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Egyptian pyramids
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A view of the pyramids at Giza from the plateau to the south of the complex. From left to right, the three largest are: the Pyramid of Menkaure, the Pyramid of Khafre and the Great Pyramid of Khufu. The three smaller pyramids in the foreground are subsidiary structures associated with Menkaure's pyramid.

Unicode: 𓍋𓅓𓂋𓉴
Pyramid
in hieroglyphs

The Egyptian pyramids are ancient pyramid-shaped masonry structures located in Egypt.
As of November 2008, sources cite either 118 or 138 as the number of identified Egyptian pyramids.[1][2] Most were built as tombs for the country's pharaohs and their consorts during the Old and Middle Kingdom periods.[3][4][5]
The earliest known Egyptian pyramids are found at Saqqara, northwest of Memphis. The earliest among these is the Pyramid of Djoser (constructed 2630 BC–2611 BC) which was built during the third dynasty. This pyramid and its surrounding complex were designed by the architect Imhotep, and are generally considered to be the world's oldest monumental structures constructed of dressed masonry.[6]
The most famous Egyptian pyramids are those found at Giza, on the outskirts of Cairo. Several of the Giza pyramids are counted among the largest structures ever built.[7] The Pyramid of Khufu at Giza is the largest Egyptian pyramid. It is the only one of the Seven Wonders of the Ancient World still in existence.
Contents
[hide]
1 Historical development
2 Pyramid symbolism
3 Number and location of pyramids
3.1 Abu Rawash
3.2 Giza
3.3 Zawyet el-Aryan
3.4 Abu Sir
3.5 Saqqara
3.6 Dahshur
3.7 Mazghuna
3.8 Lisht
3.9 Meidum
3.10 Hawara
3.11 el-Lahun
3.12 El-Kurru
3.13 Nuri
3.14 Construction dates
4 Construction techniques
5 See also
6 References
7 Bibliography
8 External links
Historical development
The Mastabat al-Fir’aun at Saqqara
By the time of the Early Dynastic Period, those with sufficient means were buried in bench-like structures known as mastabas.[8][9]
The second historically-documented Egyptian pyramid is attributed to the architect Imhotep, who planned what Egyptologists believe to be a tomb for the pharaoh Djoser. Imhotep is credited with being the first to conceive the notion of stacking mastabas on top of each other, creating an edifice composed of a number of "steps" that decreased in size towards its apex. The result was the Pyramid of Djoser, which was designed to serve as a gigantic stairway by which the soul of the deceased pharaoh could ascend to the heavens. Such was the importance of Imhotep's achievement that he was deified by later Egyptians.[10]
The most prolific pyramid-building phase coincided with the greatest degree of absolutist rule. It was during this time that the most famous pyramids, the Giza pyramid complex, were built. Over time, as authority became less centralized, the ability and willingness to harness the resources required for construction on a massive scale decreased, and later pyramids were smaller, less well-built and often hastily constructed.
Long after the end of Egypt's own pyramid-building period, a burst of pyramid-building occurred in what is present-day Sudan, after much of Egypt came under the rule of the kings of Napata. While Napatan rule was brief, ending in 661 BC, Egyptian culture made an indelible impression, and during the later Kingdom of Meroë (approximately in the period between 300 BCE – 300 CE), this flowered into a full-blown pyramid-building revival, which saw more than two hundred Egyptian-inspired indigenous royal pyramid-tombs constructed in the vicinity of the kingdom's capital cities.
Al-Aziz Uthman (1171–1198) tried to destroy the Giza pyramid complex. He gave up after damaging the Pyramid of Menkaure because the task proved too huge.[11]
Pyramid symbolism
Diagram of the interior structures of the Great Pyramid. The inner line indicates the pyramid's present profile, the outer line indicates the original profile.
The shape of Egyptian pyramids is thought to represent the primordial mound from which the Egyptians believed the earth was created. The shape of a pyramid is thought to be representative of the descending rays of the sun, and most pyramids were faced with polished, highly reflective white limestone, in order to give them a brilliant appearance when viewed from a distance. Pyramids were often also named in ways that referred to solar luminescence. For example, the formal name of the Bent Pyramid at Dahshur was The Southern Shining Pyramid, and that of Senwosret at el-Lahun was Senwosret is Shining.
While it is generally agreed that pyramids were burial monuments, there is continued disagreement on the particular theological principles that might have given rise to them. One suggestion is that they were designed as a type of "resurrection machine."[12]
The Egyptians believed the dark area of the night sky around which the stars appear to revolve was the physical gateway into the heavens. One of the narrow shafts that extend from the main burial chamber through the entire body of the Great Pyramid points directly towards the center of this part of the sky. This suggests the pyramid may have been designed to serve as a means to magically launch the deceased pharaoh's soul directly into the abode of the gods.[12]
All Egyptian pyramids were built on the west bank of the Nile, which, as the site of the setting sun, was associated with the realm of the dead in Egyptian mythology.[13]
Number and location of pyramids
In 1842, Karl Richard Lepsius produced the first modern list of pyramids – see Lepsius list of pyramids – in which he counted 67. A great many more have since been discovered. As of November 2008, 118 Egyptian pyramids have been identified.[3]
The location of Pyramid 29, which Lepsius called the "Headless Pyramid", was lost for a second time when the structure was buried by desert sands subsequent to Lepsius' survey. It was found again only during an archaeological dig conducted in 2008.[14]
