431:
49:
633:
5716:
4159:
1251:
4255:
1333:
4436:
5703:
4135:
4221:
4002:
4238:
4204:
4067:
873:
4187:
1219:", though this interpretation has been heavily debated since the 1970s; critics describe the characterization as anachronistic, since the foundations of even nascent algebra occurred many centuries later. The second book has a more focused scope and mostly provides algebraic theorems to accompany various geometric shapes. It focuses on the area of
1632:
4147:
759:
give vast amounts of information concerning Euclid's life, but are completely unverifiable. Most scholars consider them of dubious authenticity; Heath in particular contends that the fictionalization was done to strengthen the connection between a revered mathematician and the Arab world. There are
1320:. By introducing a list of 37 definitions, Book 11 contextualizes the next two. Although its foundational character resembles Book 1, unlike the latter it features no axiomatic system or postulates. The three sections of Book 11 include content on solid geometry (1–19), solid angles (20–23) and
581:
supported this theory, noting that most capable geometers lived in Athens, including many of those whose work Euclid built on; historian
Michalis Sialaros considers this a mere conjecture. In any event, the contents of Euclid's work demonstrate familiarity with the Platonic geometry tradition.
947:
essentially superseded much earlier and now-lost Greek mathematics. The classicist Markus Asper concludes that "apparently Euclid's achievement consists of assembling accepted mathematical knowledge into a cogent order and adding new proofs to fill in the gaps" and the historian
760:
also numerous anecdotal stories concerning to Euclid, all of uncertain historicity, which "picture him as a kindly and gentle old man". The best known of these is
Proclus' story about Ptolemy asking Euclid if there was a quicker path to learning geometry than reading his
800:. 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." The
4048:
568:
BC). Euclid's birthdate is unknown; some scholars estimate around 330 or 325 BC, but others refrain from speculating. It is presumed that he was of Greek descent, but his birthplace is unknown. Proclus held that Euclid followed the
1176:. Euclid then presents 10 assumptions (see table, right), grouped into five postulates (axioms) and five common notions. These assumptions are intended to provide the logical basis for every subsequent theorem, i.e. serve as an
1587:, but to "a third type of proposition—an intermediate between a theorem and a problem—the aim of which is to discover a feature of an existing geometrical entity, for example, to find the centre of a circle". The mathematician
983:
scattered throughout. Using
Aristotle's terminology, these may be generally separated into two categories: "first principles" and "second principles". The first group includes statements labeled as a "definition"
804:
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; however, Archimedes employs an older variant of the
1494:, which was later superseded by Apollonius' more comprehensive treatment of the same name. The work's existence is known primarily from Pappus, who asserts that the first four books of Apollonius'
1646:
Euclid is generally considered with
Archimedes and Apollonius of Perga as among the greatest mathematicians of antiquity. Many commentators cite him as one of the most influential figures in the
617:
institution, which was a leading center of education. Euclid is speculated to have been among the
Musaeum's first scholars. Euclid's date of death is unknown; it has been speculated that he died
4244:
1616:) is of virtually unknown contents, aside from speculation based on the work's title. Conjecture based on later accounts has suggested it discussed cones and cylinders, among other subjects.
1247:" in the context of plane geometry. It is built almost entirely of its first proposition: "Triangles and parallelograms which are under the same height are to one another as their bases".
4472:
573:, but there is no definitive confirmation for this. It is unlikely he was a contemporary of Plato, so it is often presumed that he was educated by Plato's disciples at the
3547:
Sialaros, Michalis (2020). "Euclid of
Alexandria: A Child of the Academy?". In Kalligas, Paul; Balla, Vassilis; Baziotopoulou-Valavani, Chloe; Karasmanis, Effie (eds.).
1188:
and particularly famous. Book 1 also includes 48 propositions, which can be loosely divided into those concerning basic theorems and constructions of plane geometry and
841:; by this time it was a standard school text. Some ancient Greek mathematicians mention Euclid by name, but he is usually referred to as "ὁ στοιχειώτης" ("the author of
2002:
The distinction between these categories is not immediately clear; postulates may simply refer to geometry specifically, while common notions are more general in scope.
645:. 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.
943:, while other theorems are mentioned by Plato and Aristotle. It is difficult to differentiate the work of Euclid from that of his predecessors, especially because the
430:
1358:
concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors, though the attribution is sometimes questioned.
5576:
1243:. Book 5 is among the work's most important sections and presents what is usually termed as the "general theory of proportion". Book 6 utilizes the "theory of
4080:
3819:
5654:
1546:, written to advise beginners in avoiding common fallacies. Very little is known of its specific contents aside from its scope and a few extant lines.
756:
311:
4957:
4493:
3991:
658:
5770:
5750:
4465:
673:. 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
1732:
The First Six Books of the
Elements of Euclid in Which Coloured Diagrams and Symbols Are Used Instead of Letters for the Greater Ease of Learners
3785:
5780:
5501:
3707:
4175:
5231:
3855:
3739:
3633:
3610:
3585:
3560:
3537:
3510:
3484:
3458:
3433:
3359:
3334:
3315:
3287:
3259:
3225:
3204:
3176:
1212:(46–48). The last of these includes the earliest surviving proof of the Pythagorean theorem, described by Sialaros as "remarkably delicate".
5805:
5775:
5755:
5196:
3829:
2671:
2669:
2667:
2665:
2663:
2661:
2659:
2657:
2655:
1504:
3595:
Tracy, Stephen V (2000). "Demetrius of
Phalerum: Who was He and Who was He Not?". In Fortenbaugh, William W.; Schütrumpf, Eckhart (eds.).
236:
72:
3992:
764:, which Euclid replied with "there is no royal road to geometry". This anecdote is questionable since a very similar interaction between
5564:
5176:
4967:
3789:
3476:
48:
5631:
4458:
3723:
2037:
Since antiquity, enormous amounts of scholarship have been written about the 5th postulate, usually from mathematicians attempting to
1707:
is perhaps the most successful ancient Greek text, and was the dominant mathematical textbook in the
Medieval Arab and Latin worlds.
516:—but besides this, there is nothing known for certain of him. The traditional narrative mainly follows the 5th century AD account by
4354:
3408:
3404:
1960:
version available today also includes "post-Euclidean" mathematics, probably added later by later editors such as the mathematician
1663:
1626:
150:
772:. Both accounts were written in the 5th century AD, neither indicates its source, and neither appears in ancient Greek literature.
3450:
677:
sources (now lost), eventually leading Euclid the mathematician to be ascribed details of both men's biographies and described as
5795:
4395:
4292:
4087:
3880:
3083:
796:
contains many astonishing theorems that are useful for both the syntheses and the determinations of number of solutions of solid
1579:) was, based on accounts from Pappus and Proclus, probably a three-book treatise with approximately 200 propositions. The term '
5785:
5760:
3866:
5765:
5745:
5600:
5533:
5166:
5046:
3390:
5790:
782:
is called into question by a lack of contemporary references. The earliest original reference to Euclid is in Apollonius'
605:
in 331 BC, and the rule of Ptolemy I from 306 BC onwards gave it a stability which was relatively unique amid the chaotic
4125:
5669:
5426:
5314:
4489:
3297:
1723:
1636:
1377:), is a somewhat short text which deals with the nature and implications of "given" information in geometrical problems.
491:
295:, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the
4026:
1915:, p. 355 for an English translation of the Arab account. He was long held to have been born in Megara, but by the
5309:
3952:
3834:
952:
described it as a "reservoir of results". Despite this, Sialaros furthers that "the remarkably tight structure of the
5378:
845:"). In the Middle Ages, some scholars contended Euclid was not a historical personage and that his name arose from a
745:
appended most of the extant biographical fragments about either Euclid to the preface of his 1505 translation of the
2548:
2336:
1164:
is foundational for the entire text. It begins with a series of 20 definitions for basic geometric concepts such as
910:
494:, the details of Euclid's life are mostly unknown. He is accepted as the author of four mostly extant treatises—the
271:, involved new innovations in combination with a synthesis of theories from earlier Greek mathematicians, including
5005:
4821:
4796:
4007:
3875:
3552:
940:
284:
1499:
1397:
translation, and concerns the division of geometrical figures into two or more equal parts or into parts in given
5800:
5540:
5511:
4871:
4726:
4390:
4076:
3804:
3385:
3369:
3061:
578:
1313:, book 10 is by far the largest and most complex, dealing with irrational numbers in the context of magnitudes.
5674:
4951:
963:
does not exclusively discuss geometry as is sometimes believed. It is traditionally divided into three topics:
838:
5408:
4120:, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.
632:
5636:
5612:
5486:
5421:
5362:
5299:
5289:
5025:
4944:
4806:
4716:
4596:
3929:
3839:
3731:
1944:
1878:
1699:
1429:
1347:, at least five works of Euclid have survived to the present day. They follow the same logical structure as
1294:
1216:
1181:
1155:
26:
4022:
806:
5659:
5607:
5506:
5334:
5284:
5269:
5264:
5035:
4836:
4771:
4761:
4711:
4421:
4337:
3602:
1981:. Proclus also substituted the term "hypothesis" instead of "common notion", though preserved "postulate".
1659:
1647:
1592:
1437:
877:
512:
296:
3104:
731:
5707:
5559:
5344:
5221:
5144:
5092:
4894:
4801:
4651:
4139:
3625:
2600:
2455:
2278:
1940:
1667:
1298:
1228:
753:, reevaluated this claim, proving it false via issues in chronology and contradiction in early sources.
