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Euclid's Elements

Index Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. [1]

137 relations: Adelard of Bath, Albert Einstein, Alexandria, Alfred North Whitehead, Ancient Greek, Apocrypha, Apollonius of Perga, Arabic, Area, Arethas of Caesarea, Baruch Spinoza, Bertrand Russell, Bible, Bodleian Library, Boethius, Book frontispiece, Brazilian Portuguese, Byzantine Empire, Campanus of Novara, Charles Scarborough, Chinese language, Chinese mathematics, Christopher Clavius, Cicero, Circumscribed circle, Claude Dechales, Clay Mathematics Institute, Commensurability (mathematics), Compass-and-straightedge construction, Cone, Cylinder, Data (Euclid), Denis Henrion, Dionysius Lardner, Divisibility rule, Dodecahedron, Dudley R. Herschbach, Editio princeps, Edna St. Vincent Millay, Erhard Ratdolt, Euclid, Euclid's theorem, Euclidean algorithm, Euclidean geometry, Eudoxus of Cnidus, Federico Commandino, François Peyrard, Galileo Galilei, Geometric progression, Godfried Toussaint, ..., Golden ratio, Greatest common divisor, Greek mathematics, Greek numerals, Harun al-Rashid, Henry Billingsley, Hippocrates, Hippocrates of Chios, History of algebra, Hypsicles, Icosahedron, Incircle and excircles of a triangle, Inscribed figure, Integral, Irrational number, Isaac Barrow, Isaac Newton, Isaac Todhunter, Isidore of Miletus, Jagannatha Samrat, Johan Ludvig Heiberg (historian), Johannes Kepler, Johannes Scheubel, John Dee, John Keill, John Playfair, K. V. Sarma, Least common multiple, Logic, Magnitude (mathematics), Mathematical proof, Mathematics, Matteo Ricci, Medici Oriental Press, Method of exhaustion, Mikhail Vaschenko-Zakharchenko, Movable type, Nasir al-Din al-Tusi, New York City, Niccolò Fontana Tartaglia, Nicolaus Copernicus, Number theory, Oliver Byrne (mathematician), Papyrus Oxyrhynchus 29, Parallel postulate, Parallelepiped, Perfect number, Petr Vopěnka, Pierre Hérigone, Pietro Cataldi, Platonic solid, Prime number, Proclus, Project Gutenberg, Ptolemaic Kingdom, Pyramid (geometry), Pythagoras, Pythagorean theorem, Pythagorean triple, Quadrivium, R. Catesby Taliaferro, Regiomontanus, Regular polygon, Robert Simson, Rodrigo Zamorano, Sámuel Brassai, Scholia, Science, Siku Quanshu, Similarity (geometry), Society of Jesus, Sphere, Springer Publishing, Tangent, Thales's theorem, Theaetetus (mathematician), Theon of Alexandria, Theorem, Thomas Hobbes, Thomas Little Heath, Thomas More, Thomas Perronet Thompson, Thomas Rudd, Treatise, Vatican Library, W. W. Rouse Ball, Xu Guangqi. Expand index (87 more) »

Adelard of Bath

Adelard of Bath (Adelardus Bathensis; 1080 1152 AD) was a 12th-century English natural philosopher.

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Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Alexandria (or; Arabic: الإسكندرية; Egyptian Arabic: إسكندرية; Ⲁⲗⲉⲝⲁⲛⲇⲣⲓⲁ; Ⲣⲁⲕⲟⲧⲉ) is the second-largest city in Egypt and a major economic centre, extending about along the coast of the Mediterranean Sea in the north central part of the country.

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Alfred North Whitehead

Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

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Ancient Greek

The Ancient Greek language includes the forms of Greek used in ancient Greece and the ancient world from around the 9th century BC to the 6th century AD.

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Apocrypha are works, usually written, of unknown authorship or of doubtful origin.

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Apollonius of Perga

Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος; Apollonius Pergaeus; late 3rdearly 2nd centuries BC) was a Greek geometer and astronomer known for his theories on the topic of conic sections.