Many pyramids are in a poor state of preservation or buried by desert sands. If visible at all, they may appear as little more than mounds of rubble. As a consequence, archaeologists are continuing to identify and study previously unknown pyramid structures.
The most recent pyramid to be discovered was that of Sesheshet at Saqqara, mother of the Sixth Dynasty pharaoh Teti. The discovery was announced by Zahi Hawass, Secretary General of the Egyptian Supreme Council of Antiquities, on 11 November 2008.[4][15]
All of Egypt's pyramids, except the small Third Dynasty pyramid of Zawyet el-Amwat (or Zawyet el-Mayitin), are sited on the west bank of the Nile, and most are grouped together in a number of pyramid fields. The most important of these are listed geographically, from north to south, below.
Abu Rawash
Main article: Abu Rawash
The largely destroyed Pyramid of Djedefre
Abu Rawash is the site of Egypt's most northerly pyramid (other than the ruins of Lepsius pyramid number one)[5]— the mostly ruined Pyramid of Djedefre, son and successor of Khufu. Originally it was thought that this pyramid had never been completed, but the current archaeological consensus is that not only was it completed, but that it was originally about the same size as the Pyramid of Menkaure, which would have placed it among the half-dozen or so largest pyramids in Egypt.
Its location adjacent to a major crossroads made it an easy source of stone. Quarrying – which began in Roman times – has left little apart from about 15 courses of stone superimposed upon the natural hillock that formed part of the pyramid's core. A small adjacent satellite pyramid is in a better state of preservation.
Giza
Main article: Giza pyramid complex
Map of Giza pyramid complex.
Aerial view of Giza pyramid complex
Giza is the location of the Pyramid of Khufu (also known as the "Great Pyramid" and the "Pyramid of Cheops"); the somewhat smaller Pyramid of Khafre (or Kephren); the relatively modest-sized Pyramid of Menkaure (or Mykerinus), along with a number of smaller satellite edifices known as "Queen's pyramids"; and the Great Sphinx of Giza.
Of the three, only Khafre's pyramid retains part of its original polished limestone casing, near its apex. This pyramid appears larger than the adjacent Khufu pyramid by virtue of its more elevated location, and the steeper angle of inclination of its construction – it is, in fact, smaller in both height and volume.
The Giza pyramid complex has been a popular tourist destination since antiquity, and was popularized in Hellenistic times when the Great Pyramid was listed by Antipater of Sidon as one of the Seven Wonders of the Ancient World. Today it is the only one of those wonders still in existence.
Zawyet el-Aryan
See also: Zawyet el'Aryan
This site, halfway between Giza and Abu Sir, is the location for two unfinished Old Kingdom pyramids. The northern structure's owner is believed to be pharaoh Nebka, while the southern structure, known as the Layer Pyramid, may be attributable to the Third Dynasty pharaoh Khaba, a close successor of Sekhemkhet. If this attribution is correct, Khaba's short reign could explain the seemingly unfinished state of this step pyramid. Today it stands around 17 m (56 ft) high; had it been completed, it is likely to have exceeded 40 m (130 ft).
Abu Sir
Main article: Abusir
The Pyramid of Sahure at Abu Sir, viewed from the pyramid's causeway.
There are a total of fourteen pyramids at this site, which served as the main royal necropolis during the Fifth Dynasty. The quality of construction of the Abu Sir pyramids is inferior to those of the Fourth Dynasty – perhaps signaling a decrease in royal power or a less vibrant economy. They are smaller than their predecessors, and are built of low-quality local limestone.
The three major pyramids are those of Niuserre, which is also the best preserved, Neferirkare Kakai and Sahure. The site is also home to the incomplete Pyramid of Neferefre. Most of the major pyramids at Abu Sir were built similar construction techniques, comprising a rubble core surrounded by steps of mud bricks with a limestone outer casing. The largest of these 5th-Dynasty pyramids, the Pyramid of Neferirkare Kakai, is believed to have been built originally as a step pyramid some 70 m (230 ft) high and then later transformed into a "true" pyramid by having its steps filled in with loose masonry.
Saqqara
Main article: Saqqara
The Pyramid of Djoser
Major pyramids located here include the Pyramid of Djoser – generally identified as the world's oldest substantial monumental structure to be built of dressed stone – the Pyramid of Userkaf, the Pyramid of Teti and the Pyramid of Merikare, dating to the First Intermediate Period of Egypt. Also at Saqqara is the Pyramid of Unas, which retains a pyramid causeway that is one of the best-preserved in Egypt. Together with the pyramid of Userkaf, this pyramid was the subject of one of the earliest known restoration attempts, conducted by Khaemweset, a son of Ramesses II.[16] Saqqara is also the location of the incomplete step pyramid of Djoser's successor Sekhemkhet known as the Buried Pyramid. Archaeologists believe that had this pyramid been completed, it would have been larger than Djoser's.
South of the main pyramid field at Saqqara is a second collection of later, smaller pyramids, including those of Pepi I, Isesi, Merenre, Pepi II and Ibi. Most of these are in a poor state of preservation.
The Fourth Dynasty pharaoh Shepseskaf either did not share an interest in, or have the capacity to undertake pyramid construction like his predecessors. His tomb, which is also sited at south Saqqara, was instead built as an unusually large mastaba and offering temple complex. It is commonly known as the Mastabat al-Fir’aun.[17]
A previously unknown pyramid was discovered at north Saqqara in late 2008. Believed to be the tomb of Teti's mother, it currently stands approximately 5 m (16 ft) high, although the original height was closer to 14 m (46 ft).