649:
Euclid is often referred to as 'Euclid of Alexandria' to differentiate him from the earlier philosopher
5715:
5403:
4158:
5684:
5624:
5588:
5431:
5254:
5201:
5171:
5161:
5070:
4933:
4826:
4741:
4696:
4676:
4521:
4506:
4323:
4285:
3902:
3494:
2739:
2737:
2735:
2733:
2731:
2729:
2727:
1874:
1829:
1424:) is the earliest surviving Greek treatise on perspective. It includes an introductory discussion of
1282:
932:
867:
606:
525:
481:
440:
362:
307:
276:
259:
90:
3809:
2394:
5664:
5583:
5571:
5552:
5516:
5436:
5354:
5339:
5329:
5279:
5274:
5216:
5085:
4977:
4906:
4841:
4831:
4731:
4701:
4641:
4616:
4541:
4531:
4516:
4369:
4364:
4111:
3577:
3502:
3243:
3168:
1961:
1739:
1671:
1596:
1498:
are largely based on Euclid's earlier work. Doubt has been cast on this assertion by the historian
1460:
1452:
1302:
1290:
1267:
1209:
1189:
797:
700:
602:
590:
292:
135:
130:
3499:
The Math Book: From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics
749:, subsequent publications passed on this identification. Later Renaissance scholars, particularly
5720:
5679:
5619:
5547:
5413:
5206:
5181:
5149:
4746:
4691:
4656:
4551:
4374:
4359:
4163:
3772:
3694:
3686:
3395:
3377:
3351:
3196:
2996:
2994:
2992:
2990:
2988:
1991:
1655:
1425:
1185:
1017:
818:
723:
370:
268:
145:
140:
125:
5388:
4987:
4330:
3444:
1410:
500:
391:
98:
4072:
1591:
speculated that these now-lost propositions included content related to the modern theories of
740:
736:
5393:
5304:
5154:
5080:
5053:
4816:
4636:
4626:
4561:
4481:
4261:
4043:
3851:
3847:
3735:
3629:
3606:
3601:. Rutgers University Studies in Classical Humanities. Vol. IX. New Brunswick and London:
3581:
3556:
3533:
3506:
3480:
3454:
3429:
3400:
3355:
3330:
3311:
3283:
3255:
3231:
3221:
3200:
3172:
2439:
2107:
1854:
1849:
Proclus was likely working from (now-lost) 4th-century BC histories of mathematics written by
1715:
1675:
1250:
976:
928:
670:
666:
598:
272:
267:
that largely dominated the field until the early 19th century. His system, now referred to as
5595:
5466:
5383:
5139:
5127:
5075:
4811:
4316:
4151:
4052:
3843:
3762:
3678:
3247:
3186:
2012:
1920:
1769:
1363:
1236:
1177:
674:
662:
650:
574:
506:
397:
335:
323:
315:
196:
105:
54:
22:
3870:
3345:
665:, the 1st century AD Roman compiler of anecdotes, mistakenly substituted Euclid's name for
642:
Euclide di Megara si traveste da donna per recarsi ad Atene a seguire le lezioni di Socrate
469:
5740:
5236:
5226:
5120:
4846:
4439:
4405:
4278:
3307:
1394:
1255:
1173:
1165:
1025:
846:
717:
636:
558:
4107:
3327:
Defending Hypatia: Ramus, Savile, and the Renaissance Rediscovery of Mathematical History
3040:
3038:
3036:
3717:. Euclid and His Heritage Meeting, Clay Mathematics Institute, Oxford, 7–8 October 2005.
3644:
2041:
the postulate—which would make it different from the other, unprovable, four postulates.
334:'s students and before Archimedes. There is some speculation that Euclid studied at the
5496:
5491:
5319:
5211:
5191:
5019:
4576:
4546:
3468:
3269:
3190:
2038:
1882:
1607:
1588:
1554:
1517:
1481:
1442:
1415:
1384:
1368:
1321:
1317:
1259:
1232:
1184:. While postulates 1 through 4 are relatively straightforward, the 5th is known as the
985:
972:
964:
949:
904:
711:
243:
226:
3414:
Jahnke, Hans Niels (2010). "The Conjoint Origin of Proof and Theoretical Physics". In
3057:
1332:
1024:
as a textbook, but its method of presentation makes it a natural fit. As a whole, the
5734:
5456:
5324:
5294:
5115:
4923:
4866:
4400:
3947:
3898:
3814:
3776:
3698:
3248:
3215:
2050:
Much of Book 5 was probably ascertained from earlier mathematicians, perhaps Eudoxus.
1908:
1735:
1694:
1679:
1491:
1278:
1205:
1193:
968:
610:
449:
374:
366:
246:
1016:—and common notions. The second group consists of propositions, presented alongside
302:
Very little is known of Euclid's life, and most information comes from the scholars
5398:
5186:
4861:
4621:
4611:
4227:
3650:
1850:
1337:
1306:
1286:
1281:
is covered by books 7 to 10, the former beginning with a set of 22 definitions for
1272:
3075:
2015:
is not complete: "Euclid assumed more than just what he stated in the postulates".
3990:
3596:
3571:
3521:
3419:
3301:
3273:
3162:
5012:
4900:
4606:
4591:
3425:
3421:
Explanation and Proof in Mathematics: Philosophical and Educational Perspectives
2975:
2973:
2971:
2969:
2967:
2965:
2963:
2961:
2959:
2957:
1916:
1866:
923:
892:
826:
822:
750:
319:
173:
4039:
3767:
3750:
1898:, p. 354 for an English translation on Proclus's account of Euclid's life.
1734:, which included colored diagrams intended to increase its pedagogical effect.
4998:
4917:
4856:
4851:
4791:
4776:
4721:
4706:
4661:
4601:
4586:
4566:
4536:
4501:
3924:
3682:
3529:
3415:
1973:
The use of the term "axiom" instead of "postulate" derives from the choice of
1862:
1654:
long dominated the field; however, today that system is often referred to as '
765:
594:
543:
327:
288:
4010:
was created from a revision of this article dated 29 September 2020
3823:. Vol. 20 (11th ed.). Cambridge University Press. pp. 470–471.
1277:
notes that "Euclid starts afresh. Nothing from the preceding books is used".
669:(4th century BC) as the mathematician to whom Plato sent those asking how to
4751:
4736:
4686:
4581:
4571:
4556:
4526:
4450:
4091:
3279:
3235:
1584:
1543:
1220:
783:
570:
3808:
2118:
2116:
1815:, which survives fragmented in a later Arabic source. He authored numerous
833:
in works whose dates are firmly known are not until the 2nd century AD, by
2239:
2237:
2235:
2233:
2231:
872:
465:
4888:
4666:
4511:
4193:
4061:
3217:
Math and Mathematicians: The History of Math Discoveries Around the World
1870:
1719:
1509:, owing to sparse evidence and no other corroboration of Pappus' account.
1240:
1201:
769:
654:
477:
264:
254:
250:
177:
3690:
2147:
2145:
2143:
2141:
2139:
2137:
2135:
2133:
2131:
1472:
Four other works are credibly attributed to Euclid, but have been lost.
927:. Much of its content originates from earlier mathematicians, including
5461:
4786:
4781:
4681:
4671:
4646:
3918:
1974:
1936:
1858:
1833:
1116:
Things which are equal to the same thing are also equal to one another
980:
614:
517:
435:
354:
339:
303:
4110:, with the original Greek and an English translation on facing pages,
1693:
as the most frequently translated, published, and studied book in the
4756:
1580:
1224:
936:
916:
788:
453:
386:
378:
343:
280:
4210:
2028:, pp. 195–201 for a detailed overview of postulates 1 through 4
1911:, though these accounts are considered dubious and speculative. See
1401:. It includes thirty-six propositions and is similar to Apollonius'
979:
lines) do not exactly fit this scheme. The heart of the text is the
597:, and this has been taken to imply that Euclid worked and founded a
4057:
1096:
the two straight lines, if produced indefinitely, meet on that side
257:. Considered the "father of geometry", he is chiefly known for the
5132:
5110:
4766:
4079:(c.500 editions of works by Euclid), available online through the
2162:
2160:
1690:
1631:
1630:
1398:
1331:
1249:
1244:
1169:
1068:
To produce a finite straight line continuously in a straight line
1013:
871:
834:
631:
532:
487:, or a copy thereof, and is sometimes synonymous with 'geometry'.
473:
429:
358:
331:
3786:"Oliver Byrne: The Matisse of Mathematics – Biography 1810–1829"
1919:
it was concluded that he had been confused with the philosopher
1197:
1140:
Things which coincide with one another are equal to one another
4454:
4274:
3473:
Historical Modules for the Teaching and Learning of Mathematics
1542:), was—according to Proclus in (70.1–18)—a text in geometrical
1092:
That, if a straight line falling on two straight lines make the
956:
reveals authorial control beyond the limits of a mere editor".
