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119-412: Michel de Nostredame (December 1503 – July 1566), usually Latinised as Nostradamus , was a French astrologer , apothecary , physician , and reputed seer , who is best known for his book Les Prophéties (published in 1555), a collection of 942 poetic quatrains allegedly predicting future events. Nostradamus's father's family had originally been Jewish, but had converted to Catholic Christianity
238-520: A geodesic is a generalization of the notion of a line to curved spaces . In Euclidean geometry a plane is a flat, two-dimensional surface that extends infinitely; the definitions for other types of geometries are generalizations of that. Planes are used in many areas of geometry. For instance, planes can be studied as a topological surface without reference to distances or angles; it can be studied as an affine space , where collinearity and ratios can be studied but not distances; it can be studied as
357-517: A modern Latin style. It is commonly found with historical proper names , including personal names and toponyms , and in the standard binomial nomenclature of the life sciences. It goes further than romanisation , which is the transliteration of a word to the Latin alphabet from another script (e.g. Cyrillic ). For authors writing in Latin, this change allows the name to function grammatically in
476-418: A parabola with the summation of an infinite series , and gave remarkably accurate approximations of pi . He also studied the spiral bearing his name and obtained formulas for the volumes of surfaces of revolution . Indian mathematicians also made many important contributions in geometry. The Shatapatha Brahmana (3rd century BC) contains rules for ritual geometric constructions that are similar to
595-425: A vector space and its dual space . Euclidean geometry is geometry in its classical sense. As it models the space of the physical world, it is used in many scientific areas, such as mechanics , astronomy , crystallography , and many technical fields, such as engineering , architecture , geodesy , aerodynamics , and navigation . The mandatory educational curriculum of the majority of nations includes
714-555: A "lost book" of his own prophetic paintings; he had been buried standing up; and he had been found, when dug up at the French Revolution, to be wearing a medallion bearing the exact date of his disinterment. This was first recorded by Samuel Pepys as early as 1667, long before the French Revolution. Pepys records in his celebrated diary a legend that, before his death, Nostradamus made the townsfolk swear that his grave would never be disturbed; but that 60 years later his body
833-468: A "rose pill" that purportedly protected against the plague. In 1531 Nostradamus was invited by Jules-César Scaliger , a leading Renaissance scholar , to come to Agen . There he married a woman of uncertain name (possibly Henriette d'Encausse), with whom he had two children. In 1534 his wife and children died, presumably from the plague. After their deaths, he continued to travel, passing through France and possibly Italy. On his return in 1545, he assisted
952-611: A Roman amphitheatre now known as the Arènes ) as a prediction of an undated attack on the Pentagon , despite the historical seer's clear statement in his dedicatory letter to King Henri II that his prophecies were about Europe, North Africa and part of Asia Minor. With the exception of Roberts, these books and their many popular imitators were almost unanimous not merely about Nostradamus's powers of prophecy but also in inventing intriguing aspects of his purported biography: that he had been
1071-405: A common endpoint, called the vertex of the angle. The size of an angle is formalized as an angular measure . In Euclidean geometry , angles are used to study polygons and triangles , as well as forming an object of study in their own right. The study of the angles of a triangle or of angles in a unit circle forms the basis of trigonometry . In differential geometry and calculus ,
1190-523: A decimal place value system with a dot for zero." Aryabhata 's Aryabhatiya (499) includes the computation of areas and volumes. Brahmagupta wrote his astronomical work Brāhmasphuṭasiddhānta in 628. Chapter 12, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In
1309-557: A descendant of the Israelite tribe of Issachar ; he had been educated by his grandfathers, who had both been physicians to the court of Good King René of Provence ; he had attended Montpellier University in 1525 to gain his first degree; after returning there in 1529, he had successfully taken his medical doctorate; he had gone on to lecture in the Medical Faculty there, until his views became too unpopular; he had supported
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#17328009863601428-642: A description of the methods he used to treat the plague, including bloodletting, none of which apparently worked. The same book also describes the preparation of cosmetics. A manuscript normally known as the Orus Apollo also exists in the Lyon municipal library, where upwards of 2,000 original documents relating to Nostradamus are stored under the aegis of Michel Chomarat. It is a purported translation of an ancient Greek work on Egyptian hieroglyphs based on later Latin versions, all of them unfortunately ignorant of
1547-494: A generation before Nostradamus was born. He studied at the University of Avignon , but was forced to leave after just over a year when the university closed due to an outbreak of the plague . He worked as an apothecary for several years before entering the University of Montpellier , hoping to earn a doctorate, but was almost immediately expelled after his work as an apothecary (a manual trade forbidden by university statutes)
1666-583: A line referring to "that people which stands under the sign of the crooked cross" was added as an allusion to the German people standing under the Nazi flag with its swastika. Goebbels reportedly had that line inserted into leather bound original volumes of Nostradamus' work, volumes that were then seeded in libraries across Nazi-occupied Europe so that the line would seem credible. The prophecies retold and expanded by Nostradamus figured largely in popular culture in
1785-411: A magic mirror or a bowl of water; he had been joined by his secretary Chavigny at Easter 1554; having published the first installment of his Prophéties , he had been summoned by Queen Catherine de' Medici to Paris in 1556 to discuss with her his prophecy at quatrain I.35 that her husband King Henri II would be killed in a duel; he had examined the royal children at Blois ; he had bequeathed to his son