Dahshur
Main article: Dahshur
Sneferu's Red Pyramid
This area is arguably the most important pyramid field in Egypt outside Giza and Saqqara, although until 1996 the site was inaccessible due to its location within a military base, and was relatively unknown outside archaeological circles.
The southern Pyramid of Sneferu, commonly known as the Bent Pyramid, is believed to be the first Egyptian pyramid intended by its builders to be a "true" smooth-sided pyramid from the outset; the earlier pyramid at Meidum had smooth sides in its finished state – but it was conceived and built as a step pyramid, before having its steps filled in and concealed beneath a smooth outer casing of dressed stone.
As a true smooth-sided structure, the Bent Pyramid was only a partial success – albeit a unique, visually imposing one; it is also the only major Egyptian pyramid to retain a significant proportion of its original smooth outer limestone casing intact. As such it serves as the best contemporary example of how the ancient Egyptians intended their pyramids to look.
Several kilometeres to the north of the Bent Pyramid is the last – and most successful – of the three pyramids constructed during the reign of Sneferu; the Red Pyramid is the world's first successfully completed smooth-sided pyramid. The structure is also the third largest pyramid in Egypt – after the pyramids of Khufu and Khafra at Giza.
Also at Dahshur is the pyramid known as the Pyramid of Amenemhat III, as well as a number of small, mostly ruined subsidiary pyramids.
Mazghuna
Main article: Mazghuna
Located to the south of Dahshur, several mudbrick pyramids were built in this area in the late Middle Kingdom, perhaps for Amenemhat IV and Sobekneferu.
Lisht
Main article: el-Lisht
The pyramid of Amenemhet I at Lisht
Two major pyramids are known to have been built at Lisht – those of Amenemhat I and his son, Senusret I. The latter is surrounded by the ruins of ten smaller subsidiary pyramids. One of these subsidiary pyramids is known to be that of Amenemhat's cousin, Khaba II.[18] The site which is in the vicinity of the oasis of the Faiyum, midway between Dahshur and Meidum, and about 100 kilometres south of Cairo, is believed to be in the vicinity of the ancient city of Itjtawy (the precise location of which remains unknown), which served as the capital of Egypt during the Twelfth Dynasty.
Meidum
Main article: Meidum
The pyramid at Meidum
The pyramid at Meidum is one of three constructed during the reign of Sneferu, and is believed by some to have been started by that pharaoh's father and predecessor, Huni. However, that attribution is uncertain, as no record of Huni's name has been found at the site.
It was constructed as a step pyramid, and then later converted into the first "true" smooth-sided pyramid when the steps were filled in, and an outer casing added.
The pyramid suffered several catastrophic collapses in ancient and medieval times; medieval Arab writers described it as having seven steps – although today only the three uppermost of these remain, giving the structure its odd, tower-like appearance. The hill on which the pyramid is situated is not a natural landscape feature – it is the small mountain of debris created when the lower courses and outer casing of the pyramid gave way.
Hawara
Main article: Hawara
The Pyramid of Amenemhet III at Hawarra
Amenemhat III was the last powerful ruler of the Twelfth Dynasty, and the pyramid he built at Hawarra, near the Faiyum, is believed to post-date the so-called "Black Pyramid" built by the same ruler at Dahshur. It is the Hawarra pyramid that is believed to have been Amenemhet's final resting place.
el-Lahun
Main article: el-Lahun
The Pyramid of Senusret II. The pyramid's natural limestone core is clearly visible as the yellow stratum at its base.
The pyramid of Senusret II at el-Lahun is the southernmost royal-tomb pyramid structure in Egypt. Its builders reduced the amount of work necessary to construct it by ingeniously using as its foundation and core a 12-meter-high natural limestone hill.
El-Kurru
Main article: El-Kurru
Pharaoh Piye's pyramid at El-Kurru
Piye, the first ruler of the Egyptian 25th dynasty, built a pyramid at El-Kurru. He was the first Egyptian pharaoh to be buried in a pyramid in centuries.
Nuri
Main article: Nuri
Egyptian Pharaoh Taharqa's pyramid at Nuri
Taharqa, a legitimate ruler and Pharaoh of Egypt, built his pyramid at Nuri. It was the largest in the area (North Sudan).
Construction dates
Drawing showing transportation of a colossus. The water poured in the path of the sledge, long dismissed by Egyptologists as ritual, but now confirmed as feasible, served to increase the stiffness of the sand, and likely reduced by 50% the force needed to move the statue.[19]
The following table lays out the chronology of the construction of most of the major pyramids mentioned here. Each pyramid is identified through the pharaoh who ordered it built, his approximate reign, and its location.
Pyramid / Pharaoh
Reign
Field
Djoser
c. 2670 BC Saqqara
Sneferu
c. 2612–2589 BC Dashur
Sneferu
c. 2612–2589 BC Meidum
Khufu
c. 2589–2566 BC Giza
Djedefre
c. 2566–2558 BC Abu Rawash
Khafre
c. 2558–2532 BC Giza
Menkaure
c. 2532–2504 BC Giza
Userkaf
c. 2494–2487 BC Saqqara
Sahure
c. 2487–2477 BC Abu Sir
Neferirkare Kakai
c. 2477–2467 BC Abu Sir
Nyuserre Ini
c. 2416–2392 BC Abu Sir
Amenemhat I
c. 1991–1962 BC Lisht
Senusret I
c. 1971–1926 BC Lisht
Senusret II
c. 1897–1878 BC el-Lahun
Amenemhat III
c. 1860–1814 BC Hawara
Khendjer
c. 1764–1759 BC Saqqara
Piye
c. 721 BC El-Kurru
Taharqa
c. 664 BC Nuri
Construction techniques
Main article: Egyptian pyramid construction techniques
Constructing the pyramids involved moving huge quantities of stone. The quarried blocks were likely transported to the construction site by wooden sleds, with sand in front of the sled wetted to reduce friction. Droplets of water created bridges between the grains of sand, helping them stick together.[20]
See also