342:; he is regarded as bridging the earlier Platonic tradition in
3449:. Vol. Part 2: Commentary, Index, and Figures. New York:
1132:
If equals be subtracted from equals, the remainders are equal
613:
and commissioned numerous constructions, building the massive
4169:
2642:
2640:
2638:
2636:
2623:
2621:
1778:
1611:
1558:
1521:
1485:
1446:
1419:
1388:
1372:
1007:
1001:
995:
989:
908:
459:
230:
205:
3988:
2218:
2216:
2214:
2212:
2210:
2208:
1094:
interior angles on the same side less than two right angles,
557:
BC); specifically, Proclus placed Euclid during the rule of
531:
According to Proclus, Euclid lived shortly after several of
3011:
3009:
1907:
Later Arab sources state he was a Greek born in modern-day
1289:
and other arithmetic-related concepts. Book 7 includes the
1180:. The common notions exclusively concern the comparison of
448:
The English name 'Euclid' is the anglicized version of the
326:. It is now generally accepted that he spent his career in
2513:
2511:
2509:
2507:
2505:
1012:); only the first book includes postulates—later known as
4270:
2313:
2311:
1787:
1775:
899:
Euclid is best known for his thirteen-book treatise, the
813:. The oldest physical copies of material included in the
214:
202:
3751:"A Variation of Hilbert's Axioms for Euclidean Geometry"
975:(books 11–13)—though book 5 (on proportions) and 10 (on
476:; 'fame'), meaning "renowned, glorious". In English, by
413:
has been questioned. He is thought to have written many
4117:
3598:
Demetrius of Phalerum: Text, Translation and Discussion
2944:
2942:
2940:
2927:
2925:
2840:
2838:
2836:
2834:
2758:
2756:
2702:
2700:
2359:
2357:
1943:, but it was likely founded later, during the reign of
1885:, and says that Euclid came "not long after" these men.
1098:
on which are the angles less than the two right angles
710:) explicitly conflated the two Euclids, as did printer
3669:
Acerbi, Fabio (September 2008). "Euclid's Pseudaria".
3044:
3000:
2675:
2529:
2195:
2193:
4123:
3058:"NASA Delivers Detectors for ESA's Euclid Spacecraft"
2797:
2795:
1977:
to do so in his highly influential commentary on the
1781:
1662:
discovered in the early 19th century. Among Euclid's
1235:. Book 3 focuses on circles, while the 4th discusses
208:
2540:
2538:
2492:
2490:
2488:
2431:
2429:
2427:
2386:
2384:
2328:
2326:
1790:
1784:
1301:, while book 9 includes the proposition, now called
1060:
To draw a straight line from any point to any point
217:
211:
5647:
5525:
5475:
5449:
5371:
5353:
5252:
5245:
5101:
5063:
4880:
4488:
4414:
4383:
4347:
4308:
2270:
2268:
2266:
2264:
2099:
2097:
2095:
2093:
1772:
1124:If equals be added to equals, the wholes are equal
1020:and diagrams. It is unknown if Euclid intended the
199:
169:
82:
68:
34:
3917:
3728:The Oxford Encyclopedia of Ancient Greece and Rome
2063:, pp. 547–572 for further information on the
1215:Book 2 is traditionally understood as concerning "
1076:To describe a circle with any centre and distance
1838:Commentary on the First Book of Euclid's Elements
895:, the diagram accompanies Book II, Proposition 5.
522:Commentary on the First Book of Euclid's Elements
322:scholars mistook him for the earlier philosopher
3076:"Gazetteer of Planetary Nomenclature | Euclides"
2011:The mathematician Gerard Venema notes that this
1316:The final three books (11–13) primarily discuss
1231:), and leads up to a geometric precursor of the
3526:Revolutions and Continuity in Greek Mathematics
2868:
1084:That all right angles are equal to one another
792:(early 2nd century BC): "The third book of the
263:treatise, which established the foundations of
4001:
3446:Pappus of Alexandria: Book 7 of the Collection
817:, dating from roughly 100 AD, can be found on
480:, 'Euclid' can mean his most well-known work,
438:'s impression of Euclid, teaching students in
4466:
4286:
3749:Hähl, Hermann; Peters, Hanna (10 June 2022).
3192:A Short Account of the History of Mathematics
1924:
1766:In modern English, 'Euclid' is pronounced as
640:
8:
3784:Hawes, Susan M.; Kolpas, Sid (August 2015).
3418:; Jahnke, Hans Niels; Pulte, Helmut (eds.).
3254:(2nd ed.). John Wiley & Sons, Inc.
1650:. The geometrical system established by the
1351:, with definitions and proved propositions.
829:. The oldest extant direct citations to the
314:invented a fanciful biography, and medieval
4081:Stavros Niarchos Foundation Digital Library
3125:
1832:on Euclid is now lost and was preserved in
1564:
1527:
715:
684:
678:
542:BC) followers and before the mathematician
385:, Euclid wrote a central early text in the
5479:
5249:
4473:
4459:
4451:
4293:
4279:
4271:
3137:
1035:
47:
31:
3766:
2317:
768:and Alexander the Great is recorded from
661:with whom he was historically conflated.
4018:, and does not reflect subsequent edits.
2979:
2813:
2743:
2572:
2517:
2479:
2418:
2406:
2375:
2348:
2302:
2290:
2243:
2151:
2122:
346:with the later tradition of Alexandria.
16:Ancient Greek mathematician (fl. 300 BC)
4182:
4130:
3848:10.1093/acrefore/9780199381135.013.2521
3374:The Thirteen Books of Euclid's Elements
3347:The Thirteen Books of Euclid's Elements
2948:
2931:
2904:
2892:
2880:
2844:
2786:
2706:
2077:
1759:
1297:of two numbers. The 8th book discusses
1266:From Book 7 onwards, the mathematician
1037:Euclid's postulates and common notions
120:
5502:Latin translations of the 12th century
3646:Introduction To Non-Euclidean Geometry
3027:
2916:
2825:
2762:
2612:
1726:published a well-known version of the
1583:' in this context does not refer to a
1455:, survives in Greek; it is similar to
5232:Straightedge and compass construction
3671:Archive for History of Exact Sciences
3220:. Baker, Lawrence W. Detroit: U X L.
3015:
2856:
2801:
2774:
2718:
2691:
2646:
2627:
2584:
2560:
2544:
2496:
2467:
2435:
2390:
2363:
2332:
2255:
2222:
2199:
2103:
2060:
2025:
1912:
1895:
775:Any firm dating of Euclid's activity
607:wars over dividing Alexander's empire
7:
5197:Incircle and excircles of a triangle
3573:History of Mathematics: A Supplement
2596:
2451:
2274:
3790:Mathematical Association of America
3477:Mathematical Association of America
3329:. Dordrecht: Springer Netherlands.
3164:Euclid: The Creation of Mathematics
1336:Euclid's construction of a regular
1148:The whole is greater than the part
395:, and lesser-known works including
3471:; Michalowicz, Karen Dee (2020) .
3303:The Mathematics of Plato's Academy
3045:Taisbak & Van der Waerden 2021
3001:Taisbak & Van der Waerden 2021
2676:Taisbak & Van der Waerden 2021
2530:Taisbak & Van der Waerden 2021
593:studied with Euclid's students in
524:, as well as a few anecdotes from
14:
2678:, § "Sources and contents of the
2084:
1710:The first English edition of the
1627:List of things named after Euclid
1305:, that there are infinitely many
1052:Let the following be postulated:
5714:
5701:
4435:
4434:
4253:
4236:
4219:
4202:
4185:
4157:
4145:
4133:
4065:
4000:
3867:Van der Waerden, Bartel Leendert
3084:International Astronomical Union
2181:
2166:
1768:
1028:remains general and impersonal.
821:in an ancient rubbish heap from
195:
3524:. In Sialaros, Michalis (ed.).
3522:"How Much Does a Theorem Cost?"
3451:Springer Science+Business Media
1939:would later include the famous
1816:
1658:' to distinguish it from other
1639:'s 1847 colored edition of the
1463:, who flourished around 310 BC.
601:there. The city was founded by
563:
414:
330:and lived around 300 BC, after
312:Medieval Islamic mathematicians
5771:3rd-century BC Egyptian people
5751:4th-century BC Egyptian people
5534:A History of Greek Mathematics
5047:The Quadrature of the Parabola
3755:Mathematische Semesterberichte
3710:"Euclid, the Elusive Geometer"
3443:Jones, Alexander, ed. (1986).
3391:A History of Greek Mathematics
1689:is often considered after the
1103:
1042:
1:
5781:3rd-century BC mathematicians
3881:Encyclopædia Britannica, Inc.
3726:. In Gagarin, Michael (ed.).
1828:Some of the information from
1697:'s history. With Aristotle's
1674:spacecraft, the lunar crater
1393:) survives only partially in
1258:, foundational components of
885:
849:of Greek mathematical terms.
776:
704:
618:
609:. Ptolemy began a process of
547:
58:
5315:Intersecting secants theorem
3865:Taisbak, Christian Marinus;
3828:Sialaros, Michalis (2021) .
3810:"Pappus of Alexandria"
1490:) was a four-book survey on
1262:which feature in Books 11–13
917:
726:'s Latin translation of the
537:
492:ancient Greek mathematicians
454:
5806:Philosophers of mathematics
5776:3rd-century BC Greek people
5756:4th-century BC Greek people
5310:Intersecting chords theorem
5177:Doctrine of proportionality
4064:(public domain audiobooks)
3953:Online Etymology Dictionary
3835:Oxford Classical Dictionary
3622:The Foundations of Geometry
3520:Sialaros, Michalis (2018).