1904-440: A more rigorous foundation for geometry, treated congruence as an undefined term whose properties are defined by axioms . Congruence and similarity are generalized in transformation geometry , which studies the properties of geometric objects that are preserved by different kinds of transformations. Classical geometers paid special attention to constructing geometric objects that had been described in some other way. Classically,
2023-428: A multitude of forms, including the graphics of Leonardo da Vinci , M. C. Escher , and others. In the second half of the 19th century, the relationship between symmetry and geometry came under intense scrutiny. Felix Klein 's Erlangen program proclaimed that, in a very precise sense, symmetry, expressed via the notion of a transformation group , determines what geometry is . Symmetry in classical Euclidean geometry
2142-451: A number of apparently different definitions, which are all equivalent in the most common cases. The theme of symmetry in geometry is nearly as old as the science of geometry itself. Symmetric shapes such as the circle , regular polygons and platonic solids held deep significance for many ancient philosophers and were investigated in detail before the time of Euclid. Symmetric patterns occur in nature and were artistically rendered in
2261-505: A one-thirteenth share in a huge canal project, organised by Adam de Craponne , to create the Canal de Craponne to irrigate the largely waterless Salon-de-Provence and the nearby Désert de la Crau from the river Durance . After another visit to Italy, Nostradamus began to move away from medicine and toward the "occult". Following popular trends, he wrote an almanac for 1550, for the first time in print Latinising his name to Nostradamus. He
2380-444: A physical system, which has a dimension equal to the system's degrees of freedom . For instance, the configuration of a screw can be described by five coordinates. In general topology , the concept of dimension has been extended from natural numbers , to infinite dimension ( Hilbert spaces , for example) and positive real numbers (in fractal geometry ). In algebraic geometry , the dimension of an algebraic variety has received
2499-528: A plane or 3-dimensional space. Mathematicians have found many explicit formulas for area and formulas for volume of various geometric objects. In calculus , area and volume can be defined in terms of integrals , such as the Riemann integral or the Lebesgue integral . Other geometrical measures include the curvature and compactness . The concept of length or distance can be generalized, leading to
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#17328009863602618-713: A playful element of punning. Such names could be a cover for humble social origins. The title of the " Wilhelmus ", national anthem of the Netherlands , preserves a Latinised form of the name of William the Silent . In English, place names often appear in Latinised form. This is a result of many early text books mentioning the places being written in Latin. Because of this, the English language often uses Latinised forms of foreign place names instead of anglicised forms or
2737-564: A process sometimes known as "retroactive clairvoyance" ( postdiction ). No Nostradamus quatrain is known to have been interpreted as predicting a specific event before it occurred, other than in vague, general terms that could equally apply to any number of other events. This even applies to quatrains that contain specific dates, such as III.77, which predicts "in 1727, in October, the king of Persia [shall be] captured by those of Egypt"—a prophecy that has, as ever, been interpreted retrospectively in
2856-602: A purely algebraic context. Scheme theory allowed to solve many difficult problems not only in geometry, but also in number theory . Wiles' proof of Fermat's Last Theorem is a famous example of a long-standing problem of number theory whose solution uses scheme theory and its extensions such as stack theory . One of seven Millennium Prize problems , the Hodge conjecture , is a question in algebraic geometry. Algebraic geometry has applications in many areas, including cryptography and string theory . Complex geometry studies
2975-525: A recent royal decree by publishing his 1562 almanac without the prior permission of a bishop. By 1566, Nostradamus' gout , which had plagued him painfully for many years and made movement very difficult, turned into edema . In late June he summoned his lawyer to draw up an extensive will bequeathing his property plus 3,444 crowns (around US$ 300,000 today), minus a few debts, to his wife pending her remarriage, in trust for her sons pending their twenty-fifth birthdays and her daughters pending their marriages. This
3094-463: A sentence through declension . In a scientific context, the main purpose of Latinisation may be to produce a name which is internationally consistent. Latinisation may be carried out by: Humanist names, assumed by Renaissance humanists , were largely Latinised names, though in some cases (e.g. Melanchthon ) they invoked Ancient Greek . Latinisation in humanist names may consist of translation from vernacular European languages, sometimes involving
3213-485: A single person or small group of people. Some cover a single town, others several towns in several countries. A major, underlying theme is an impending invasion of Europe by Muslim forces from farther east and south headed by the expected Antichrist , directly reflecting the then-current Ottoman invasions and the earlier Saracen equivalents, as well as the prior expectations of the Mirabilis Liber . All of this
3332-427: A size or measure to sets , where the measures follow rules similar to those of classical area and volume. Congruence and similarity are concepts that describe when two shapes have similar characteristics. In Euclidean geometry, similarity is used to describe objects that have the same shape, while congruence is used to describe objects that are the same in both size and shape. Hilbert , in his work on creating
3451-600: A technical sense a type of transformation geometry , in which transformations are homeomorphisms . This has often been expressed in the form of the saying 'topology is rubber-sheet geometry'. Subfields of topology include geometric topology , differential topology , algebraic topology and general topology . Algebraic geometry is fundamentally the study by means of algebraic methods of some geometrical shapes, called algebraic sets , and defined as common zeros of multivariate polynomials . Algebraic geometry became an autonomous subfield of geometry c. 1900 , with
