demonstrate familiarity with the Platonic geometry tradition.{{sfn|Ball|1960|p=[https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up 52]}}

<!--Later life-->
In his ''Collection'', Pappus mentions that [[Apollonius of Perga|Apollonius]] studied with Euclid's students in [[Alexandria]], and this has been taken to imply that Euclid worked and founded a [[school of thought|mathematical tradition]] there.{{sfn|Asper|2010|loc=§ para. 1}}{{sfn|Sialaros|2020|p=142}}{{sfn|Heath|1908|p=[https://archive.org/details/bub_gb_UhgPAAAAIAAJ/page/n13/mode/2up 2]}} The city was founded by [[Alexander the Great]] in 331 BC,{{sfn|Bruno|2003|p=[https://archive.org/details/mathmathematicia00brun/page/126 126]}} and the rule of Ptolemy I from 306 BC onwards gave it a stability which was relatively unique amid the chaotic [[Wars of the Diadochi|wars over dividing Alexander's empire]].{{sfn|Ball|1960|p=[https://archive.org/details/shortaccountofhi0000ball/page/50/mode/2up 51]}} Ptolemy began a process of [[hellenization]] and commissioned numerous constructions, building the massive [[Musaeum]] institution, which was a leading center of education.{{sfn|Boyer|1991|p=[https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater 100]}}{{efn|The [[Musaeum]] would later include the famous [[Library of Alexandria]], but it was likely founded later, during the reign of [[Ptolemy II Philadelphus]] (285–246 BC).{{sfn|Tracy|2000|pp=343–344}}}} Euclid is speculated to have been among the Musaeum's first scholars.{{sfn|Bruno|2003|p=[https://archive.org/details/mathmathematicia00brun/page/126 126]}} Euclid's date of death is unknown; it has been speculated that he died {{circa|270 BC}}.{{sfn|Bruno|2003|p=[https://archive.org/details/mathmathematicia00brun/page/126 126]}}

===Identity and historicity===
[[File:Domenico Marolì - Euclid of Megara.jpg|thumb|upright=1.5|[[Domenico Maroli]]'s 1650s painting {{lang|it|Euclide di Megara si traveste da donna per recarsi ad Atene a seguire le lezioni di Socrate}} [''Euclid of Megara Dressing as a Woman to Hear Socrates Teach in Athens'']. At the time, Euclid the philosopher and Euclid the mathematician were wrongly considered the same person, so this painting includes mathematical objects on the table.{{sfn|Sialaros|2021|loc=§ "Life" and Note 5}}]]

Euclid is often referred to as 'Euclid of Alexandria' to differentiate him from the earlier philosopher [[Euclid of Megara]], a pupil of [[Socrates]] included in [[List of speakers in Plato's dialogues|dialogues of Plato]] with whom he was historically conflated.{{sfn|Sialaros|2021|loc=§ "Life"}}{{sfn|Smorynski|2008|p=2}} [[Valerius Maximus]], the 1st century AD Roman compiler of anecdotes, mistakenly substituted Euclid's name for [[Eudoxus of Cnidus|Eudoxus]] (4th century BC) as the mathematician to whom Plato sent those asking how to [[Doubling the cube|double the cube]].{{sfn|Jones|2005}} Perhaps on the basis of this mention of a mathematical Euclid roughly a century early, Euclid became mixed up with Euclid of Megara in medieval [[Byzantine Empire|Byzantine]] sources (now lost),{{sfn|Goulding|2010|p=120}} eventually leading Euclid the mathematician to be ascribed details of both men's biographies and described as {{lang|la|Megarensis}} ({{lit|of Megara}}).{{sfn|Sialaros|2021|loc=§ "Life"}}{{sfn|Taisbak|Van der Waerden|2021|loc=§ "Life"}} The Byzantine scholar [[Theodore Metochites]] ({{c.|1300}}) explicitly conflated the two Euclids, as did printer [[Erhard Ratdolt]]'s 1482 {{lang|la|[[editio princeps]]}} of [[Campanus of Novara]]'s Latin translation of the ''Elements''.{{sfn|Goulding|2010|p=120}} After the mathematician {{ill|Bartolomeo Zamberti|fr||de}} appended most of the extant biographical fragments about either Euclid to the preface of his 1505 translation of the ''Elements'', subsequent publications passed on this identification.{{sfn|Goulding|2010|p=120}} A further confusion, which gives the birthplace of Euclid as [[Gela|Gela, Sicily]], arises from the fact that [[Euclid of Megara]] is sometimes said to have been born in Gela.<ref name=":0">{{Cite web |title=Euclid, Elements, volume 1, page 4 |url=http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086:volume=1:page=4 |access-date=2025-04-15 |website=www.perseus.tufts.edu}}</ref> Later Renaissance scholars, particularly [[Peter Ramus]], reevaluated this claim, proving it false via issues in chronology and contradiction in early sources.{{sfn|Goulding|2010|p=120}}