3344:Heath, Thomas, ed. (1908).
3214:Bruno, Leonard C. (2003) .
2869:Katz & Michalowicz 2020
1859:Proclus explicitly mentions
1811:also includes the treatise
1293:, a method for finding the
819:papyrus fragments unearthed
5822:
5006:On the Sphere and Cylinder
4959:On the Sizes and Distances
3768:10.1007/s00591-022-00320-3
3553:Cambridge University Press
3105:"4354 Euclides (2142 P-L)"
1624:
1612:
1559:
1522:
1486:
1447:
1420:
1389:
1373:
1153:
1008:
1002:
996:
990:
909:
865:
809:than the one found in the
730:. After the mathematician
528:in the early 4th century.
460:
231:
20:
5708:Ancient Greece portal
5697:
5512:Philosophy of mathematics
5482:
5427:Ptolemy's table of chords
4482:Ancient Greek mathematics
4430:
4077:University College London
3706:Jones, Alexander (2005).
3683:10.1007/s00407-007-0017-3
3643:Wolfe, Harold E. (1945).
3570:Smorynski, Craig (2008).
3394:. Vol. 2. New York:
3376:. Vol. 2. New York:
3350:. Vol. 1. New York:
3325:Goulding, Robert (2010).
3195:(4th ed.). Mineola:
3062:Jet Propulsion Laboratory
1925:§Identity and historicity
1714:was published in 1570 by
1107:
1102:
1051:
1046:
1041:
1006:), or a "common notion" (
699:). The Byzantine scholar
405:. Euclid's authorship of
361:. He also wrote works on
184:
162:
46:
41:
21:For the philosopher, see
5379:Aristarchus's inequality
4952:On Conoids and Spheroids
4049:Works by or about Euclid
3306:(2nd ed.). Oxford:
3250:A History of Mathematics
3161:Artmann, Benno (2012) .
1660:non-Euclidean geometries
839:Alexander of Aphrodisias
628:Identity and historicity
338:and later taught at the
151:Numerous other namesakes
5796:Ancient Greek geometers
5487:Ancient Greek astronomy
5300:Inscribed angle theorem
5290:Greek geometric algebra
4945:Measurement of a Circle
3942:(subscription required)
3930:Oxford University Press
3876:Encyclopædia Britannica
3840:Oxford University Press
3820:Encyclopædia Britannica
3732:Oxford University Press
3620:Venema, Gerard (2006).
3278:. London and New York:
3126:Hawes & Kolpas 2015
1945:Ptolemy II Philadelphus
1678:, and the minor planet
1295:greatest common divisor
1156:Foundations of geometry
757:Medieval Arabic sources
589:, Pappus mentions that
464:). It is derived from '
407:On Divisions of Figures
27:Euclid (disambiguation)
5786:3rd-century BC writers
5761:4th-century BC writers
5721:Mathematics portal
5507:Non-Euclidean geometry
5462:Mouseion of Alexandria
5335:Tangent-secant theorem
5285:Geometric mean theorem
5270:Exterior angle theorem
5265:Angle bisector theorem
4969:On Sizes and Distances
4422:Papyrus Oxyrhynchus 29
3996:
3976:Listen to this article
3722:Asper, Markus (2010).
3603:Transaction Publishers
3138:Hähl & Peters 2022
2482:, § "Life" and Note 5.
1879:Hermotimus of Colophon
1861:Amyclas of Heracleia,
1648:history of mathematics
1643:
1340:
1299:geometric progressions
1263:
896:
716:
679:
646:
641:
599:mathematical tradition
472:; 'well') and 'klês' (
445:
310:many centuries later.
297:history of mathematics
25:. For other uses, see
5766:3rd-century BC deaths
5746:4th-century BC births
5409:Pappus's area theorem
5345:Theorem of the gnomon
5222:Quadratrix of Hippias
5145:Circles of Apollonius
5093:Problem of Apollonius
5071:Constructible numbers
4895:Archimedes Palimpsest
4174:at Knowledge (XXG)'s
3995:
3626:Pearson Prentice Hall
3495:Pickover, Clifford A.
3107:. Minor Planet Center
3003:, § "Other writings".
1941:Library of Alexandria
1740:modern axiomatization
1668:European Space Agency
1634:
1335:
1253:
875:
807:theory of proportions
635:
577:in Athens. Historian
433:
426:Traditional narrative
381:. In addition to the
353:, Euclid deduced the
5791:Ancient Alexandrians
5625:prehistoric counting
5422:Ptolemy's inequality
5363:Apollonius's theorem
5202:Method of exhaustion
5172:Diophantine equation
5162:Circumscribed circle
4979:On the Moving Sphere
4396:Johan Ludvig Heiberg
4027:More spoken articles
3903:J. Paul Getty Museum
3805:Heath, Thomas Little
3555:. pp. 141–152.
1875:Athenaeus of Cyzicus
1871:Theudius of Magnesia
1830:Pappus of Alexandria
1722:. The mathematician
1613:Τόποι πρὸς ἐπιφανείᾳ
1457:On the Moving Sphere
933:Hippocrates of Chios
526:Pappus of Alexandria
441:The School of Athens
357:from a small set of
308:Pappus of Alexandria
277:Hippocrates of Chios
5711: •
5517:Neusis construction
5437:Spiral of Theodorus
5330:Pythagorean theorem
5275:Euclidean algorithm
5217:Lune of Hippocrates
5086:Squaring the circle
4842:Theon of Alexandria
4517:Aristaeus the Elder
4365:Euclidean algorithm
4112:University of Texas
3578:Springer Publishing
3532:. pp. 89–106.
3503:Sterling Publishing
3475:. Washington D.C.:
3275:Ancient Mathematics
3169:Springer Publishing
3018:, pp. 399–400.
2777:, pp. 154–155.
2615:, pp. 210–211.
2470:, pp. 343–344.
2409:, pp. 147–148.
1964:in the 4th century.
1962:Theon of Alexandria
1597:projective geometry
1461:Autolycus of Pitane
1453:spherical astronomy
1451:) is a treatise on
1428:and basic rules of
1343:In addition to the
1291:Euclidean algorithm
1210:Pythagorean theorem
1190:triangle congruence
1038:
1018:mathematical proofs
967:(books 1–6), basic
732:Bartolomeo Zamberti
701:Theodore Metochites
603:Alexander the Great
379:mathematical rigour
293:Apollonius of Perga
131:Euclidean algorithm
5404:Menelaus's theorem
5394:Irrational numbers
5207:Parallel postulate
5182:Euclidean geometry
5150:Apollonian circles
4692:Isidore of Miletus
4375:Euclidean relation
4360:Euclidean geometry
4118:All thirteen books
4094:at wilbourhall.org
3997:
3948:"Euclidean (adj.)"
3869:(5 January 2021).
3396:Dover Publications
3378:Dover Publications
3352:Dover Publications
3197:Dover Publications
2982:, § "Other Works".
1992:Euclidean relation
1883:Philippus of Mende
1656:Euclidean geometry
1644:
1635:The cover page of
1426:geometrical optics
1341:
1264:
1186:parallel postulate
1036:
921:), considered his
897:
724:Campanus of Novara
659:dialogues of Plato
647:
639:'s 1650s painting
571:Platonic tradition
566: 305/304–282
446:
371:spherical geometry
269:Euclidean geometry
141:Euclidean relation
126:Euclidean geometry
5728:
5727:
5693:
5692:
5445:
5444:
5432:Ptolemy's theorem
5305:Intercept theorem
5155:Apollonian gasket
5081:Doubling the cube
5054:The Sand Reckoner
4448:
4447:
4092:edition of Euclid
4073:Euclid Collection
4044:Project Gutenberg
3993:
3857:978-0-19-938113-5
3741:978-0-19-517072-6
3635:978-0-13-143700-5
3612:978-1-3513-2690-2
3587:978-0-387-75480-2
3562:978-1-108-42644-2
3539:978-3-11-056595-9
3512:978-1-4027-5796-9
3486:978-1-4704-5711-2
3460:978-3-540-96257-1
3435:978-1-4419-0576-5
3361:978-0-486-60088-8
3336:978-90-481-3542-4
3317:978-0-19-850258-6
3289:978-1-134-71019-5
3261:978-0-471-54397-8
3227:978-0-7876-3813-9
3206:978-0-486-20630-1
3178:978-1-4612-1412-0
1855:Eudemus of Rhodes
1730:in 1847 entitled
1716:Henry Billingsley
1239:, especially the
1217:geometric algebra
1208:(35–45); and the
1152:
1151:
971:(books 7–10) and
868:Euclid's Elements
273:Eudoxus of Cnidus
188:
187:
164:Scientific career
69:Years active
5813:
5801:Number theorists
5719:
5718:
5706:
5705:
5704:
5480:
5467:Platonic Academy
5414:Problem II.8 of
5384:Crossbar theorem
5340:Thales's theorem
5280:Euclid's theorem
5250:
5167:Commensurability
5128:Axiomatic system
5076:Angle trisection
5041:
5031:
4993:
4983:
4973:
4963:
4939:
4929:
4912:
4475:
4468:
4461:
4452:
4438:
4437:
4370:Euclid's theorem
4295:
4288:
4281:
4272:
4266:
4265:from Wikiversity
4258:
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4069:
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4053:Internet Archive
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3439:
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3386:Heath, Thomas L.