3570-518: A theorem called Hilbert's Nullstellensatz that establishes a strong correspondence between algebraic sets and ideals of polynomial rings . This led to a parallel development of algebraic geometry, and its algebraic counterpart, called commutative algebra . From the late 1950s through the mid-1970s algebraic geometry had undergone major foundational development, with the introduction by Alexander Grothendieck of scheme theory , which allows using topological methods , including cohomology theories in
3689-494: A theory of ratios that avoided the problem of incommensurable magnitudes , which enabled subsequent geometers to make significant advances. Around 300 BC, geometry was revolutionized by Euclid, whose Elements , widely considered the most successful and influential textbook of all time, introduced mathematical rigor through the axiomatic method and is the earliest example of the format still used in mathematics today, that of definition, axiom, theorem, and proof. Although most of
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3808-402: A title here. Not that I am foolish enough to claim to be a prophet. Given this reliance on literary sources, it is unlikely that Nostradamus used any particular methods for entering a trance state , other than contemplation , meditation and incubation . His sole description of this process is contained in 'letter 41' of his collected Latin correspondence. The popular legend that he attempted
3927-411: Is diffeomorphic to Euclidean space. Manifolds are used extensively in physics, including in general relativity and string theory . Euclid defines a plane angle as the inclination to each other, in a plane, of two lines which meet each other, and do not lie straight with respect to each other. In modern terms, an angle is the figure formed by two rays , called the sides of the angle, sharing
4046-540: Is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic , one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a geometer . Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry , which includes the notions of point , line , plane , distance , angle , surface , and curve , as fundamental concepts. Originally developed to model
4165-400: Is a part of some ambient flat Euclidean space). Topology is the field concerned with the properties of continuous mappings , and can be considered a generalization of Euclidean geometry. In practice, topology often means dealing with large-scale properties of spaces, such as connectedness and compactness . The field of topology, which saw massive development in the 20th century, is in
4284-413: Is a persistent tradition that he was educated by his maternal great-grandfather Jean de St. Rémy—a tradition which is somewhat undermined by the fact that the latter disappears from the historical record after 1504 when the child was only one year old. At the age of 14, Nostradamus entered the University of Avignon to study for his baccalaureate . After little more than a year (when he would have studied
4403-413: Is a three-dimensional object bounded by a closed surface; for example, a ball is the volume bounded by a sphere. A manifold is a generalization of the concepts of curve and surface. In topology , a manifold is a topological space where every point has a neighborhood that is homeomorphic to Euclidean space. In differential geometry , a differentiable manifold is a space where each neighborhood
4522-409: Is defined. The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC. Early geometry was a collection of empirically discovered principles concerning lengths, angles, areas, and volumes, which were developed to meet some practical need in surveying , construction , astronomy , and various crafts. The earliest known texts on geometry are
4641-440: Is no warrant for assuming—as would-be "code-breakers" are prone to do—that either the spellings or the punctuation of any edition are Nostradamus's originals. The Almanacs , by far the most popular of his works, were published annually from 1550 until his death. He often published two or three in a year, entitled either Almanachs (detailed predictions), Prognostications or Presages (more generalised predictions). Nostradamus
4760-437: Is not viewed as the set of the points through which it passes. However, there are modern geometries in which points are not primitive objects, or even without points. One of the oldest such geometries is Whitehead's point-free geometry , formulated by Alfred North Whitehead in 1919–1920. Euclid described a line as "breadthless length" which "lies equally with respect to the points on itself". In modern mathematics, given
4879-415: Is of importance to mathematical physics due to Albert Einstein 's general relativity postulation that the universe is curved . Differential geometry can either be intrinsic (meaning that the spaces it considers are smooth manifolds whose geometric structure is governed by a Riemannian metric , which determines how distances are measured near each point) or extrinsic (where the object under study
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4998-557: Is presented in the context of the supposedly imminent end of the world—even though this is not in fact mentioned—a conviction that sparked numerous collections of end-time prophecies at the time, including an unpublished collection by Christopher Columbus . Views on Nostradamus have varied widely throughout history. Academic views, such as those of Jacques Halbronn, regard Nostradamus's Prophecies as antedated forgeries written by later authors for political reasons. Many of Nostradamus's supporters believe his prophecies are genuine. Owing to
5117-468: Is reflected in the fact that he explicitly rejected the label "prophet" (i.e. a person having prophetic powers of his own) on several occasions: Although, my son, I have used the word prophet , I would not attribute to myself a title of such lofty sublimity. Not that I would attribute to myself either the name or the role of a prophet. [S]ome of [the prophets] predicted great and marvelous things to come: [though] for me, I in no way attribute to myself such
5236-482: Is represented by congruences and rigid motions, whereas in projective geometry an analogous role is played by collineations , geometric transformations that take straight lines into straight lines. However it was in the new geometries of Bolyai and Lobachevsky, Riemann, Clifford and Klein, and Sophus Lie that Klein's idea to 'define a geometry via its symmetry group ' found its inspiration. Both discrete and continuous symmetries play prominent roles in geometry,
5355-753: The Sulba Sutras . According to ( Hayashi 2005 , p. 363), the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians. They contain lists of Pythagorean triples , which are particular cases of Diophantine equations . In the Bakhshali manuscript , there are a handful of geometric problems (including problems about volumes of irregular solids). The Bakhshali manuscript also "employs