Egyptian pyramid construction techniques
Pyramidion
Ziggurat
Al Ahram, Arabic for "the pyramids", name of Egyptian newspaper
List
List of Egyptian pyramids
List of megalithic sites
References
Jump up ^ Slackman, Michael (17 November 2008). "In the Shadow of a Long Past, Patiently Awaiting the Future". The New York Times. Retrieved 1 May 2010.
Jump up ^ Mark Lehner (2008). The Complete Pyramids: Solving the Ancient Mysteries. p. 34. Thames & Hudson. 2008-03-25. ISBN 978-0-500-28547-3.
^ Jump up to: a b "Egypt says has found pyramid built for ancient queen". Reuters. 11 November 2008. Retrieved 2 November 2017. The pyramid, which Hawass said was the 118th found in Egypt, was uncovered near the world's oldest pyramid at Saqqara, a burial ground for the rulers of ancient Egypt.
^ Jump up to: a b Slackman, Michael (16 November 2007). "In the Shadow of a Long Past, Patiently Awaiting the Future". New York Times. Retrieved 17 November 2008. Deep below the Egyptian desert, archaeologists have found evidence of yet another pyramid, this one constructed 4,300 years ago to store the remains of a pharaoh’s mother. That makes 138 pyramids discovered here so far, and officials say they expect to find more.
^ Jump up to: a b Michael Ritter (2003) "Archived copy". Archived from the original on 11 May 2008. Retrieved 15 May 2008. Dating the Pyramids. Retrieved 13 April 2005
Jump up ^ Lehner, Mark (1997). The Complete Pyramids. New York: Thames and Hudson. p. 84. ISBN 978-0-500-05084-2.
Jump up ^ Watkin, David (2005). A History of Western Architecture (4th ed.). Laurence King Publishing. p. 14. ISBN 978-1-85669-459-9. "The Great Pyramid...is still one of the largest structures ever raised by man, its plan twice the size of St. Peter's in Rome"
Jump up ^ [1] Burial customs: mastabas. University College London (2001) Retrieved 14 April 2005
Jump up ^ "Early Dynastic burial customs". Digitalegypt.ucl.ac.uk. Retrieved 2012-11-16.
Jump up ^ Quirke, Stephen (2001). The Cult of Ra: Sun Worship in Ancient Egypt. Thames & Hudson, pp. 118–120.
Jump up ^ Lehner, Mark. The Complete Pyramids, London: Thames and Hudson (1997), p.41. ISBN 0-500-05084-8
^ Jump up to: a b Toby Wilkinson (2004). "Before the Pyramids". Egypt at its Origins. Studies in Memory of Barbara Adams Proceedings of the International Conference "Origin of the State. Predynastic and Early Dynastic Egypt", Krakow, 28th August - 1st September 2002. Peeters. p. 1142. ISBN 978-90-429-1469-8. Retrieved 18 June 2015. A final echo of earlier practices is seen in the domain established by Djoser to supply his mortuary cult. He called it Hr-sb3-/mti-pt, “Horus, the foremost star in the sky”. We could not wish for a clearer statement of the belief underlying the Step Pyramid: that it was a resurrection machine designed to propel its royal owner, Horus, to the pre-eminent place among the undying stars.
Jump up ^ "Discovery Channel Nederland". Discoverychannel.co.uk. Archived from the original on 5 December 2004. Retrieved 16 November 2012.
Jump up ^ https://web.archive.org/web/20080609220846/http://news.yahoo.com/s/ap/20080606/ap_on_re_mi_ea/egypt_missing_pyramid%3B_ylt%3DAtJMeqg4khfjCZgFw4P7z5us0NUE. Archived from the original on 9 June 2008. Retrieved 6 June 2008. Missing or empty |title= (help)
Jump up ^ "New Pyramid Found in Egypt: 4,300-Year-Old Queen's Tomb". News.nationalgeographic.com. 2010-10-28. Retrieved 2012-11-16.
Jump up ^ Kenneth Kitchen: Rammeside Inscriptions, Translated & Annotated, Translations, Volume II, Blackwell Publishers, ISBN 0-631-18435-X, 1996
Jump up ^ [2] The Mastaba of Shepseskaf
Jump up ^ Allen, James; Manuelian, Peter (2005). The Ancient Egyptian Pyramid Texts (Writings from the Ancient World, No. 23). Brill Academic. ISBN 978-90-04-13777-6.
Jump up ^ Terrence McCoy (2014-05-02). "The surprisingly simple way Egyptians moved massive pyramid stones without modern technology". The Washington Post.
Jump up ^ [3]
Bibliography
Edwards, I. E. S., The Pyramids of Egypt Penguin Books Ltd; New edition (5 Dec 1991), ISBN 978-0-14-013634-0
Lehner, Mark, The Complete Pyramids, Thames & Hudson, 1997, ISBN 978-0-500-05084-2
Mendelssohn, Kurt, The Riddle of the Pyramids, Thames & Hudson Ltd (6 May 1974), ISBN 978-0-500-05015-6
External links
Wikimedia Commons has media related to Pyramids of Egypt.
Ancient Egyptians from BBC History
Pyramids World Heritage Site in panographies – 360 degree interactive imaging
The Pyramids of Egypt – The meaning and construction of the Egyptian pyramids by Egyptologist Professor Nabil S welim.
Ancient Authors – A site that quotes descriptions of the "Labyrinth" of Amenemhet III's pyramid at el-Lahun by various ancient authors.
Ancient Egypt – History & Chronology – A site detailing the major pyramid sites of ancient Egypt and Nubia (Sudan).
[show]
v
t
e
Egyptian pyramids
List of Egyptian pyramids (Lepsius)
Commons
Period
Dynasty
Pyramids
Old Kingdom
(2686–2181 BC)
III
Djoser
Buried
Layer
Lepsius I (de)
Athribis
Elephantine
Edfu South
el-Kula (de)
Naqada
Saujet el-Meitin (de)
Sinki (de)
IV
Seila (de)
Meidum
Bent
Red
Khufu
Djedefre
Unfinished Northern Pyramid of Zawyet el'Aryan
Khafre
Menkaure
Khentkaus I (de)
Mastabet el-Fara'un
G1-a
G1-b
G1-c
G1-d
Lepsius L (de)
V
Userkaf
Neferhetepes (de)
Sahure
Neferirkare
Khentkaus II
Neferefre
Unfinished
Niuserre (de)
Lepsius XXIV
Double
Headless
Djedkare-Isesi
Unas
VI
Teti
Pepi I
Merenre
Pepi II
Sesheshet
1st Intermediate Period
(2181–2040 BC)
VII | VIII
Ity
Neferkare Neby
Ibi
Khui
X
Merikare
Middle Kingdom
(2040–1650 BC)
XI
Reherishefnakht
XII
Amenemhat I
Senusret I
White
Senusret II (de)
Senusret III
Black
Hawara
Neferuptah (de)
Central Dahshur (de)
South Mazghuna
North Mazghuna
XIII
Ameny Qemau
Khendjer
Southern South Saqqara
SAK S 3
SAK S 7 (de)
South Dahshur A (de)
South Dahshur B (de)
DAS 46
DAS 49
DAS 50
DAS 51
DAS 53 (de)
S 9
S 10
Merneferre Ay
Second Intermediate
(1650–1570 BC)
XVII
Sobekemsaf I
Sobekemsaf II
Sekhemre-Wepmaat Intef
Nubkheperre Intef
Senakhtenre Ahmose
Seqenenre Tao
Kamose