3381:
3365:
3340:
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3293:
3265:
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3187:Ball, W.W. Rouse
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2022:
2016:
2013:axiomatic system
2009:
2003:
2000:
1994:
1988:
1982:
1971:
1965:
1954:
1948:
1933:
1927:
1921:Euclid of Megara
1905:
1899:
1892:
1886:
1865:and his brother
1847:
1841:
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1489:
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1423:
1422:
1392:
1391:
1376:
1375:
1324:solids (24–37).
1322:parallelepipedal
1303:Euclid's theorem
1276:
1237:regular polygons
1178:axiomatic system
1174:regular polygons
1105:
1044:
1039:
1011:
1010:
1005:
1004:
1000:), "postulate" (
999:
998:
993:
992:
920:
914:
913:
890:
889: 75–125 AD
887:
878:papyrus fragment
781:
778:
744:
721:
709:
706:
698:
695:
692:
689:
686:
682:
663:Valerius Maximus
651:Euclid of Megara
644:
623:
620:
575:Platonic Academy
567:
565:
556:
552:
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541:
539:
463:
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457:
336:Platonic Academy
324:Euclid of Megara
241:
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146:Euclid's formula
136:Euclid's theorem
117:
116:Various concepts
77:
74:
63:
62: 1630–1635
60:
55:Jusepe de Ribera
51:
32:
23:Euclid of Megara
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5655:Arabian/Islamic
5643:
5632:numeral systems
5521:
5471:
5441:
5389:Heron's formula
5367:
5349:
5241:
5237:Triangle center
5227:Regular polygon
5104:and definitions
5103:
5097:
5059:
5039:
5029:
4991:
4981:
4971:
4961:
4937:
4927:
4910:
4876:
4847:Theon of Smyrna
4492:
4484:
4479:
4449:
4444:
4426:
4410:
4406:Isaac Todhunter
4379:
4343:
4304:
4299:
4269:
4259:
4254:
4252:
4242:
4237:
4235:
4231:from Wikisource
4225:
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4208:
4203:
4201:
4191:
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4184:
4181:
4177:sister projects
4176:
4168:
4156:
4146:
4144:
4134:
4132:
4124:
4066:
4058:Works by Euclid
4040:Works by Euclid
4031:
4030:
4019:
4013:
4011:
4008:This audio file
4005:
3998:
3989:
3986:
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3975:
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3827:
3803:
3794:
3792:
3783:
3748:
3742:
3721:
3714:
3705:
3668:
3657:
3642:
3636:
3619:
3613:
3594:
3588:
3569:
3563:
3549:Plato's Academy
3546:
3540:
3519:
3513:
3493:
3487:
3469:Katz, Victor J.
3467:
3461:
3442:
3436:
3413:
3384:
3372:, ed. (1908b).
3368:
3362:
3343:
3337:
3324:
3318:
3308:Clarendon Press
3296:
3290:
3270:Cuomo, Serafina
3268:
3262:
3242:
3228:
3213:
3207:
3185:
3179:
3160:
3149:
3144:
3136:
3132:
3124:
3120:
3110:
3108:
3103:
3102:
3098:
3088:
3086:
3074:
3073:
3069:
3056:
3055:
3051:
3043:
3034:
3026:
3022:
3014:
3007:
2999:
2986:
2978:
2955:
2947:
2938:
2930:
2923:
2915:
2911:
2903:
2899:
2895:, pp. 5–6.
2891:
2887:
2879:
2875:
2867:
2863:
2855:
2851:
2843:
2832:
2824:
2820:
2812:
2808:
2800:
2793:
2785:
2781:
2773:
2769:
2761:
2754:
2742:
2725:
2717:
2713:
2705:
2698:
2690:
2686:
2674:
2653:
2645:
2634:
2626:
2619:
2611:
2607:
2595:
2591:
2583:
2579:
2571:
2567:
2559:
2555:
2543:
2536:
2528:
2524:
2516:
2503:
2495:
2486:
2478:
2474:
2466:
2462:
2450:
2446:
2434:
2425:
2417:
2413:
2405:
2401:
2389:
2382:
2374:
2370:
2362:
2355:
2347:
2343:
2331:
2324:
2316:
2309:
2301:
2297:
2289:
2285:
2273:
2262:
2254:
2250:
2242:
2229:
2221:
2206:
2198:
2191:
2180:
2176:
2165:
2158:
2150:
2129:
2121:
2114:
2102:
2091:
2083:
2079:
2075:
2070:
2058:
2054:
2049:
2045:
2036:
2032:
2023:
2019:
2010:
2006:
2001:
1997:
1989:
1985:
1972:
1968:
1955:
1951:
1934:
1930:
1906:
1902:
1893:
1889:
1848:
1844:
1827:
1823:
1806:
1802:
1771:
1767:
1765:
1761:
1757:
1752:
1629:
1623:
1576:
1573:
1570:
1567:
1539:
1536:
1533:
1530:
1502:
1500:Alexander Jones
1470:
1390:Περὶ Διαιρέσεων
1330:
1270:
1256:Platonic solids
1158:
1108:Common notions
1097:
1095:
1093:
1034:
1026:authorial voice
888:
870:
862:
855:
779:
734:
718:editio princeps
707:
696:
693:
690:
687:
671:double the cube
637:Domenico Maroli
630:
621:
562:
554:
550:
536:
428:
423:
239:
198:
194:
158:
155:
119:
118:
115:
111:
75:
64:
61:
37:
30:
17:
12:
11:
5:
5819:
5817:
5809:
5808:
5803:
5798:
5793:
5788:
5783:
5778:
5773:
5768:
5763:
5758:
5753:
5748:
5743:
5733:
5732:
5726:
5725:
5698:
5695:
5694:
5691:
5690:
5688:
5687:
5682:
5677:
5672:
5667:
5662:
5657:
5651:
5649:
5648:Other cultures
5645:
5644:
5642:
5641:
5640:
5639:
5629:
5628:
5627:
5617:
5616:
5615:
5605:
5604:
5603:
5593:
5592:
5591:
5581:
5580:
5579:
5569:
5568:
5567:
5557:
5556:
5555:
5545:
5544:
5543:
5529:
5527:
5523:
5522:
5520:
5519:
5514:
5509:
5504:
5499:
5497:Greek numerals
5494:
5492:Attic numerals
5489:
5483:
5477:
5473:
5472:
5470:
5469:
5464:
5459:
5453:
5451:
5447:
5446:
5443:
5442:
5440:
5439:
5434:
5429:
5424:
5419:
5411:
5406:
5401:
5396:
5391:
5386:
5381:
5375:
5373:
5369:
5368:
5366:
5365:
5359:
5357:
5351:
5350:
5348:
5347:
5342:
5337:
5332:
5327:
5322:
5320:Law of cosines
5317:
5312:
5307:
5302:
5297:
5292:
5287:
5282:
5277:
5272:
5267:
5261:
5259:
5247:
5243:
5242:
5240:
5239:
5234:
5229:
5224:
5219:
5214:
5212:Platonic solid
5209:
5204:
5199:
5194:
5192:Greek numerals
5189:
5184:
5179:
5174:
5169:
5164:
5159:
5158:
5157:
5152:
5142:
5137:
5136:
5135:
5125:
5124:
5123:
5118:
5107:
5105:
5099:
5098:
5096:
5095:
5090:
5089:
5088:
5083:
5078:
5067:
5065:
5061:
5060:
5058:
5057:
5050:
5043:
5033:
5023:
5020:Planisphaerium
5016:
5009:
5002:
4995:
4985:
4975:
4965:
4955:
4948:
4941:
4931:
4921:
4914:
4904:
4897:
4892:
4884:
4882:
4878:
4877:
4875:
4874:
4869:
4864:
4859:
4854:
4849:
4844:
4839:
4834:
4829:
4824:
4819:
4814:
4809:
4804:
4799:
4794:
4789:
4784:
4779:
4774:
4769:
4764:
4759:
4754:
4749:
4744:
4739:
4734:
4729:
4724:
4719:
4714:
4709:
4704:
4699:
4694:
4689:
4684:
4679:
4674:
4669:
4664:
4659:
4654:
4649:
4644:
4639:
4634:
4629:
4624:
4619:
4614:
4609:
4604:
4599:
4594:
4589:
4584:
4579:
4574:
4569:
4564:
4559:
4554:
4549:
4544:
4539:
4534:
4529:
4524:
4519:
4514:
4509:
4504:
4498:
4496:
4490:Mathematicians
4486:
4485:
4480:
4478:
4477:
4470:
4463:
4455:
4446:
4445:
4443:
4442:
4431:
4428:
4427:
4425:
4424:
4418:
4416:
4412:
4411:
4409:
4408:
4403:
4398:
4393:
4387:
4385:
4381:
4380:
4378:
4377:
4372:
4367:
4362:
4357:
4351:
4349:
4345:
4344:
4342:
4341:
4334:
4327:
4320:
4312:
4310:
4306:
4305:
4300:
4298:
4297:
4290:
4283:
4275:
4268:
4267:
4250:
4248:from Wikibooks
4233:
4216:
4214:from Wikiquote
4199:
4170:
4167:
4166:
4154:
4142:
4140:Ancient Greece
4122:
4121:
4115:
4104:
4103:
4096:
4095:
4084:
4070:
4055:
4046:
4036:
4035:
4020:
4006:
3999:
3987:
3974:
3973:
3971:
3970:External links
3968:
3966:
3965:
3944:
3914:
3894:
3893:
3892:
3885:
3884:
3862:
3856:
3825:
3815:Chisholm, Hugh
3801:
3781:
3761:(2): 253–258.