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Arabic (العَرَبِيَّة) or (عَرَبِيّ) or) is a Central Semitic language that first emerged in Iron Age northwestern Arabia and is now the lingua franca of the Arab world. It is named after the Arabs, a term initially used to describe peoples living from Mesopotamia in the east to the Anti-Lebanon mountains in the west, in northwestern Arabia, and in the Sinai peninsula. Arabic is classified as a macrolanguage comprising 30 modern varieties, including its standard form, Modern Standard Arabic, which is derived from Classical Arabic. As the modern written language, Modern Standard Arabic is widely taught in schools and universities, and is used to varying degrees in workplaces, government, and the media. The two formal varieties are grouped together as Literary Arabic (fuṣḥā), which is the official language of 26 states and the liturgical language of Islam. Modern Standard Arabic largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties, and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary is used to denote concepts that have arisen in the post-classical era, especially in modern times. During the Middle Ages, Literary Arabic was a major vehicle of culture in Europe, especially in science, mathematics and philosophy. As a result, many European languages have also borrowed many words from it. Arabic influence, mainly in vocabulary, is seen in European languages, mainly Spanish and to a lesser extent Portuguese, Valencian and Catalan, owing to both the proximity of Christian European and Muslim Arab civilizations and 800 years of Arabic culture and language in the Iberian Peninsula, referred to in Arabic as al-Andalus. Sicilian has about 500 Arabic words as result of Sicily being progressively conquered by Arabs from North Africa, from the mid 9th to mid 10th centuries. Many of these words relate to agriculture and related activities (Hull and Ruffino). Balkan languages, including Greek and Bulgarian, have also acquired a significant number of Arabic words through contact with Ottoman Turkish. Arabic has influenced many languages around the globe throughout its history. Some of the most influenced languages are Persian, Turkish, Spanish, Urdu, Kashmiri, Kurdish, Bosnian, Kazakh, Bengali, Hindi, Malay, Maldivian, Indonesian, Pashto, Punjabi, Tagalog, Sindhi, and Hausa, and some languages in parts of Africa. Conversely, Arabic has borrowed words from other languages, including Greek and Persian in medieval times, and contemporary European languages such as English and French in modern times. Classical Arabic is the liturgical language of 1.8 billion Muslims and Modern Standard Arabic is one of six official languages of the United Nations. All varieties of Arabic combined are spoken by perhaps as many as 422 million speakers (native and non-native) in the Arab world, making it the fifth most spoken language in the world. Arabic is written with the Arabic alphabet, which is an abjad script and is written from right to left, although the spoken varieties are sometimes written in ASCII Latin from left to right with no standardized orthography.

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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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Arethas of Caesarea

Arethas of Caesarea (Ἀρέθας; born c. 860 AD) was Archbishop of Caesarea Mazaca in Cappadocia (modern Kayseri, Turkey) early in the 10th century, and is considered one of the most scholarly theologians of the Greek Orthodox Church.

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Baruch Spinoza

Baruch Spinoza (born Benedito de Espinosa,; 24 November 1632 – 21 February 1677, later Benedict de Spinoza) was a Dutch philosopher of Sephardi/Portuguese origin.

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Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

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The Bible (from Koine Greek τὰ βιβλία, tà biblía, "the books") is a collection of sacred texts or scriptures that Jews and Christians consider to be a product of divine inspiration and a record of the relationship between God and humans.

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Bodleian Library

The Bodleian Library is the main research library of the University of Oxford, and is one of the oldest libraries in Europe.

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Anicius Manlius Severinus Boëthius, commonly called Boethius (also Boetius; 477–524 AD), was a Roman senator, consul, magister officiorum, and philosopher of the early 6th century.

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Book frontispiece

A frontispiece in books is a decorative or informative illustration facing a book's title page — on the left-hand, or verso, page opposite the right-hand, or recto, page.

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Brazilian Portuguese

Brazilian Portuguese (português do Brasil or português brasileiro) is a set of dialects of the Portuguese language used mostly in Brazil.

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Byzantine Empire

The Byzantine Empire, also referred to as the Eastern Roman Empire and Byzantium, was the continuation of the Roman Empire in its eastern provinces during Late Antiquity and the Middle Ages, when its capital city was Constantinople (modern-day Istanbul, which had been founded as Byzantium).