New Kingdom
(1570–1070 BC)
XVIII
Ahmose

Step pyramid
Construction techniques
Seked
Texts
Pyramidion
Pyramidology
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Euclid
From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Not to be confused with Euclid of Megara.
For other uses, see Euclid (disambiguation).
Euclid
Eukleides of Alexandria
Born
Mid-4th century BC
Died
Mid-3rd century BC
Residence
Alexandria, Hellenistic Egypt
Known for
Euclidean geometry
Euclid's Elements
Euclidean algorithm
Scientific career
Fields
Mathematics
Bramante as Euclid or Archimedes in the School of Athens.
Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης – Eukleídēs, pronounced [eu̯.klěː.dɛːs]; fl. 300 BC), sometimes given the name Euclid of Alexandria[1] to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry"[1] or the "father of geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century.[2][3][4] In the Elements, Euclid deduced the theorems of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory, and rigor.
Euclid is the anglicized version of the Greek name Εὐκλείδης, which means "renowned, glorious".[5]
Contents
1 Life
2 Elements
2.1 Fragments
3 Other works
3.1 Lost works
4 Legacy
5 See also
6 Notes
7 References
8 Further reading
9 External links
Life
Very few original references to Euclid survive, so little is known about his life. He was likely born c. 325 BC, although the place and circumstances of both his birth and death are unknown and may only be estimated roughly relative to other people mentioned with him. He is rarely mentioned by name by other Greek mathematicians from Archimedes (c. 287 BC – c. 212 BC) onward, and is usually referred to as "ὁ στοιχειώτης" ("the author of Elements").[6] The few historical references to Euclid were written centuries after he lived, by Pappus of Alexandria c. 320 AD and Proclus c. 450 AD.[7]
A detailed biography of Euclid is given by Arabian authors, mentioning, for example, a birth town of Tyre. This biography is generally believed to be fictitious.[8] If he came from Alexandria, he would have known the Serapeum of Alexandria, and the Library of Alexandria, and may have worked there during his time.
Euclid's arrival in Alexandria came about ten years after its founding by Alexander the Great (356 BC – 323 BC), which means he arrived c. 322 BC.[9]
Proclus introduces Euclid only briefly in his Commentary on the Elements. According to Proclus, Euclid supposedly belonged to Plato's "persuasion" and brought together the Elements, drawing on prior work of Eudoxus of Cnidus and of several pupils of Plato (particularly Theaetetus and Philip of Opus.) Proclus believes that Euclid is not much younger than these, and that he must have lived during the time of Ptolemy I because he was mentioned by Archimedes (287–212 BC). Although the apparent citation of Euclid by Archimedes has been judged to be an interpolation by later editors of his works, it is still believed that Euclid wrote his works before those of Archimedes.[10]
Euclidis quae supersunt omnia (1704)
Proclus later retells a story that, when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements, "Euclid replied there is no royal road to geometry."[11] This anecdote is questionable since it is similar to a story told about Menaechmus and Alexander the Great.[12]
In the only other key reference to Euclid, Pappus briefly mentioned in the fourth century that Apollonius "spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought" c. 247–222 BC.[13][14]
Euclid died c. 270 BC, presumably in Alexandria.[9]
Because the lack of biographical information is unusual for the period (extensive biographies are available for most significant Greek mathematicians for several centuries before and after Euclid), some researchers have proposed that Euclid was not, in fact, a historical character and that his works were written by a team of mathematicians who took the name Euclid from the historical character Euclid of Megara (compare Bourbaki). However, this hypothesis is not well accepted by scholars and there is little evidence in its favor.[15]
Elements
One of the oldest surviving fragments of Euclid's Elements, found at Oxyrhynchus and dated to circa AD 100 (P. Oxy. 29). The diagram accompanies Book II, Proposition 5.[16]
Main article: Euclid's Elements
Although many of the results in Elements originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later.[17]
There is no mention of Euclid in the earliest remaining copies of the Elements, and most of the copies say they are "from the edition of Theon" or the "lectures of Theon",[18] while the text considered to be primary, held by the Vatican, mentions no author. The only reference that historians rely on of Euclid having written the Elements was from Proclus, who briefly in his Commentary on the Elements ascribes Euclid as its author.
Although best known for its geometric results, the Elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid–Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers.
The geometrical system described in the Elements was long known simply as geometry, and was considered to be the only geometry possible. Today, however, that system is often referred to as Euclidean geometry to distinguish it from other so-called non-Euclidean geometries that mathematicians discovered in the 19th century.
Fragments
See also: Oxyrhynchus Papyri
The Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the Elements of Euclid, unearthed by Grenfell and Hunt 1897 in Oxyrhynchus. More recent scholarship suggests a date of 75–125 AD.[19]
The classic translation of T. L. Heath, reads:[20]
If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.
Other works
Euclid's construction of a regular dodecahedron.
Construction of a dodecahedron by placing faces on the edges of a cube.
In addition to the Elements, at least five works of Euclid have survived to the present day. They follow the same logical structure as Elements, with definitions and proved propositions.
Data deals with the nature and implications of "given" information in geometrical problems; the subject matter is closely related to the first four books of the Elements.
On Divisions of Figures, which survives only partially in Arabic translation, concerns the division of geometrical figures into two or more equal parts or into parts in given ratios. It is similar to a first-century AD work by Heron of Alexandria.
Catoptrics, which concerns the mathematical theory of mirrors, particularly the images formed in plane and spherical concave mirrors. The attribution is held to be anachronistic however by J J O'Connor and E F Robertson who name Theon of Alexandria as a more likely author.[21]
Phaenomena, a treatise on spherical astronomy, survives in Greek; it is quite similar to On the Moving Sphere by Autolycus of Pitane, who flourished around 310 BC.
20th Century statue by Joseph Durham in honor of Euclid in the Oxford University Museum of Natural History
Optics is the earliest surviving Greek treatise on perspective. In its definitions Euclid follows the Platonic tradition that vision is caused by discrete rays which emanate from the eye. One important definition is the fourth: "Things seen under a greater angle appear greater, and those under a lesser angle less, while those under equal angles appear equal." In the 36 propositions that follow, Euclid relates the apparent size of an object to its distance from the eye and investigates the apparent shapes of cylinders and cones when viewed from different angles. Proposition 45 is interesting, proving that for any two unequal magnitudes, there is a point from which the two appear equal. Pappus believed these results to be important in astronomy and included Euclid's Optics, along with his Phaenomena, in the Little Astronomy, a compendium of smaller works to be studied before the Syntaxis (Almagest) of Claudius Ptolemy.