3746:
3740:
3719:
3703:
3677:(5): 511–551.
3665:
3664:
3663:
3656:
3655:
3640:
3634:
3617:
3611:
3592:
3586:
3567:
3561:
3544:
3538:
3517:
3511:
3491:
3485:
3465:
3459:
3440:
3434:
3411:
3382:
3366:
3360:
3341:
3335:
3322:
3316:
3294:
3288:
3266:
3260:
3244:Boyer, Carl B.
3240:
3226:
3211:
3205:
3183:
3177:
3157:
3156:
3155:
3148:
3145:
3143:
3142:
3130:
3118:
3096:
3067:
3049:
3032:
3030:, p. 511.
3020:
3005:
2984:
2953:
2936:
2921:
2919:, p. 191.
2909:
2897:
2885:
2873:
2861:
2859:, p. 202.
2849:
2830:
2818:
2806:
2791:
2789:, p. 3–4.
2779:
2767:
2752:
2723:
2711:
2696:
2694:, p. 131.
2684:
2651:
2632:
2617:
2605:
2589:
2587:, p. 357.
2577:
2565:
2553:
2534:
2522:
2520:, p. 120.
2501:
2484:
2472:
2460:
2444:
2423:
2421:, p. 142.
2411:
2399:
2380:
2378:, p. 126.
2368:
2366:, p. 355.
2353:
2351:, p. 118.
2341:
2322:
2318:Smorynski 2008
2307:
2305:, p. 125.
2295:
2293:, p. 141.
2283:
2260:
2258:, p. 741.
2248:
2227:
2204:
2202:, p. 354.
2189:
2174:
2156:
2127:
2125:, § "Summary".
2112:
2089:
2076:
2074:
2071:
2069:
2068:
2052:
2043:
2030:
2017:
2004:
1995:
1983:
1966:
1949:
1928:
1900:
1887:
1842:
1821:
1800:
1758:
1756:
1753:
1751:
1748:
1664:many namesakes
1622:
1619:
1618:
1617:
1600:
1589:Michel Chasles
1547:
1510:
1492:conic sections
1469:
1466:
1465:
1464:
1433:
1406:
1378:
1359:
1329:
1326:
1318:solid geometry
1260:solid geometry
1233:law of cosines
1206:parallelograms
1194:parallel lines
1160:Book 1 of the
1150:
1149:
1146:
1142:
1141:
1138:
1134:
1133:
1130:
1126:
1125:
1122:
1118:
1117:
1114:
1110:
1109:
1106:
1100:
1099:
1090:
1086:
1085:
1082:
1078:
1077:
1074:
1070:
1069:
1066:
1062:
1061:
1058:
1054:
1053:
1049:
1048:
1045:
1033:
1030:
973:solid geometry
965:plane geometry
950:Serafina Cuomo
866:Main article:
861:
856:
854:
851:
786:letter to the
712:Erhard Ratdolt
629:
626:
427:
424:
422:
419:
367:conic sections
186:
185:
182:
181:
171:
167:
166:
160:
159:
157:
156:
154:
153:
148:
143:
138:
133:
128:
122:
114:
113:
112:
110:
109:
102:
95:
86:
84:
83:Known for
80:
79:
70:
66:
65:
52:
44:
43:
39:
38:
35:
15:
13:
10:
9:
6:
4:
3:
2:
5818:
5807:
5804:
5802:
5799:
5797:
5794:
5792:
5789:
5787:
5784:
5782:
5779:
5777:
5774:
5772:
5769:
5767:
5764:
5762:
5759:
5757:
5754:
5752:
5749:
5747:
5744:
5742:
5739:
5738:
5736:
5723:
5722:
5717:
5710:
5709:
5696:
5686:
5683:
5681:
5678:
5676:
5673:
5671:
5668:
5666:
5663:
5661:
5658:
5656:
5653:
5652:
5650:
5646:
5638:
5635:
5634:
5633:
5630:
5626:
5623:
5622:
5621:
5618:
5614:
5611:
5610:
5609:
5606:
5602:
5599:
5598:
5597:
5594:
5590:
5587:
5586:
5585:
5582:
5578:
5575:
5574:
5573:
5570:
5566:
5563:
5562:
5561:
5558:
5554:
5551:
5550:
5549:
5546:
5542:
5538:
5537:
5536:
5535:
5531:
5530:
5528:
5524:
5518:
5515:
5513:
5510:
5508:
5505:
5503:
5500:
5498:
5495:
5493:
5490:
5488:
5485:
5484:
5481:
5478:
5474:
5468:
5465:
5463:
5460:
5458:
5455:
5454:
5452:
5448:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5417:
5412:
5410:
5407:
5405:
5402:
5400:
5397:
5395:
5392:
5390:
5387:
5385:
5382:
5380:
5377:
5376:
5374:
5370:
5364:
5361:
5360:
5358:
5356:
5352:
5346:
5343:
5341:
5338:
5336:
5333:
5331:
5328:
5326:
5325:Pons asinorum
5323:
5321:
5318:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5298:
5296:
5295:Hinge theorem
5293:
5291:
5288:
5286:
5283:
5281:
5278:
5276:
5273:
5271:
5268:
5266:
5263:
5262:
5260:
5258:
5257:
5251:
5248:
5244:
5238:
5235:
5233:
5230:
5228:
5225:
5223:
5220:
5218:
5215:
5213:
5210:
5208:
5205:
5203:
5200:
5198:
5195:
5193:
5190:
5188:
5185:
5183:
5180:
5178:
5175:
5173:
5170:
5168:
5165:
5163:
5160:
5156:
5153:
5151:
5148:
5147:
5146:
5143:
5141:
5138:
5134:
5131:
5130:
5129:
5126:
5122:
5119:
5117:
5114:
5113:
5112:
5109:
5108:
5106:
5100:
5094:
5091:
5087:
5084:
5082:
5079:
5077:
5074:
5073:
5072:
5069:
5068:
5066:
5062:
5056:
5055:
5051:
5049:
5048:
5044:
5042:
5038:
5034:
5032:
5028:
5024:
5022:
5021:
5017:
5015:
5014:
5010:
5008:
5007:
5003:
5001:
5000:
4996:
4994:
4990:
4986:
4984:
4980:
4976:
4974:
4970:
4966:
4964:
4962:(Aristarchus)
4960:
4956:
4954:
4953:
4949:
4947:
4946:
4942:
4940:
4936:
4932:
4930:
4926:
4922:
4920:
4919:
4915:
4913:
4909:
4905:
4903:
4902:
4898:
4896:
4893:
4891:
4890:
4886:
4885:
4883:
4879:
4873:
4870:
4868:
4867:Zeno of Sidon
4865:
4863:
4860:
4858:
4855:
4853:
4850:
4848:
4845:
4843:
4840:
4838:
4835:
4833:
4830:
4828:
4825:
4823:
4820:
4818:
4815:
4813:
4810:
4808:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4780:
4778:
4775:
4773:
4770:
4768:
4765:
4763:
4760:
4758:
4755:
4753:
4750:
4748:
4745:
4743:
4740:
4738:
4735:
4733:
4730:
4728:
4725:
4723:
4720:
4718:
4715:
4713:
4710:
4708:
4705:
4703:
4700:
4698:
4695:
4693:
4690:
4688:
4685:
4683:
4680:
4678:
4675:
4673:
4670:
4668:
4665:
4663:
4660:
4658:
4655:
4653:
4650:
4648:
4645:
4643:
4640:
4638:
4635:
4633:
4630:
4628:
4625:
4623:
4620:
4618:
4615:
4613:
4610:
4608:
4605:
4603:
4600:
4598:
4595:
4593:
4590:
4588:
4585:
4583:
4580:
4578:
4575:
4573:
4570:
4568:
4565:
4563:
4560:
4558:
4555:
4553:
4550:
4548:
4545:
4543:
4540:
4538:
4535:
4533:
4530:
4528:
4525:
4523:
4520:
4518:
4515:
4513:
4510:
4508:
4505:
4503:
4500:
4499:
4497:
4495:
4491:
4487:
4483:
4476:
4471:
4469:
4464:
4462:
4457:
4456:
4453:
4441:
4433:
4432:
4429:
4423:
4420:
4419:
4417:
4413:
4407:
4404:
4402:
4401:Robert Simson
4399:
4397:
4394:
4392:
4389:
4388:
4386:
4382:
4376:
4373:
4371:
4368:
4366:
4363:
4361:
4358:
4356:
4353:
4352:
4350:
4346:
4340:
4339:
4335:
4333:
4332:
4328:
4326:
4325:
4321:
4319:
4318:
4314:
4313:
4311:
4307:
4303:
4296:
4291:
4289:
4284:
4282:
4277:
4276:
4273:
4264:
4263:
4251:
4247:
4246:
4234:
4230:
4229:
4217:
4213:
4212:
4200:
4196:
4195:
4183:
4179:
4173:
4165:
4160:
4155:
4153:
4143:
4141:
4131:
4127:
4119:
4116:
4113:
4109:
4106:
4105:
4102:
4098:
4097:
4093:
4089:
4088:Johan Heiberg
4085:
4082:
4078:
4074:
4071:
4063:
4059:
4056:
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4047:
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4041:
4038:
4037:
4033:
4032:
4028:
4024:
4009:
3969:
3955:
3954:
3949:
3945:
3931:
3927:
3926:
3920:
3915:
3904:
3900:
3896:
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3891:
3888:
3887:
3882:
3878:
3877:
3872:
3868:
3863:
3859:
3853:
3849:
3845:
3841:
3837:
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3831:
3826:
3822:
3821:
3816:
3811:
3806:
3802:
3791:
3787:
3782:
3778:
3774:
3769:
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3747:
3743:
3737:
3733:
3729:
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3709:
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3676:
3672:
3667:
3666:
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3659:
3658:
3652:
3648:
3647:
3641:
3637:
3631:
3627:
3623:
3618:
3614:
3608:
3604:
3600:
3599:
3593:
3589:
3583:
3579:
3575:
3574:
3568:
3564:
3558:
3554:
3551:. Cambridge:
3550:
3545:
3541:
3535:
3531:
3527:
3523:
3518:
3514:
3508:
3504:
3500:
3496:
3492:
3488:
3482:
3478:
3474:
3470:
3466:
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3456:
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3448:
3447:
3441:
3437:
3431:
3427:
3423:
3422:
3417:
3412:
3410:
3409:0-486-24074-6
3406:
3405:0-486-24073-8
3402:
3397:
3393:
3392:
3387:
3383:
3379:
3375:
3371:
3370:Heath, Thomas
3367:
3363:
3357:
3353:
3349:
3348:
3342:
3338:
3332:
3328:
3323:
3319:
3313:
3309:
3305:
3304:
3299:
3298:Fowler, David
3295:
3291:
3285:
3281:
3277:
3276:
3271:
3267:
3263:
3257:
3252:
3251:
3245:
3241:
3237:
3233:
3229:
3223:
3219:
3218:
3212:
3208:
3202:
3198:
3194:
3193:
3188:
3184:
3180:
3174:
3170:
3166:
3165:
3159:
3158:
3154:
3151:
3150:
3146:
3139:
3134:
3131:
3127:
3122:
3119:
3106:
3100:
3097:
3085:
3081:
3077:
3071:
3068:
3064:. 9 May 2017.