[[Mathematics in the medieval Islamic world|Medieval Arabic sources]] give vast amounts of information concerning Euclid's life, but are completely unverifiable.{{sfn|Sialaros|2021|loc=§ "Life"}} Euclid, who was supposedly a [[Tyre, Lebanon|Tyre]]-born Greek domiciled at [[Damascus]], was claimed to have been the son of Naucrates.<ref name=":0" /> Most scholars consider them of dubious authenticity.{{sfn|Asper|2010|loc=§ para. 1}} Heath in particular contends that the fictionalization was done to strengthen the connection between a revered mathematician and the Arab world.{{sfn|Heath|1981|p=355}} There are also numerous anecdotal stories concerning to Euclid, all of uncertain historicity, which "picture him as a kindly and gentle old man".{{sfn|Boyer|1991|p=[https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater 101]}} The best known of these is Proclus' story about Ptolemy asking Euclid if there was a quicker path to learning geometry than reading his ''Elements'', which Euclid replied with "there is no royal road to geometry".{{sfn|Boyer|1991|p=[https://archive.org/details/historyofmathema00boye/page/100/mode/2up?view=theater 101]}} This anecdote is questionable since a very similar interaction between [[Menaechmus]] and Alexander the Great is recorded from [[Stobaeus]].{{sfn|Boyer|1991|p=96}} Both accounts were written in the 5th century AD, neither indicates its source, and neither appears in ancient Greek literature.{{sfn|Sialaros|2018|p=90}}

Any firm dating of Euclid's activity {{c.|300 BC}} is called into question by a lack of contemporary references.{{sfn|Sialaros|2021|loc=§ "Life"}} The earliest original reference to Euclid is in Apollonius' [[prefatory]] letter to the ''[[Conics]]'' (early 2nd century BC): "The third book of the ''Conics'' contains many astonishing theorems that are useful for both the syntheses and the determinations of number of solutions of solid [[locus (mathematics)|loci]]. Most of these, and the finest of them, are novel. And when we discovered them we realized that Euclid had not made the synthesis of the locus on three and four lines but only an accidental fragment of it, and even that was not felicitously done."{{sfn|Jones|2005}} The ''Elements'' is speculated to have been at least partly in circulation by the 3rd century BC, as Archimedes and Apollonius take several of its propositions for granted;{{sfn|Sialaros|2021|loc=§ "Life"}} however, Archimedes employs an older variant of the [[theory of proportions]] than the one found in the ''Elements''.{{sfn|Asper|2010|loc=§ para. 1}} The oldest physical copies of material included in the ''Elements'', dating from roughly 100 AD, can be found on [[Oxyrhynchus Papyri|papyrus fragments unearthed]] in an ancient rubbish heap from [[Oxyrhynchus]], [[Roman Egypt]]. The oldest extant direct citations to the ''Elements'' in works whose dates are firmly known are not until the 2nd century AD, by [[Galen]] and [[Alexander of Aphrodisias]]; by this time it was a standard school text.{{sfn|Jones|2005}} Some ancient Greek mathematicians mention Euclid by name, but he is usually referred to as "ὁ στοιχειώτης" ("the author of ''Elements''").{{sfn|Heath|1981|p=357}} In the Middle Ages, some scholars contended Euclid was not a historical personage and that his name arose from a [[Language change|corruption]] of Greek mathematical terms.{{sfn|Ball|1960|pp=[https://archive.org/details/shortaccountofhi0000ball/page/52/mode/2up 52–53]}}