Lost works
Other works are credibly attributed to Euclid, but have been lost.
Conics was a work on conic sections that was later extended by Apollonius of Perga into his famous work on the subject. It is likely that the first four books of Apollonius's work come directly from Euclid. According to Pappus, "Apollonius, having completed Euclid's four books of conics and added four others, handed down eight volumes of conics." The Conics of Apollonius quickly supplanted the former work, and by the time of Pappus, Euclid's work was already lost.
Porisms might have been an outgrowth of Euclid's work with conic sections, but the exact meaning of the title is controversial.
Pseudaria, or Book of Fallacies, was an elementary text about errors in reasoning.
Surface Loci concerned either loci (sets of points) on surfaces or loci which were themselves surfaces; under the latter interpretation, it has been hypothesized that the work might have dealt with quadric surfaces.
Several works on mechanics are attributed to Euclid by Arabic sources. On the Heavy and the Light contains, in nine definitions and five propositions, Aristotelian notions of moving bodies and the concept of specific gravity. On the Balance treats the theory of the lever in a similarly Euclidean manner, containing one definition, two axioms, and four propositions. A third fragment, on the circles described by the ends of a moving lever, contains four propositions. These three works complement each other in such a way that it has been suggested that they are remnants of a single treatise on mechanics written by Euclid.
Legacy
The European Space Agency's (ESA) Euclid spacecraft was named in his honor.[22]
See also
Axiomatic method
Euclid's orchard
Euclidean algorithm
Euclidean geometry
Euclidean relation
Extended Euclidean algorithm
List of topics named after Euclid
Notes
^ Jump up to: a b Bruno, Leonard C. (2003) [1999]. Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 125. ISBN 0787638137. OCLC 41497065.
Jump up ^ Ball, pp. 50–62.
Jump up ^ Boyer, pp. 100–19.
Jump up ^ Macardle, et al. (2008). Scientists: Extraordinary People Who Altered the Course of History. New York: Metro Books. g. 12.
Jump up ^ Harper, Douglas. "Euclidean (adj.)". Online Etymology Dictionary. Retrieved March 18, 2015.
Jump up ^ Heath (1981), p. 357
Jump up ^ Joyce, David. Euclid. Clark University Department of Mathematics and Computer Science. [1]
Jump up ^ O'Connor, John J.; Robertson, Edmund F., "Euclid of Alexandria"; Heath 1956, p. 4; Heath 1981, p. 355.
^ Jump up to: a b Bruno, Leonard C. (2003) [1999]. Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 126. ISBN 0787638137. OCLC 41497065.
Jump up ^ Proclus, p. XXX; O'Connor, John J.; Robertson, Edmund F., "Euclid of Alexandria"
Jump up ^ Proclus, p. 57
Jump up ^ Boyer, p. 96.
Jump up ^ Heath (1956), p. 2.
Jump up ^ "Conic Sections in Ancient Greece".
Jump up ^ O'Connor, John J.; Robertson, Edmund F., "Euclid of Alexandria"; Jean Itard (1962). Les livres arithmétiques d'Euclide.
Jump up ^ Bill Casselman. "One of the Oldest Extant Diagrams from Euclid". University of British Columbia. Retrieved 2008-09-26.
Jump up ^ Struik p. 51 ("their logical structure has influenced scientific thinking perhaps more than any other text in the world").
Jump up ^ Heath (1981), p. 360.
Jump up ^ Fowler, David (1999). The Mathematics of Plato's Academy (Second ed.). Oxford: Clarendon Press. ISBN 0-19-850258-3.
Jump up ^ Bill Casselman, One of the oldest extant diagrams from Euclid
Jump up ^ O'Connor, John J.; Robertson, Edmund F., "Theon of Alexandria"
Jump up ^ "NASA Delivers Detectors for ESA's Euclid Spacecraft". NASA. 2017.
References
Artmann, Benno (1999). Euclid: The Creation of Mathematics. New York: Springer. ISBN 0-387-98423-2.
Ball, W.W. Rouse (1960) [1908]. A Short Account of the History of Mathematics (4th ed.). Dover Publications. pp. 50–62. ISBN 0-486-20630-0.
Boyer, Carl B. (1991). A History of Mathematics (2nd ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7.
Douglass, Charlene (2007). Page, John D., ed. "Euclid". Math Open Reference. With extensive bibliography.
Heath, Thomas (ed.) (1956) [1908]. The Thirteen Books of Euclid's Elements. 1. Dover Publications. ISBN 0-486-60088-2. CS1 maint: Extra text: authors list (link)
Heath, Thomas L. (1908). "Euclid and the Traditions About Him". In Heath, Thomas L. Euclid, Elements. 1. pp. 1–6. As reproduced in the Perseus Digital Library.
Heath, Thomas L. (1981). A History of Greek Mathematics, 2 Vols. New York: Dover Publications. ISBN 0-486-24073-8 / ISBN 0-486-24074-6.
Kline, Morris (1980). Mathematics: The Loss of Certainty. Oxford: Oxford University Press. ISBN 0-19-502754-X.
O'Connor, John J.; Robertson, Edmund F., "Euclid of Alexandria", MacTutor History of Mathematics archive, University of St Andrews .
O'Connor, John J.; Robertson, Edmund F., "Theon of Alexandria", MacTutor History of Mathematics archive, University of St Andrews .
Proclus, A commentary on the First Book of Euclid's Elements, translated by Glenn Raymond Morrow, Princeton University Press, 1992. ISBN 978-0-691-02090-7.
Struik, Dirk J. (1967). A Concise History of Mathematics. Dover Publications. ISBN 0-486-60255-9.
Van der Waerden, Bartel Leendert; Taisbak, Christian Marinus (October 30, 2014). "Euclid". Encyclopædia Britannica. Retrieved November 21, 2014.
Further reading
DeLacy, Estelle Allen (1963). Euclid and Geometry. New York: Franklin Watts.
Knorr, Wilbur Richard (1975). The Evolution of the Euclidean Elements: A Study of the Theory of Incommensurable Magnitudes and Its Significance for Early Greek Geometry. Dordrecht, Holland: D. Reidel. ISBN 90-277-0509-7.
Mueller, Ian (1981). Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge, MA: MIT Press. ISBN 0-262-13163-3.
Reid, Constance (1963). A Long Way from Euclid. New York: Crowell.
Szabó, Árpád (1978). The Beginnings of Greek Mathematics. A.M. Ungar, trans. Dordrecht, Holland: D. Reidel. ISBN 90-277-0819-3.
External links
Wikiquote has quotations related to: Euclid
Wikisource has original works written by or about:
Euclid
Wikimedia Commons has media related to Euclid.
Wikisource has the text of the 1911 Encyclopædia Britannica article Euclid.
Works by Euclid at Project Gutenberg
Works by or about Euclid at Internet Archive
Works by Euclid at LibriVox (public domain audiobooks)
Euclid's Elements, All thirteen books, with interactive diagrams using Java. Clark University
Euclid's Elements, with the original Greek and an English translation on facing pages (includes PDF version for printing). University of Texas.
Euclid's Elements, books I–VI, in English pdf, in a Project Gutenberg Victorian textbook edition with diagrams.
Euclid's Elements, All thirteen books, in several languages as Spanish, Catalan, English, German, Portuguese, Arabic, Italian, Russian and Chinese.
Elementa Geometriae 1482, Venice. From Rare Book Room.
Elementa 888 AD, Byzantine. From Rare Book Room.
Texts on Ancient Mathematics and Mathematical Astronomy PDF scans (Note: many are very large files). Includes editions and translations of Euclid's Elements, Data, and Optica, Proclus's Commentary on Euclid, and other historical sources.
The Elements of Geometrie of the Most Auncient Philosopher Euclide of Megara (1570) from the English Printing Collection in the Rare Book and Special Collection Division at the Library of Congress
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BIBSYS: 90205202
BNE: XX1000405
BNF: cb11901997s (data)
GND: 118638955
ISNI: 0000 0001 2321 3955
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https://ia.wikipedia.org/wiki/Euclide
Euclide – Interlingua
ia
ia
interlanguage-link-target