3063:
3059:
3053:
3050:
3047:, § "Legacy".
3046:
3041:
3039:
3037:
3033:
3029:
3024:
3021:
3017:
3012:
3010:
3006:
3002:
2997:
2995:
2993:
2991:
2989:
2985:
2981:
2980:Sialaros 2021
2976:
2974:
2972:
2970:
2968:
2966:
2964:
2962:
2960:
2958:
2954:
2950:
2945:
2943:
2941:
2937:
2933:
2928:
2926:
2922:
2918:
2913:
2910:
2906:
2901:
2898:
2894:
2889:
2886:
2882:
2877:
2874:
2871:, p. 59.
2870:
2865:
2862:
2858:
2853:
2850:
2846:
2841:
2839:
2837:
2835:
2831:
2828:, p. 10.
2827:
2822:
2819:
2816:, p. 56.
2815:
2814:Pickover 2009
2810:
2807:
2803:
2798:
2796:
2792:
2788:
2783:
2780:
2776:
2771:
2768:
2765:, p. 18.
2764:
2759:
2757:
2753:
2749:
2745:
2744:Sialaros 2021
2740:
2738:
2736:
2734:
2732:
2730:
2728:
2724:
2720:
2715:
2712:
2708:
2703:
2701:
2697:
2693:
2688:
2685:
2681:
2677:
2672:
2670:
2668:
2666:
2664:
2662:
2660:
2658:
2656:
2652:
2648:
2643:
2641:
2639:
2637:
2633:
2629:
2624:
2622:
2618:
2614:
2609:
2606:
2602:
2598:
2593:
2590:
2586:
2581:
2578:
2575:, p. 90.
2574:
2573:Sialaros 2018
2569:
2566:
2563:, p. 96.
2562:
2557:
2554:
2550:
2546:
2541:
2539:
2535:
2531:
2526:
2523:
2519:
2518:Goulding 2010
2514:
2512:
2510:
2508:
2506:
2502:
2498:
2493:
2491:
2489:
2485:
2481:
2480:Sialaros 2021
2476:
2473:
2469:
2464:
2461:
2457:
2453:
2448:
2445:
2441:
2437:
2432:
2430:
2428:
2424:
2420:
2419:Sialaros 2020
2415:
2412:
2408:
2407:Sialaros 2020
2403:
2400:
2396:
2392:
2387:
2385:
2381:
2377:
2376:Goulding 2010
2372:
2369:
2365:
2360:
2358:
2354:
2350:
2349:Goulding 2010
2345:
2342:
2338:
2334:
2329:
2327:
2323:
2319:
2314:
2312:
2308:
2304:
2303:Goulding 2010
2299:
2296:
2292:
2291:Sialaros 2020
2287:
2284:
2280:
2276:
2271:
2269:
2267:
2265:
2261:
2257:
2252:
2249:
2245:
2244:Sialaros 2021
2240:
2238:
2236:
2234:
2232:
2228:
2224:
2219:
2217:
2215:
2213:
2211:
2209:
2205:
2201:
2196:
2194:
2190:
2186:
2184:
2178:
2175:
2171:
2169:
2163:
2161:
2157:
2153:
2152:Sialaros 2021
2148:
2146:
2144:
2142:
2140:
2138:
2136:
2134:
2132:
2128:
2124:
2123:Sialaros 2021
2119:
2117:
2113:
2109:
2105:
2100:
2098:
2096:
2094:
2090:
2086:
2081:
2078:
2072:
2066:
2062:
2056:
2053:
2047:
2044:
2040:
2034:
2031:
2027:
2021:
2018:
2014:
2008:
2005:
1999:
1996:
1993:
1987:
1984:
1980:
1976:
1970:
1967:
1963:
1959:
1953:
1950:
1947:(285–246 BC).
1946:
1942:
1938:
1932:
1929:
1926:
1922:
1918:
1914:
1910:
1909:Tyre, Lebanon
1904:
1901:
1897:
1891:
1888:
1884:
1880:
1876:
1872:
1868:
1864:
1860:
1856:
1852:
1846:
1843:
1839:
1835:
1831:
1825:
1822:
1818:
1814:
1810:
1804:
1801:
1795:
1763:
1760:
1754:
1749:
1747:
1745:
1741:
1737:
1736:David Hilbert
1733:
1729:
1725:
1721:
1717:
1713:
1708:
1706:
1702:
1701:
1696:
1695:Western World
1692:
1688:
1683:
1681:
1680:4354 Euclides
1677:
1673:
1669:
1665:
1661:
1657:
1653:
1649:
1642:
1638:
1633:
1628:
1620:
1609:
1605:
1601:
1598:
1594:
1590:
1586:
1582:
1556:
1552:
1548:
1545:
1519:
1515:
1511:
1506:
1501:
1497:
1493:
1483:
1479:
1475:
1474:
1473:
1467:
1462:
1458:
1454:
1444:
1440:
1439:
1434:
1431:
1427:
1417:
1413:
1412:
1407:
1404:
1400:
1396:
1386:
1382:
1379:
1370:
1366:
1365:
1360:
1357:
1354:
1353:
1352:
1350:
1346:
1339:
1334:
1327:
1325:
1323:
1319:
1314:
1312:
1308:
1307:prime numbers
1304:
1300:
1296:
1292:
1288:
1287:prime numbers
1284:
1280:
1279:Number theory
1274:
1269:
1268:Benno Artmann
1261:
1257:
1252:
1248:
1246:
1242:
1238:
1234:
1230:
1226:
1222:
1218:
1213:
1211:
1207:
1203:
1199:
1196:(27–34); the
1195:
1191:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
1157:
1147:
1144:
1143:
1139:
1136:
1135:
1131:
1128:
1127:
1123:
1120:
1119:
1115:
1112:
1111:
1101:
1091:
1088:
1087:
1083:
1080:
1079:
1075:
1072:
1071:
1067:
1064:
1063:
1059:
1056:
1055:
1050:
1040:
1031:
1029:
1027:
1023:
1019:
1015:
987:
982:
978:
974:
970:
969:number theory
966:
962:
957:
955:
951:
946:
942:
938:
934:
930:
926:
925:
919:
912:
906:
902:
894:
883:
879:
874:
869:
864:
860:
857:
852:
850:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
808:
803:
799:
795:
791:
790:
785:
780: 300 BC
773:
771:
767:
763:
758:
754:
752:
748:
742:
738:
733:
729:
725:
720:
719:
713:
702:
681:
676:
672:
668:
664:
660:
656:
653:, a pupil of
652:
643:
638:
634:
627:
625:
622: 270 BC
616:
612:
611:hellenization
608:
604:
600:
596:
592:
588:
583:
580:
576:
572:
560:
545:
534:
529:
527:
523:
519:
515:
514:
509:
508:
503:
502:
497:
493:
490:As with many
488:
486:
485:
479:
475:
471:
467:
456:
451:
450:Ancient Greek
443:
442:
437:
432:
425:
420:
418:
416:
412:
408:
404:
400:
399:
394:
393:
388:
384:
380:
376:
375:number theory
372:
368:
364:
360:
356:
352:
347:
345:
341:
337:
333:
329:
325:
321:
317:
313:
309:
305:
300:
298:
294:
290:
286:
282:
278:
274:
270:
266:
262:
261:
256:
252:
248:
247:mathematician
245:
244:ancient Greek
228:
222:
192:
183:
179:
175:
172:
168:
165:
161:
152:
149:
147:
144:
142:
139:
137:
134:
132:
129:
127:
124:
123:
121:
108:
107:
103:
101:
100:
96:
94:
93:
88:
87:
85:
81:
71:
67:
56:
50:
45:
40:
33:
28:
24:
19:
5712:
5699:
5541:Thomas Heath
5532:
5415:
5399:Law of sines
5255:
5187:Golden ratio
5052:
5045:
5036:
5030:(Theodosius)
5026:
5018:
5011:
5004:
4997:
4988:
4978:
4972:(Hipparchus)
4968:
4958:
4950:
4943:
4934:
4924:
4916:
4911:(Apollonius)
4907:
4899:
4887:
4862:Zeno of Elea
4631:
4622:Eratosthenes
4612:Dionysodorus
4391:Thomas Heath
4336:
4329:
4322:
4315:
4301:
4260:
4243:
4226:
4209:
4197:from Commons
4192:
4171:
4100:
3957:. Retrieved
3951:
3933:. Retrieved
3923:
3906:. Retrieved
3889:
3874:
3833:
3818:
3793:. Retrieved
3758:
3754:
3727:
3711:
3708:
3674:
3670:
3660:
3651:Dryden Press
3649:. New York:
3645:
3621:
3597:
3576:. New York:
3572:
3548:
3525:
3501:. New York:
3498:
3472:
3445:
3420:
3389:
3373:
3346:
3326:
3302:
3274:
3249:
3216:
3191:
3167:. New York:
3163:
3152:
3140:, § para. 1.