5474-690: The Egyptian Rhind Papyrus (2000–1800 BC) and Moscow Papyrus ( c. 1890 BC ), and the Babylonian clay tablets , such as Plimpton 322 (1900 BC). For example, the Moscow Papyrus gives a formula for calculating the volume of a truncated pyramid, or frustum . Later clay tablets (350–50 BC) demonstrate that Babylonian astronomers implemented trapezoid procedures for computing Jupiter's position and motion within time-velocity space. These geometric procedures anticipated
5593-523: The Lambert quadrilateral and Saccheri quadrilateral , were part of a line of research on the parallel postulate continued by later European geometers, including Vitello ( c. 1230 – c. 1314 ), Gersonides (1288–1344), Alfonso, John Wallis , and Giovanni Girolamo Saccheri , that by the 19th century led to the discovery of hyperbolic geometry . In the early 17th century, there were two important developments in geometry. The first
5712-518: The Oxford Calculators , including the mean speed theorem , by 14 centuries. South of Egypt the ancient Nubians established a system of geometry including early versions of sun clocks. In the 7th century BC, the Greek mathematician Thales of Miletus used geometry to solve problems such as calculating the height of pyramids and the distance of ships from the shore. He is credited with
5831-509: The Riemann surface , and Henri Poincaré , the founder of algebraic topology and the geometric theory of dynamical systems . As a consequence of these major changes in the conception of geometry, the concept of " space " became something rich and varied, and the natural background for theories as different as complex analysis and classical mechanics . The following are some of the most important concepts in geometry. Euclid took an abstract approach to geometry in his Elements , one of
5950-599: The University of Montpellier to study for a doctorate in medicine. He was expelled shortly afterwards by the student procurator , Guillaume Rondelet , when it was discovered that he had been an apothecary, a "manual trade" expressly banned by the university statutes, and had been slandering doctors. The expulsion document, BIU Montpellier, Register S 2 folio 87 , still exists in the faculty library. Some of his publishers and correspondents would later call him "Doctor". After his expulsion, Nostradamus continued working, presumably still as an apothecary, and became famous for creating
6069-399: The complex plane using techniques of complex analysis ; and so on. A curve is a 1-dimensional object that may be straight (like a line) or not; curves in 2-dimensional space are called plane curves and those in 3-dimensional space are called space curves . In topology, a curve is defined by a function from an interval of the real numbers to another space. In differential geometry,
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#17328009863606188-556: The heliocentric view of the universe; he had travelled to the Habsburg Netherlands, where he had composed prophecies at the abbey of Orval; in the course of his travels, he had performed a variety of prodigies, including identifying future Pope, Sixtus V , who was then only a seminary monk. He is credited with having successfully cured the Plague at Aix-en-Provence and elsewhere; he had engaged in scrying , using either
6307-539: The "bronze tripod" of the Delphic rite are usually preceded by the words "as though" (compare, once again, External References to the original texts). Most of the quatrains deal with disasters, such as plagues, earthquakes, wars, floods, invasions, murders, droughts, and battles—all undated and based on foreshadowings by the Mirabilis Liber . Some quatrains cover these disasters in overall terms; others concern
6426-641: The 'quality' (and thus potential) of events such as births, weddings, coronations etc.—but was heavily criticised by professional astrologers of the day such as Laurens Videl for incompetence and for assuming that "comparative horoscopy" (the comparison of future planetary configurations with those accompanying known past events) could actually predict what would happen in the future. Research suggests that much of his prophetic work paraphrases collections of ancient end-of-the-world prophecies (mainly Bible-based), supplemented with references to historical events and anthologies of omen reports, and then projects those into
6545-471: The 16th-century French texts; or on pure invention. Even the often-advanced suggestion that quatrain I.35 had successfully prophesied King Henry II's death did not actually appear in print for the first time until 1614, 55 years after the event. Skeptics such as James Randi suggest that his reputation as a prophet is largely manufactured by modern-day supporters who fit his words to events that have either already occurred or are so imminent as to be inevitable,
6664-631: The 19th century changed the way it had been studied previously. These were the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky, János Bolyai and Carl Friedrich Gauss and of the formulation of symmetry as the central consideration in the Erlangen programme of Felix Klein (which generalized the Euclidean and non-Euclidean geometries). Two of the master geometers of the time were Bernhard Riemann (1826–1866), working primarily with tools from mathematical analysis , and introducing
6783-496: The 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss 's Theorema Egregium ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space . This implies that surfaces can be studied intrinsically , that is, as stand-alone spaces, and has been expanded into
6902-474: The 19th century, the discovery of non-Euclidean geometries by Nikolai Ivanovich Lobachevsky (1792–1856), János Bolyai (1802–1860), Carl Friedrich Gauss (1777–1855) and others led to a revival of interest in this discipline, and in the 20th century, David Hilbert (1862–1943) employed axiomatic reasoning in an attempt to provide a modern foundation of geometry. Points are generally considered fundamental objects for building geometry. They may be defined by
7021-422: The 20th and 21st centuries. As well as being the subject of hundreds of books (both fiction and nonfiction), Nostradamus' life has been depicted in several films and videos, and his life and writings continue to be a subject of media interest. Latinisation of names Latinisation (or Latinization ) of names , also known as onomastic Latinisation , is the practice of rendering a non - Latin name in
7140-495: The Christian name "Pierre" and the surname "Nostredame" (Our Lady), the saint on whose day his conversion was solemnised. The earliest ancestor who can be identified on the paternal side is Astruge of Carcassonne , who died about 1420. Michel's known siblings included Delphine, Jean (c. 1507–1577), Pierre, Hector, Louis, Bertrand, Jean II (born 1522) and Antoine (born 1523). Little else is known about his childhood, although there