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Campanus of Novara

Campanus of Novara (1220 – 1296) was an Italian mathematician, astronomer, astrologer, and physician who is best known for his work on Euclid's ''Elements''.

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Charles Scarborough

Sir Charles Scarborough or Scarburgh MP FRS FRCP (29 December 1615 – 26 February 1694) was an English physician and mathematician.

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Chinese language

Chinese is a group of related, but in many cases mutually unintelligible, language varieties, forming a branch of the Sino-Tibetan language family.

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Chinese mathematics

Mathematics in China emerged independently by the 11th century BC.

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Christopher Clavius

Christopher Clavius (25 March 1538 – 6 February 1612) was a German Jesuit mathematician and astronomer who modified the proposal of the modern Gregorian calendar after the death of its primary author, Aloysius Lilius.

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Marcus Tullius Cicero (3 January 106 BC – 7 December 43 BC) was a Roman statesman, orator, lawyer and philosopher, who served as consul in the year 63 BC.

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Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

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Claude Dechales

Claude François Milliet Dechales (1621 – 28 March 1678) was a French Jesuit priest and mathematician.

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Clay Mathematics Institute

The Clay Mathematics Institute (CMI) is a private, non-profit foundation, based in Peterborough, New Hampshire, United States.

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Commensurability (mathematics)

In mathematics, two non-zero real numbers a and b are said to be commensurable if their ratio is a rational number; otherwise a and b are called incommensurable.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

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A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

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Data (Euclid)

Data (Greek: Δεδομένα, Dedomena) is a work by Euclid.

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Denis Henrion

Denis (sometimes Didier) Henrion, was a French mathematician born at the end of the 16th century in France.

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Dionysius Lardner

Prof Dionysius Lardner FRS FRSE (3 April 179329 April 1859) was an Irish scientific writer who popularised science and technology, and edited the 133-volume Cabinet Cyclopædia.

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Divisibility rule

A divisibility rule is a shorthand way of determining whether a given integer is divisible by a fixed divisor without performing the division, usually by examining its digits.

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In geometry, a dodecahedron (Greek δωδεκάεδρον, from δώδεκα dōdeka "twelve" + ἕδρα hédra "base", "seat" or "face") is any polyhedron with twelve flat faces.

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Dudley R. Herschbach

Dudley Robert Herschbach (born June 18, 1932) is an American chemist at Harvard University.

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Editio princeps

In classical scholarship, the editio princeps (plural: editiones principes) of a work is the first printed edition of the work, that previously had existed only in manuscripts, which could be circulated only after being copied by hand.

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Edna St. Vincent Millay

Edna St.

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Erhard Ratdolt

Erhard Ratdolt (1442–1528) was an early German printer from Augsburg.

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Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's theorem

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

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Euclidean algorithm


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Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

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Eudoxus of Cnidus

Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, scholar, and student of Archytas and Plato.

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Federico Commandino

Federico Commandino (1509 – 5 September 1575) was an Italian humanist and mathematician.

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François Peyrard

François Peyrard (1760–1822) was a French mathematician, educator and librarian.

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Galileo Galilei

Galileo Galilei (15 February 1564Drake (1978, p. 1). The date of Galileo's birth is given according to the Julian calendar, which was then in force throughout Christendom. In 1582 it was replaced in Italy and several other Catholic countries with the Gregorian calendar. Unless otherwise indicated, dates in this article are given according to the Gregorian calendar. – 8 January 1642) was an Italian polymath.

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Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

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Godfried Toussaint

Godfried T. Toussaint is a Canadian Computer Scientist, a Professor of Computer Science, and the Head of the Computer Science Program at New York University Abu Dhabi (NYUAD) in Abu Dhabi, United Arab Emirates.

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Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

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Greatest common divisor

In mathematics, the greatest common divisor (gcd) of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.

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Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

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Greek numerals

Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet.