3133:
3121:
3109:. Retrieved
3099:
3087:. Retrieved
3079:
3070:
3052:
3023:
2951:, p. 9.
2949:Artmann 2012
2934:, p. 7.
2932:Artmann 2012
2912:
2907:, p. 6.
2905:Artmann 2012
2900:
2893:Artmann 2012
2888:
2883:, p. 5.
2881:Artmann 2012
2876:
2864:
2852:
2847:, p. 4.
2845:Artmann 2012
2821:
2809:
2804:, p. 4.
2787:Artmann 2012
2782:
2770:
2747:
2721:, § para. 4.
2714:
2709:, p. 3.
2707:Artmann 2012
2687:
2679:
2649:, § para. 6.
2630:, § para. 2.
2608:
2592:
2580:
2568:
2556:
2525:
2475:
2463:
2447:
2414:
2402:
2371:
2344:
2320:, p. 2.
2298:
2286:
2251:
2246:, § "Works".
2225:, § para. 1.
2182:
2177:
2167:
2080:
2064:
2055:
2046:
2033:
2020:
2007:
1998:
1986:
1978:
1969:
1957:
1952:
1931:
1903:
1890:
1851:Theophrastus
1845:
1837:
1824:
1813:On Divisions
1812:
1808:
1803:
1762:
1743:
1731:
1727:
1724:Oliver Byrne
1711:
1709:
1704:
1698:
1686:
1684:
1651:
1645:
1640:
1637:Oliver Byrne
1604:Surface Loci
1603:
1593:transversals
1550:
1513:
1495:
1477:
1471:
1456:
1436:
1409:
1402:
1381:On Divisions
1380:
1362:
1355:
1348:
1344:
1342:
1338:dodecahedron
1315:
1310:
1265:
1214:
1172:and various
1161:
1159:
1021:
1009:κοινὴ ἔννοια
960:
958:
953:
944:
922:
900:
898:
881:
880:of Euclid's
863:
858:
842:
830:
814:
810:
801:
793:
787:
774:
761:
755:
746:
727:
657:included in
648:
586:
584:
579:Thomas Heath
530:
521:
511:
505:
499:
495:
489:
483:
447:
439:
410:
406:
402:
396:
390:
382:
350:
348:
301:
258:
249:active as a
190:
189:
163:
104:
97:
91:
18:
5608:mathematics
5416:Arithmetica
5013:Ostomachion
4982:(Autolycus)
4901:Arithmetica
4677:Hippocrates
4607:Dinostratus
4592:Dicaearchus
4522:Aristarchus
4164:Mathematics
3919:"Euclid, n"
3879:. Chicago:
3624:. Hoboken:
3426:Springer US
3416:Hanna, Gila
3089:3 September
3028:Acerbi 2008
2917:Heath 1908b
2826:Venema 2006
2763:Jahnke 2010
2613:Fowler 1999
2599:, pp.
2532:, § "Life".
2154:, § "Life".
1917:Renaissance
1867:Dinostratus
1738:authored a
1700:Metaphysics
1574:Corollaries
1503: [
1430:perspective
1328:Other works
1271: [
1047:Postulates
924:magnum opus
893:Oxyrhynchus
891:. Found at
827:Roman Egypt
823:Oxyrhynchus
751:Peter Ramus
735: [
708: 1300
444:(1509–1511)
363:perspective
320:Renaissance
242:BC) was an
174:Mathematics
5735:Categories
5660:Babylonian
5560:arithmetic
5526:History of
5355:Apollonius
5040:(Menelaus)
4999:On Spirals
4918:Catoptrics
4857:Xenocrates
4852:Thymaridas
4837:Theodosius
4822:Theaetetus
4802:Simplicius
4792:Pythagoras
4777:Posidonius
4762:Philonides
4722:Nicomachus
4717:Metrodorus
4707:Menaechmus
4662:Hipparchus
4652:Heliodorus
4602:Diophantus
4587:Democritus
4567:Chrysippus
4537:Archimedes
4532:Apollonius
4502:Anaxagoras
4494:(timeline)
4338:Phaenomena
4211:Quotations
4023:Audio help
4014:2020-09-29
3928:. Oxford:
3925:OED Online
3838:. Oxford:
3730:. Oxford:
3530:De Gruyter
3528:. Berlin:
3424:. Berlin:
3016:Jones 1986
2857:Heath 1908
2802:Wolfe 1945
2775:Heath 1908
2719:Asper 2010
2692:Cuomo 2005
2647:Asper 2010
2628:Asper 2010
2585:Heath 1981
2561:Boyer 1991
2547:, p.
2545:Boyer 1991
2497:Jones 2005
2468:Tracy 2000
2454:, p.
2438:, p.
2436:Bruno 2003
2393:, p.
2391:Heath 1908
2364:Heath 1981
2335:, p.
2333:Boyer 1991
2277:, p.
2256:Heath 1911
2223:Asper 2010
2200:Heath 1981
2106:, p.
2104:Bruno 2003
2061:Jones 1986
2026:Heath 1908
1990:See also:
1913:Heath 1981
1896:Heath 1981
1863:Menaechmus
1817:lost works
1750:References
1625:See also:
1468:Lost works
1438:Phaenomena
1356:Catoptrics
1229:Quadrature
1221:rectangles
1182:magnitudes
1154:See also:
977:irrational
941:Theaetetus
847:corruption
766:Menaechmus
680:Megarensis
595:Alexandria
591:Apollonius
587:Collection
555: 212
553: – c.
551: 287
544:Archimedes
540: 347
513:Phaenomena
434:Detail of
415:lost works
411:Catoptrics
403:Phaenomena
328:Alexandria
318:and early
289:Archimedes
285:Theaetetus
240: 300
76: 300
53:Euclid by
5121:Inscribed
4881:Treatises
4872:Zenodorus
4832:Theodorus
4807:Sosigenes
4752:Philolaus
4737:Oenopides
4732:Nicoteles
4727:Nicomedes
4687:Hypsicles
4582:Ctesibius
4572:Cleomedes
4557:Callippus
4542:Autolycus
4527:Aristotle
4507:Anthemius
4355:Namesakes
4262:Resources
4245:Textbooks
4152:Biography
4086:Scans of
3935:10 August
3908:11 August
3795:10 August
3777:249581871
3699:120860272
3388:(1981) .
3280:Routledge
3272:(2005) .
3246:(1991) .
3189:(1960) .
2746:, § "The
2597:Ball 1960
2452:Ball 1960
2275:Ball 1960
2073:Citations
1807:Euclid's
1670:'s (ESA)
1585:corollary
1560:Πορίσματα
1544:reasoning
1537:Fallacies
1514:Pseudaria
1448:Φαινόμενα
1309:. Of the
1254:The five
1202:triangles
918:Stoicheia
884:dated to
784:prefatory
694:of Megara
675:Byzantine
559:Ptolemy I
482:Euclid's
461:Εὐκλείδης
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4938:(Euclid)
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4025: ·
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3899:"Euclid"
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3830:"Euclid"
3807:(1911).
3724:"Euclid"
3691:41134289
3661:Articles
3497:(2009).
3300:(1999).
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3080:usgs.gov
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2680:Elements
1979:Elements
1958:Elements
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1641:Elements
1523:Ψευδάρια
1374:Δεδομένα
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1345:Elements
1311:Elements
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1192:(1–26);
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802:Elements
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4051:at the
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3817:(ed.).
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1937:Musaeum
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1531:
1225:squares
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4034:Works
3813:. In
3773:S2CID
3715:(PDF)
3695:S2CID
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3153:Books
2601:52–53
2085:Getty
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1755:Notes
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