7259-534: The Millennium: Predictions of the Future , Nostradamus: The Complete Prophecies (1999) and Nostradamus: A Life and Myth (2003). In 1992 one commentator who claimed to be able to contact Nostradamus under hypnosis even had him "interpreting" his own verse X.6 (a prediction specifically about floods in southern France around the city of Nîmes and people taking refuge in its collosse , or Colosseum,
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#17328009863607378-553: The ancient methods of flame gazing, water gazing or both simultaneously is based on a naive reading of his first two verses, which merely liken his efforts to those of the Delphic and Branchidic oracles . The first of these is reproduced at the bottom of this article and the second can be seen by visiting the relevant facsimile site (see External Links). In his dedication to King Henry II, Nostradamus describes "emptying my soul, mind and heart of all care, worry and unease through mental calm and tranquility", but his frequent references to
7497-590: The angles between plane curves or space curves or surfaces can be calculated using the derivative . Length , area , and volume describe the size or extent of an object in one dimension, two dimension, and three dimensions respectively. In Euclidean geometry and analytic geometry , the length of a line segment can often be calculated by the Pythagorean theorem . Area and volume can be defined as fundamental quantities separate from length, or they can be described and calculated in terms of lengths in
7616-527: The basis for the documentary The Man Who Saw Tomorrow and both did indeed mention possible generalised future attacks on New York (via nuclear weapons ), though not specifically on the World Trade Center or on any particular date. A two-part translation of Jean-Charles de Fontbrune's Nostradamus: historien et prophète was published in 1980, and John Hogue has published a number of books on Nostradamus from about 1987, including Nostradamus and
7735-420: The birth charts on which these would be based, rather than calculating them himself as a professional astrologer would have done. When obliged to attempt this himself on the basis of the published tables of the day, he frequently made errors and failed to adjust the figures for his clients' place or time of birth. He then began his project of writing a book of one thousand mainly French quatrains, which constitute
7854-412: The concept of angle and distance, finite geometry that omits continuity , and others. This enlargement of the scope of geometry led to a change of meaning of the word "space", which originally referred to the three-dimensional space of the physical world and its model provided by Euclidean geometry; presently a geometric space , or simply a space is a mathematical structure on which some geometry
7973-513: The contents of the Elements were already known, Euclid arranged them into a single, coherent logical framework. The Elements was known to all educated people in the West until the middle of the 20th century and its contents are still taught in geometry classes today. Archimedes ( c. 287–212 BC ) of Syracuse, Italy used the method of exhaustion to calculate the area under the arc of
8092-821: The early 19th century, Europe had largely abandoned Latin as a scholarly language (most scientific studies and scholarly publications are printed in English), but a variety of fields still use Latin terminology as the norm. By tradition, it is still common in some fields to name new discoveries in Latin. And because Western science became dominant during the 18th and 19th centuries, the use of Latin names in many scholarly fields has gained worldwide acceptance, at least when European languages are being used for communication. Geometry Geometry (from Ancient Greek γεωμετρία ( geōmetría ) 'land measurement'; from γῆ ( gê ) 'earth, land' and μέτρον ( métron ) 'a measure')
8211-401: The end of his life, which eventually developed into edema . He died on 1 or 2 July 1566. Many popular authors have retold apocryphal legends about his life. In the years since the publication of his Les Prophéties , Nostradamus has attracted many supporters, who, along with some of the popular press, credit him with having accurately predicted many major world events. Academic sources reject
8330-428: The field has been split in many subfields that depend on the underlying methods— differential geometry , algebraic geometry , computational geometry , algebraic topology , discrete geometry (also known as combinatorial geometry ), etc.—or on the properties of Euclidean spaces that are disregarded— projective geometry that consider only alignment of points but not distance and parallelism, affine geometry that omits
8449-520: The first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales's theorem . Pythagoras established the Pythagorean School , which is credited with the first proof of the Pythagorean theorem , though the statement of the theorem has a long history. Eudoxus (408– c. 355 BC ) developed the method of exhaustion , which allowed the calculation of areas and volumes of curvilinear figures, as well as
8568-526: The former in topology and geometric group theory , the latter in Lie theory and Riemannian geometry . A different type of symmetry is the principle of duality in projective geometry , among other fields. This meta-phenomenon can roughly be described as follows: in any theorem , exchange point with plane , join with meet , lies in with contains , and the result is an equally true theorem. A similar and closely related form of duality exists between
8687-550: The future in part with the aid of comparative horoscopy. Hence the many predictions involving ancient figures such as Sulla , Gaius Marius , Nero , and others, as well as his descriptions of "battles in the clouds" and "frogs falling from the sky". Astrology itself is mentioned only twice in Nostradamus's Preface and 41 times in the Centuries themselves, but more frequently in his dedicatory Letter to King Henry II . In
8806-598: The idea of metrics . For instance, the Euclidean metric measures the distance between points in the Euclidean plane , while the hyperbolic metric measures the distance in the hyperbolic plane . Other important examples of metrics include the Lorentz metric of special relativity and the semi- Riemannian metrics of general relativity . In a different direction, the concepts of length, area and volume are extended by measure theory , which studies methods of assigning