values:
interlanguage-link interwiki-ia
display: none;

values:
https://xh.wikipedia.org/wiki/U-Euclid
U-Euclid – Xhosa
xh
xh
interlanguage-link-target

values:
interlanguage-link interwiki-xh
display: none;

values:
interlanguage-link interwiki-is
display: none;

values:
https://it.wikipedia.org/wiki/Euclide
Euclide – Italian
it
it
interlanguage-link-target

values:
interlanguage-link interwiki-it
display: none;

values: אוקלידס – Hebrew

values:
interlanguage-link interwiki-he
display: none;

values:
https://jv.wikipedia.org/wiki/Euklides
Euklides – Javanese
jv
jv
interlanguage-link-target

values:
interlanguage-link interwiki-jv
display: none;

values: ევკლიდე – Georgian

values:
interlanguage-link interwiki-ka
display: none;

values: Евклид – Kazakh

values:
interlanguage-link interwiki-kk
display: none;

values:
https://sw.wikipedia.org/wiki/Euklides
Euklides – Swahili
sw
sw
interlanguage-link-target

values:
interlanguage-link interwiki-sw
display: none;

values:
interlanguage-link interwiki-ku
display: none;

values: Евклид – Kyrgyz

values:
interlanguage-link interwiki-ky
display: none;

values:
interlanguage-link interwiki-lez
display: none;

values:
https://la.wikipedia.org/wiki/Euclides
Euclides – Latin
la
la
interlanguage-link-target

values:
interlanguage-link interwiki-la
display: none;

values:
interlanguage-link interwiki-lv
display: none;

values:
interlanguage-link interwiki-lt
display: none;

values:
https://lij.wikipedia.org/wiki/Euclide
Euclide – Ligurian
lij
lij
interlanguage-link-target

values:
interlanguage-link interwiki-lij
display: none;

values:
interlanguage-link interwiki-olo
display: none;

values:
https://jbo.wikipedia.org/wiki/euklides
euklides – Lojban
jbo
jbo
interlanguage-link-target

values:
interlanguage-link interwiki-jbo
display: none;

values:
https://lmo.wikipedia.org/wiki/Euclide
Euclide – Lombard
lmo
lmo
interlanguage-link-target

values:
interlanguage-link interwiki-lmo
display: none;

values:
interlanguage-link interwiki-hu
display: none;

values:
interlanguage-link interwiki-mk
display: none;

values:
https://mg.wikipedia.org/wiki/Eoklida
Eoklida – Malagasy
mg
mg
interlanguage-link-target

values:
interlanguage-link interwiki-mg
display: none;

values: യൂക്ലിഡ് – Malayalam

values:
interlanguage-link interwiki-ml
display: none;

values:
https://mt.wikipedia.org/wiki/Ewklide
Ewklide – Maltese
mt
mt
interlanguage-link-target

values:
interlanguage-link interwiki-mt
display: none;

values: युक्लीड – Marathi

values:
interlanguage-link interwiki-mr
display: none;

values:
interlanguage-link interwiki-xmf
display: none;

values:
interlanguage-link interwiki-arz
display: none;

values:
https://ms.wikipedia.org/wiki/Euclid
Euclid – Malay
ms
ms
interlanguage-link-target

values:
https://mwl.wikipedia.org/wiki/Ouclides
Ouclides – Mirandese
mwl
mwl
interlanguage-link-target

values:
interlanguage-link interwiki-mwl
display: none;

values:
interlanguage-link interwiki-mn
display: none;

values: ယူကလစ် – Burmese

values:
interlanguage-link interwiki-my
display: none;

values:
interlanguage-link interwiki-nl
display: none;

values: エウクレイデス – Japanese

values:
interlanguage-link interwiki-ja
display: none;

values: Евклид – Chechen

values:
interlanguage-link interwiki-ce
display: none;

values:
https://frr.wikipedia.org/wiki/Euklid
Euklid – Northern Frisian
frr
frr
interlanguage-link-target

values:
interlanguage-link interwiki-frr
display: none;

values:
https://no.wikipedia.org/wiki/Evklid
Evklid – Norwegian
no
no
interlanguage-link-target

values:
interlanguage-link interwiki-no
display: none;

values:
https://nn.wikipedia.org/wiki/Evklid
Evklid – Norwegian Nynorsk
nn
nn
interlanguage-link-target

values:
interlanguage-link interwiki-nn
display: none;

values:
https://oc.wikipedia.org/wiki/Euclides
Euclides – Occitan
oc
oc
interlanguage-link-target

values:
interlanguage-link interwiki-oc
display: none;

values: ୟୁକ୍ଲିଡ୍ – Odia

values:
interlanguage-link interwiki-or
display: none;

values:
https://om.wikipedia.org/wiki/Yuukiliid
Yuukiliid – Oromo
om
om
interlanguage-link-target