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Harun al-Rashid

Harun al-Rashid (هَارُون الرَشِيد Hārūn Ar-Rašīd; "Harun the Orthodox" or "Harun the Rightly-Guided," 17 March 763 or February 766 — 24 March 809 (148–193 Hijri) was the fifth Abbasid Caliph. His birth date is debated, with various sources giving dates from 763 to 766. His epithet "al-Rashid" translates to "the Orthodox," "the Just," "the Upright," or "the Rightly-Guided." Al-Rashid ruled from 786 to 809, during the peak of the Islamic Golden Age. His time was marked by scientific, cultural, and religious prosperity. Islamic art and music also flourished significantly during his reign. He established the legendary library Bayt al-Hikma ("House of Wisdom") in Baghdad in present-day Iraq, and during his rule Baghdad began to flourish as a center of knowledge, culture and trade. During his rule, the family of Barmakids, which played a deciding role in establishing the Abbasid Caliphate, declined gradually. In 796, he moved his court and government to Raqqa in present-day Syria. A Frankish mission came to offer Harun friendship in 799. Harun sent various presents with the emissaries on their return to Charlemagne's court, including a clock that Charlemagne and his retinue deemed to be a conjuration because of the sounds it emanated and the tricks it displayed every time an hour ticked. The fictional The Book of One Thousand and One Nights is set in Harun's magnificent court and some of its stories involve Harun himself. Harun's life and court have been the subject of many other tales, both factual and fictitious. Some of the Twelver sect of Shia Muslims blame Harun for his supposed role in the murder of their 7th Imam (Musa ibn Ja'far).

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Henry Billingsley

Sir Henry Billingsley (died 22 November 1606) was an English merchant, Lord Mayor of London and the first translator of Euclid into English.

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Hippocrates of Kos (Hippokrátēs ho Kṓos), also known as Hippocrates II, was a Greek physician of the Age of Pericles (Classical Greece), and is considered one of the most outstanding figures in the history of medicine.

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Hippocrates of Chios

Hippocrates of Chios (Ἱπποκράτης ὁ Χῖος) was an ancient Greek mathematician, geometer, and astronomer who lived c. 470 – c. 410 BC.

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History of algebra

As a branch of mathematics, algebra emerged at the end of the 16th century in Europe, with the work of François Viète.

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Hypsicles (Ὑψικλῆς; c. 190 – c. 120 BCE) was an ancient Greek mathematician and astronomer known for authoring On Ascensions (Ἀναφορικός) and the Book XIV of Euclid's ''Elements''.

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In geometry, an icosahedron is a polyhedron with 20 faces.

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Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

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Inscribed figure

An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid.

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In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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Irrational number

In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

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Isaac Barrow

Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus.

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

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Isaac Todhunter

Isaac Todhunter FRS (23 November 1820 – 1 March 1884), was an English mathematician who is best known today for the books he wrote on mathematics and its history.

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Isidore of Miletus

Isidore of Miletus (Ἰσίδωρος ὁ Μιλήσιος; Medieval Greek pronunciation:; Isidorus Miletus) was one of the two main Byzantine Greek architects (Anthemius of Tralles was the other) that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537.

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Jagannatha Samrat

Paṇḍita Jagannātha Samrāṭ (1652–1744) was an Indian astronomer and mathematician who served in the court of Jai Singh II of Amber, and was also his guru.

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Johan Ludvig Heiberg (historian)

Johan Ludvig Heiberg (27 November 1854 – 4 January 1928) was a Danish philologist and historian.

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Johannes Kepler

Johannes Kepler (December 27, 1571 – November 15, 1630) was a German mathematician, astronomer, and astrologer.

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Johannes Scheubel

Johannes Scheubel (18 August 1494 – 20 February 1570) was a German mathematician.

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John Dee

John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, astrologer, occult philosopher, and advisor to Queen Elizabeth I. He devoted much of his life to the study of alchemy, divination, and Hermetic philosophy.

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John Keill

John Keill (1 December 1671 – 31 August 1721) was a Scottish mathematician, academic and author who was an important disciple of Isaac Newton.

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John Playfair

Rev Prof John Playfair FRSE, FRS (10 March 1748 – 20 July 1819) was a Church of Scotland minister, remembered as a scientist and mathematician, and a professor of natural philosophy at the University of Edinburgh.

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K. V. Sarma


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Least common multiple

In arithmetic and number theory, the least common multiple, lowest common multiple, or smallest common multiple of two integers a and b, usually denoted by LCM(a, b), is the smallest positive integer that is divisible by both a and b. Since division of integers by zero is undefined, this definition has meaning only if a and b are both different from zero.