8925-486: The idea of reducing geometrical problems such as duplicating the cube to problems in algebra. Thābit ibn Qurra (known as Thebit in Latin ) (836–901) dealt with arithmetic operations applied to ratios of geometrical quantities, and contributed to the development of analytic geometry . Omar Khayyam (1048–1131) found geometric solutions to cubic equations . The theorems of Ibn al-Haytham (Alhazen), Omar Khayyam and Nasir al-Din al-Tusi on quadrilaterals , including
9044-465: The largely undated prophecies for which he is most famous today. Feeling vulnerable to opposition on religious grounds, he devised a method of obscuring his meaning by using " Virgilianised " syntax, word games and a mixture of other languages such as Greek , Italian, Latin , and Provençal . For technical reasons connected with their publication in three instalments (the publisher of the third and last instalment seems to have been unwilling to start it in
9163-515: The last quatrain of his sixth century he specifically attacks astrologers. His historical sources include easily identifiable passages from Livy , Suetonius ' The Twelve Caesars , Plutarch and other classical historians, as well as from medieval chroniclers such as Geoffrey of Villehardouin and Jean Froissart . Many of his astrological references are taken almost word for word from Richard Roussat 's Livre de l'estat et mutations des temps of 1549–50. One of his major prophetic sources
9282-552: The latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral . Chapter 12 also included a formula for the area of a cyclic quadrilateral (a generalization of Heron's formula ), as well as a complete description of rational triangles ( i.e. triangles with rational sides and rational areas). In the Middle Ages , mathematics in medieval Islam contributed to the development of geometry, especially algebraic geometry . Al-Mahani (b. 853) conceived
9401-477: The light of later events, in this case as though it presaged the known peace treaty between the Ottoman Empire and Persia of that year; Egypt was also an important Ottoman territory at this time. Similarly, Nostradamus's notorious "1999" prophecy at X.72 (see Nostradamus in popular culture ) describes no event that commentators have succeeded in identifying either before or since, other than by twisting
9520-464: The middle of a "Century," or book of 100 verses), the last fifty-eight quatrains of the seventh "Century" have not survived in any extant edition. The quatrains, published in a book titled Les Prophéties (The Prophecies), received a mixed reaction when they were published. Some people thought Nostradamus was a servant of evil, a fake, or insane, while many of the elite evidently thought otherwise. Catherine de' Medici , wife of King Henry II of France ,
9639-411: The most influential books ever written. Euclid introduced certain axioms , or postulates , expressing primary or self-evident properties of points, lines, and planes. He proceeded to rigorously deduce other properties by mathematical reasoning. The characteristic feature of Euclid's approach to geometry was its rigor, and it has come to be known as axiomatic or synthetic geometry. At the start of
9758-429: The multitude of geometries, the concept of a line is closely tied to the way the geometry is described. For instance, in analytic geometry , a line in the plane is often defined as the set of points whose coordinates satisfy a given linear equation , but in a more abstract setting, such as incidence geometry , a line may be an independent object, distinct from the set of points which lie on it. In differential geometry,
9877-465: The next forty years, which contained both transcriptions and translations, with brief commentaries. This was followed in 1961 (reprinted in 1982) by Edgar Leoni's Nostradamus and His Prophecies . After that came Erika Cheetham 's The Prophecies of Nostradamus , incorporating a reprint of the posthumous 1568 edition, which was reprinted, revised and republished several times from 1973 onwards, latterly as The Final Prophecies of Nostradamus . This served as
9996-484: The notion that Nostradamus had any genuine supernatural prophetic abilities and maintain that the associations made between world events and Nostradamus's quatrains are the result of (sometimes deliberate) misinterpretations or mistranslations. These academics also argue that Nostradamus's predictions are characteristically vague, meaning they could be applied to virtually anything, and are useless for determining whether their author had any real prophetic powers. Nostradamus
10115-411: The omnibus edition that was published after his death in 1568. This version contains one unrhymed and 941 rhymed quatrains, grouped into nine sets of 100 and one of 42, called "Centuries". Given printing practices at the time (which included type-setting from dictation), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same. Certainly there
10234-441: The only instruments used in most geometric constructions are the compass and straightedge . Also, every construction had to be complete in a finite number of steps. However, some problems turned out to be difficult or impossible to solve by these means alone, and ingenious constructions using neusis , parabolas and other curves, or mechanical devices, were found. The geometrical concepts of rotation and orientation define part of
10353-543: The original editions of 1555 and 1557 discovered by Chomarat and Benazra, together with the unearthing of much original archival material revealed that much that was claimed about Nostradamus did not fit the documented facts. The academics revealed that not one of the claims just listed was backed up by any known contemporary documentary evidence. Most of them had evidently been based on unsourced rumours relayed as fact by much later commentators, such as Jaubert (1656), Guynaud (1693) and Bareste (1840); on modern misunderstandings of
10472-691: The original names. Examples of Latinised names for countries or regions are: Latinisation is a common practice for scientific names . For example, Livistona , the name of a genus of palm trees, is a Latinisation of Livingstone . During the age of the Roman Empire , translation of names into Latin (in the West) or Greek (in the East) was common. Additionally, Latinised versions of Greek substantives , particularly proper nouns , could easily be declined by Latin speakers with minimal modification of
10591-600: The original word. During the medieval period , after the Empire collapsed in Western Europe , the main bastion of scholarship was the Roman Catholic Church , for which Latin was the primary written language. In the early medieval period, most European scholars were priests and most educated people spoke Latin, and as a result, Latin became firmly established as the scholarly language for the West. By