values:
interlanguage-link interwiki-om
display: none;

values:
https://uz.wikipedia.org/wiki/Yevklid
Yevklid – Uzbek
uz
uz
interlanguage-link-target

values:
interlanguage-link interwiki-uz
display: none;

values: ਯੂਕਲਿਡ – Punjabi

values:
interlanguage-link interwiki-pa
display: none;

values:
interlanguage-link interwiki-pnb
display: none;

values: اقليدس – Pashto

values:
interlanguage-link interwiki-ps
display: none;

values:
https://jam.wikipedia.org/wiki/Euclid
Euclid – Jamaican Creole English
jam
jam
interlanguage-link-target

values:
interlanguage-link interwiki-jam
display: none;

values:
https://pms.wikipedia.org/wiki/Euclid
Euclid – Piedmontese
pms
pms
interlanguage-link-target

values:
interlanguage-link interwiki-pms
display: none;

values:
https://pl.wikipedia.org/wiki/Euklides
Euklides – Polish
pl
pl
interlanguage-link-target

values:
interlanguage-link interwiki-pl
display: none;

values:
https://pt.wikipedia.org/wiki/Euclides
Euclides – Portuguese
pt
pt
interlanguage-link-target

values:
https://kaa.wikipedia.org/wiki/Evklid
Evklid – Kara-Kalpak
kaa
kaa
interlanguage-link-target

values:
interlanguage-link interwiki-kaa
display: none;

values:
interlanguage-link interwiki-ksh
display: none;

values:
https://ro.wikipedia.org/wiki/Euclid
Euclid – Romanian
ro
ro
interlanguage-link-target

values:
interlanguage-link interwiki-ro
display: none;

values: Евклід – Rusyn

values:
interlanguage-link interwiki-rue
display: none;

values: Евклид – Russian

values: Эклид – Sakha

values:
interlanguage-link interwiki-sah
display: none;

values: ᱤᱣᱠᱞᱤᱰ – Santali

values:
interlanguage-link interwiki-sat
display: none;

values:
https://sco.wikipedia.org/wiki/Euclid
Euclid – Scots
sco
sco
interlanguage-link-target

values:
interlanguage-link interwiki-sco
display: none;

values:
https://sq.wikipedia.org/wiki/Euklidi
Euklidi – Albanian
sq
sq
interlanguage-link-target

values:
interlanguage-link interwiki-sq
display: none;

values:
https://scn.wikipedia.org/wiki/Euclidi
Euclidi – Sicilian
scn
scn
interlanguage-link-target

values:
interlanguage-link interwiki-scn
display: none;

values:
interlanguage-link interwiki-simple
display: none;

values: اقليدس – Sindhi

values:
interlanguage-link interwiki-sd
display: none;

values:
interlanguage-link interwiki-sk
display: none;

values:
https://sl.wikipedia.org/wiki/Evklid
Evklid – Slovenian
sl
sl
interlanguage-link-target

values:
interlanguage-link interwiki-sl
display: none;

values:
interlanguage-link interwiki-ckb
display: none;

values: Еуклид – Serbian

values:
interlanguage-link interwiki-sr
display: none;

values:
https://sh.wikipedia.org/wiki/Euklid
Euklid – Serbo-Croatian
sh
sh
interlanguage-link-target

values:
interlanguage-link interwiki-sh
display: none;

values:
https://fi.wikipedia.org/wiki/Eukleides
Eukleides – Finnish
fi
fi
interlanguage-link-target

values:
interlanguage-link interwiki-fi
display: none;

values:
https://sv.wikipedia.org/wiki/Euklides
Euklides – Swedish
sv
sv
interlanguage-link-target

values:
interlanguage-link interwiki-sv
display: none;

values:
https://tl.wikipedia.org/wiki/Euclid
Euclid – Tagalog
tl
tl
interlanguage-link-target

values:
interlanguage-link interwiki-tl
display: none;

values: யூக்ளிடு – Tamil

values:
interlanguage-link interwiki-ta
display: none;

values: Эуклид – Tatar

values:
interlanguage-link interwiki-tt
display: none;

values: యూక్లిడ్ – Telugu

values:
interlanguage-link interwiki-te
display: none;

values: ยุคลิด – Thai

values:
interlanguage-link interwiki-th
display: none;

values: Эвклид – Tajik

values:
interlanguage-link interwiki-tg
display: none;

values:
interlanguage-link interwiki-tr
display: none;

values:
interlanguage-link interwiki-uk
display: none;

values: اقلیدس – Urdu

values:
https://za.wikipedia.org/wiki/Euclid
Euclid – Zhuang
za
za
interlanguage-link-target

values:
interlanguage-link interwiki-za
display: none;

values:
https://vec.wikipedia.org/wiki/Euclide
Euclide – Venetian
vec
vec
interlanguage-link-target

values:
interlanguage-link interwiki-vec
display: none;

values:
https://vep.wikipedia.org/wiki/Evklid
Evklid – Veps
vep
vep
interlanguage-link-target

values:
interlanguage-link interwiki-vep
display: none;

values:
https://vi.wikipedia.org/wiki/Euclid
Euclid – Vietnamese
vi
vi
interlanguage-link-target

values:
interlanguage-link interwiki-vi
display: none;

values:
https://vo.wikipedia.org/wiki/Eukleides
Eukleides – Volapük
vo
vo
interlanguage-link-target

values:
interlanguage-link interwiki-vo
display: none;

values:
interlanguage-link interwiki-fiu-vro
display: none;

values:
interlanguage-link interwiki-war
display: none;

values:
interlanguage-link interwiki-wuu
display: none;

values: אוקלידוס – Yiddish

values:
interlanguage-link interwiki-yi
display: none;

values:
https://yo.wikipedia.org/wiki/Euclid
Euclid – Yoruba
yo
yo
interlanguage-link-target

values:
interlanguage-link interwiki-yo
display: none;

values:
interlanguage-link interwiki-zh-yue
display: none;

values:
interlanguage-link interwiki-bat-smg
display: none;

values:
https://kbp.wikipedia.org/wiki/Euclid
Euclid – Kabiye
kbp
kbp
interlanguage-link-target

values:
interlanguage-link interwiki-kbp
display: none;

values: All languages (initial selection from common choices by you and others)

values: mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Euclid rootpage-Euclid skin-vector action-view