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Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

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Magnitude (mathematics)

In mathematics, magnitude is the size of a mathematical object, a property which determines whether the object is larger or smaller than other objects of the same kind.

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Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

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Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Matteo Ricci

Matteo Ricci, S.J. (Mattheus Riccius Maceratensis; 6 October 1552 – 11 May 1610), was an Italian Jesuit priest and one of the founding figures of the Jesuit China missions.

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Medici Oriental Press

The Medici Oriental Press (also Typographia Medicea) was a press established by Ferdinand de Medici in the 16th century.

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Method of exhaustion

The method of exhaustion (methodus exhaustionibus, or méthode des anciens) is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.

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Mikhail Vaschenko-Zakharchenko

Mikhail Yegorovich Vaschenko-Zakharchenko (Михаи́л Его́рович Ва́щенко-Заха́рченко, Миха́йло Єго́рович Ва́щенко-Заха́рченко) (October 31 (old style) (November 12) 1825 in Malievka, Zolotonosha uyezd, Poltava Governorate, Russian Empire – August 14 (old style) (August 27) 1912 in Kiev, Russian Empire) was a Russian mathematician, member of Moscow Mathematical Society from 1866 and Privy Councillor of Russia from 1908.

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Movable type

Movable type (US English; moveable type in British English) is the system and technology of printing and typography that uses movable components to reproduce the elements of a document (usually individual letters or punctuation) usually on the medium of paper.

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Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (محمد بن محمد بن حسن طوسی‎ 18 February 1201 – 26 June 1274), better known as Nasir al-Din Tusi (نصیر الدین طوسی; or simply Tusi in the West), was a Persian polymath, architect, philosopher, physician, scientist, and theologian.

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New York City

The City of New York, often called New York City (NYC) or simply New York, is the most populous city in the United States.

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Niccolò Fontana Tartaglia

Niccolò Fontana Tartaglia (1499/1500, Brescia – 13 December 1557, Venice) was a Venetian mathematician, engineer (designing fortifications), a surveyor (of topography, seeking the best means of defense or offense) and a bookkeeper from the then-Republic of Venice (now part of Italy).

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Nicolaus Copernicus

Nicolaus Copernicus (Mikołaj Kopernik; Nikolaus Kopernikus; Niklas Koppernigk; 19 February 1473 – 24 May 1543) was a Renaissance-era mathematician and astronomer who formulated a model of the universe that placed the Sun rather than the Earth at the center of the universe, likely independently of Aristarchus of Samos, who had formulated such a model some eighteen centuries earlier.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Oliver Byrne (mathematician)

Oliver Byrne (31 July 1810 – 9 December 1880) was a civil engineer and prolific author of works on subjects including mathematics, geometry, and engineering.

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Papyrus Oxyrhynchus 29

Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the Elements of Euclid in Greek.

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Parallel postulate

In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry.

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In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

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Perfect number

In number theory, a perfect number is a positive integer that is equal to the sum of its proper positive divisors, that is, the sum of its positive divisors excluding the number itself (also known as its aliquot sum).

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Petr Vopěnka

Petr Vopěnka (16 May 1935 – 20 March 2015) was a Czech mathematician.

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Pierre Hérigone

Pierre Hérigone (Latinized as Petrus Herigonius) (1580–1643) was a French mathematician and astronomer.

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Pietro Cataldi

Pietro Antonio Cataldi (15 April 1548, Bologna – 11 February 1626, Bologna) was an Italian mathematician.

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Platonic solid

In three-dimensional space, a Platonic solid is a regular, convex polyhedron.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Proclus Lycaeus (8 February 412 – 17 April 485 AD), called the Successor (Greek Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonist philosopher, one of the last major classical philosophers (see Damascius).

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Project Gutenberg

Project Gutenberg (PG) is a volunteer effort to digitize and archive cultural works, to "encourage the creation and distribution of eBooks".

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Ptolemaic Kingdom

The Ptolemaic Kingdom (Πτολεμαϊκὴ βασιλεία, Ptolemaïkḕ basileía) was a Hellenistic kingdom based in Egypt.

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Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

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Pythagoras of Samos was an Ionian Greek philosopher and the eponymous founder of the Pythagoreanism movement.

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Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

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Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that.