10710-514: The physical world, geometry has applications in almost all sciences, and also in art, architecture , and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem , a problem that was stated in terms of elementary arithmetic , and remained unsolved for several centuries. During
10829-407: The placement of objects embedded in the plane or in space. Traditional geometry allowed dimensions 1 (a line or curve), 2 (a plane or surface), and 3 (our ambient world conceived of as three-dimensional space ). Furthermore, mathematicians and physicists have used higher dimensions for nearly two centuries. One example of a mathematical use for higher dimensions is the configuration space of
10948-661: The prominent physician Louis Serre in his fight against a major plague outbreak in Marseille , and then tackled further outbreaks of disease on his own in Salon-de-Provence and in the regional capital, Aix-en-Provence . Finally, in 1547, he settled in Salon-de-Provence in the house which exists today, where he married a rich widow named Anne Ponsarde, with whom he had six children—three daughters and three sons. Between 1556 and 1567 he and his wife acquired
11067-482: The properties that they must have, as in Euclid's definition as "that which has no part", or in synthetic geometry . In modern mathematics, they are generally defined as elements of a set called space , which is itself axiomatically defined. With these modern definitions, every geometric shape is defined as a set of points; this is not the case in synthetic geometry, where a line is another fundamental object that
11186-460: The regular trivium of grammar , rhetoric and logic rather than the later quadrivium of geometry , arithmetic , music , and astronomy / astrology ), he was forced to leave Avignon when the university closed its doors during an outbreak of the plague. After leaving Avignon, Nostradamus, by his own account, traveled the countryside for eight years from 1521 researching herbal remedies. In 1529, after some years as an apothecary , he entered
11305-574: The restaurant La Brocherie ) but re-interred during the French Revolution in the Collégiale Saint-Laurent, where his tomb remains to this day. In The Prophecies Nostradamus compiled his collection of major, long-term predictions. The first installment was published in 1555 and contained 353 quatrains . The third edition, with three hundred new quatrains, was reportedly printed in 1558, but now survives as only part of
11424-554: The same definition is used, but the defining function is required to be differentiable. Algebraic geometry studies algebraic curves , which are defined as algebraic varieties of dimension one. A surface is a two-dimensional object, such as a sphere or paraboloid. In differential geometry and topology , surfaces are described by two-dimensional 'patches' (or neighborhoods ) that are assembled by diffeomorphisms or homeomorphisms , respectively. In algebraic geometry, surfaces are described by polynomial equations . A solid
11543-430: The second case almost literally) in his first two verses, the first of which is appended to this article. While it is true that Nostradamus claimed in 1555 to have burned all of the occult works in his library, no one can say exactly what books were destroyed in this fire. Only in the 17th century did people start to notice his reliance on earlier, mainly classical sources. Nostradamus's reliance on historical precedent
11662-589: The study of Euclidean concepts such as points , lines , planes , angles , triangles , congruence , similarity , solid figures , circles , and analytic geometry . Euclidean vectors are used for a myriad of applications in physics and engineering, such as position , displacement , deformation , velocity , acceleration , force , etc. Differential geometry uses techniques of calculus and linear algebra to study problems in geometry. It has applications in physics , econometrics , and bioinformatics , among others. In particular, differential geometry
11781-535: The subjective nature of these interpretations, no two of them completely agree on what Nostradamus predicted, whether for the past or for the future. Many supporters do agree, for example, that he predicted the Great Fire of London , the French Revolution, the rise of Napoleon and of Adolf Hitler , both world wars , and the nuclear destruction of Hiroshima and Nagasaki . Popular authors frequently claim that he predicted whatever major event had just happened at
11900-418: The texts, whether with the aid of anagrams, numerical codes, graphs or otherwise. An additional indictment is found in a connection to Nazi propaganda. Goebbels reportedly adduced some of Nostradamus' work to be Third Reich references. This allegedly was done to make it look like the 1,000-year triumphant reign of the German people that was expected under Nazism had been prophesied by Nostradamus. In particular,
12019-409: The theory of manifolds and Riemannian geometry . Later in the 19th century, it appeared that geometries without the parallel postulate ( non-Euclidean geometries ) can be developed without introducing any contradiction. The geometry that underlies general relativity is a famous application of non-Euclidean geometry. Since the late 19th century, the scope of geometry has been greatly expanded, and
12138-761: The time of each of their books' publication, such as the Apollo Moon landing in 1969, the Space Shuttle Challenger disaster in 1986, the death of Diana, Princess of Wales in 1997, and the September 11 attacks on the World Trade Center in 2001. This 'movable feast' aspect appears to be characteristic of the genre. Possibly the first of these books to become popular in English was Henry C. Roberts' The Complete Prophecies of Nostradamus of 1947, reprinted at least seven times during
12257-423: The translator believed they were supposed to refer (or vice versa). None of them were based on the original editions: Roberts had based his writings on that of 1672, Cheetham and Hogue on the posthumous edition of 1568. Even Leoni accepted on page 115 that he had never seen an original edition, and on earlier pages, he indicated that much of his biographical material was unsourced. None of this research and criticism
12376-755: The true meanings of the ancient Egyptian script, which was not correctly deciphered until Champollion in the 19th century. Since his death, only the Prophecies have continued to be popular, but in this case they have been quite extraordinarily so. Over two hundred editions of them have appeared in that time, together with over 2,000 commentaries. Their persistence in popular culture seems to be partly because their vagueness and lack of dating make it easy to quote them selectively after every major dramatic event and retrospectively claim them as "hits". Nostradamus claimed to base his published predictions on judicial astrology —the astrological 'judgment', or assessment, of