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The quadrivium (plural: quadrivia) is the four subjects, or arts, taught after teaching the trivium.

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R. Catesby Taliaferro

Robert Catesby Taliaferro (1907–1989) was an American mathematician, science historian, classical philologist, philosopher, and translator of ancient Greek and Latin works into English.

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Johannes Müller von Königsberg (6 June 1436 – 6 July 1476), better known as Regiomontanus, was a mathematician and astronomer of the German Renaissance, active in Vienna, Buda and Nuremberg.

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Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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Robert Simson

Robert Simson (14 October 1687 – 1 October 1768) was a Scottish mathematician and professor of mathematics at the University of Glasgow.

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Rodrigo Zamorano

Rodrigo Zamorano (1542–1620) was a cosmographer of the royal house of Philip II of Spain.

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Sámuel Brassai

Sámuel Brassai (15 June 1797 – 24 June 1897) was a Hungarian linguist and teacher sometimes called "The Last Transylvanian Polymath." In addition to being a linguist and pedagogue he was also a natural scientist, mathematician, musician, philosopher, essay writer, and a regular member of the Hungarian Academy of Sciences.

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Scholia (singular scholium or scholion, from σχόλιον, "comment, interpretation") are grammatical, critical, or explanatory comments, either original or extracted from pre-existing commentaries, which are inserted on the margin of the manuscript of an ancient author, as glosses.

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R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.

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Siku Quanshu

The Siku Quanshu, variously translated as the Complete Library in Four Sections, Imperial Collection of Four, Emperor's Four Treasuries, Complete Library in Four Branches of Literature, or Complete Library of the Four Treasuries, is the largest collection of books in Chinese history.

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Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

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Society of Jesus

The Society of Jesus (SJ – from Societas Iesu) is a scholarly religious congregation of the Catholic Church which originated in sixteenth-century Spain.

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A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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Springer Publishing

Springer Publishing is an American publishing company of academic journals and books, focusing on the fields of nursing, gerontology, psychology, social work, counseling, public health, and rehabilitation (neuropsychology).

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In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

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Thales's theorem

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.

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Theaetetus (mathematician)

Theaetetus of Athens (Θεαίτητος; c. 417 – 369 BC), possibly the son of Euphronius of the Athenian deme Sunium, was a Greek mathematician.

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Theon of Alexandria

Theon of Alexandria (Θέων ὁ Ἀλεξανδρεύς; 335 – c. 405) was a Greek scholar and mathematician who lived in Alexandria, Egypt.

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In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.

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Thomas Hobbes

Thomas Hobbes (5 April 1588 – 4 December 1679), in some older texts Thomas Hobbes of Malmesbury, was an English philosopher who is considered one of the founders of modern political philosophy.

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Thomas Little Heath

Sir Thomas Little Heath (5 October 1861 – 16 March 1940) was a British civil servant, mathematician, classical scholar, historian of ancient Greek mathematics, translator, and mountaineer.

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Thomas More

Sir Thomas More (7 February 14786 July 1535), venerated in the Catholic Church as Saint Thomas More, was an English lawyer, social philosopher, author, statesman, and noted Renaissance humanist.

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Thomas Perronet Thompson

Thomas Perronet Thompson (1783–1869) was a British Parliamentarian, a governor of Sierra Leone and a radical reformer.

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Thomas Rudd

Thomas Rudd (1583?–1656) was an English military engineer and mathematician.

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A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject.

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Vatican Library

The Vatican Apostolic Library (Bibliotheca Apostolica Vaticana), more commonly called the Vatican Library or simply the Vat, is the library of the Holy See, located in Vatican City.

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W. W. Rouse Ball

Walter William Rouse Ball, known as W. W. Rouse Ball (14 August 1850 – 4 April 1925), was a British mathematician, lawyer, and fellow at Trinity College, Cambridge from 1878 to 1905.

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Xu Guangqi

Xu Guangqi or Hsü Kuang-ch'i (April 24, 1562– November 8, 1633), also known by his baptismal name Paul, was a Chinese scholar-bureaucrat, Catholic convert, agricultural scientist, astronomer, and mathematician under the Ming dynasty.

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[1] https://en.wikipedia.org/wiki/Euclid's_Elements

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