12495-459: The words to fit whichever of the many contradictory happenings they claim as "hits". Moreover, no quatrain suggests, as is often claimed by books and films on the alleged Mayan Prophecy , that the world would end in December 2012. In his preface to the Prophecies , Nostradamus himself stated that his prophecies extend "from now to the year 3797"—an extraordinary date which, given that the preface
12614-582: Was afraid of being persecuted for heresy by the Inquisition , but neither prophecy nor astrology fell in this bracket, and he would have been in danger only if he had practised magic to support them. In 1538 he came into conflict with the Church in Agen after an Inquisitor visited the area looking for anti-Catholic views. His brief imprisonment at Marignane in late 1561 was solely because he had violated
12733-682: Was born on either 14 or 21 December 1503 in Saint-Rémy-de-Provence , Provence , France, where his claimed birthplace still exists, and baptized Michel. He was one of at least nine children of notary Jaume (or Jacques) de Nostredame and Reynière, granddaughter of Pierre de Saint-Rémy who worked as a physician in Saint-Rémy. Jaume's family had originally been Jewish , but his father, Cresquas, a grain and money dealer based in Avignon , had converted to Catholicism around 1459–60, taking
12852-646: Was discovered. He first married in 1531, but his wife and two children died in 1534 during another plague outbreak. He worked against the plague alongside other doctors before remarrying to Anne Ponsarde, with whom he had six children. He wrote an almanac for 1550 and, as a result of its success, continued writing them for future years as he began working as an astrologer for various wealthy patrons. Catherine de' Medici became one of his foremost supporters. His Les Prophéties , published in 1555, relied heavily on historical and literary precedent , and initially received mixed reception. He suffered from severe gout toward
12971-627: Was evidently the Mirabilis Liber of 1522, which contained a range of prophecies by Pseudo-Methodius , the Tiburtine Sibyl , Joachim of Fiore , Savonarola and others (his Preface contains 24 biblical quotations, all but two in the order used by Savonarola). This book had enjoyed considerable success in the 1520s, when it went through half a dozen editions, but did not sustain its influence, perhaps owing to its mostly Latin text (mixed with ancient Greek and modern French and Provençal), Gothic script and many difficult abbreviations. Nostradamus
13090-719: Was exhumed, whereupon a brass plaque was found on his chest correctly stating the date and time when his grave would be opened and cursing the exhumers. In 2000, Li Hongzhi claimed that the 1999 prophecy at X.72 was a prediction of the Chinese Falun Gong persecution which began in July 1999, leading to an increased interest in Nostradamus among Falun Gong members. From the 1980s onward, an academic reaction set in, especially in France. The publication in 1983 of Nostradamus' private correspondence and, during succeeding years, of
13209-510: Was followed by a much shorter codicil . On the evening of 1 July, he is alleged to have told his secretary Jean de Chavigny, "You will not find me alive at sunrise." The next morning he was reportedly found dead, lying on the floor next to his bed and a bench (Presage 141 [originally 152] for November 1567 , as posthumously edited by Chavigny to fit what happened). He was buried in the local Franciscan chapel in Salon (part of it now incorporated into
13328-533: Was gleaned from the De honesta disciplina of 1504 by Petrus Crinitus , which included extracts from Michael Psellos 's De daemonibus , and the De Mysteriis Aegyptiorum ( Concerning the mysteries of Egypt ), a book on Chaldean and Assyrian magic by Iamblichus , a 4th-century Neo-Platonist . Latin versions of both had recently been published in Lyon , and extracts from both are paraphrased (in
13447-471: Was not only a diviner , but a professional healer. It is known that he wrote at least two books on medical science. One was an extremely free translation (or rather a paraphrase) of The Protreptic of Galen ( Paraphrase de C. GALIEN, sus l'Exhortation de Menodote aux estudes des bonnes Artz, mesmement Medicine ), and in his so-called Traité des fardemens (basically a medical cookbook containing, once again, materials borrowed mainly from others), he included
13566-475: Was one of Nostradamus's greatest admirers. After reading his almanacs for 1555, which hinted at unnamed threats to the royal family, she summoned him to Paris to explain them and to draw up horoscopes for her children. At the time, he feared that he would be beheaded, but by the time of his death in 1566, Queen Catherine had made him Counselor and Physician-in-Ordinary to her son, the young King Charles IX of France . Some accounts of Nostradamus's life state that he
13685-551: Was one of the first to re-paraphrase these prophecies in French, which may explain why they are credited to him. Modern views of plagiarism did not apply in the 16th century; authors frequently copied and paraphrased passages without acknowledgement, especially from the classics. The latest research suggests that he may in fact have used bibliomancy for this—randomly selecting a book of history or prophecy and taking his cue from whatever page it happened to fall open at. Further material
13804-628: Was originally known to most of the English-language commentators, by dint of the dates when they were writing and, to some extent, the language in which it was written. Hogue was in a position to take advantage of it, but it was only in 2003 that he accepted that some of his earlier biographical material had in fact been apocryphal. Meanwhile, some of the more recent sources listed (Lemesurier, Gruber, Wilson) have been particularly scathing about later attempts by some lesser-known authors and Internet enthusiasts to extract alleged hidden meanings from
13923-559: Was so encouraged by the almanac's success that he decided to write one or more annually. Taken together, they are known to have contained at least 6,338 prophecies, as well as at least eleven annual calendars, all of them starting on 1 January and not, as is sometimes supposed, in March. It was mainly in response to the almanacs that the nobility and other prominent people from far away soon started asking for horoscopes and "psychic" advice from him, though he generally expected his clients to supply
14042-596: Was the creation of analytic geometry, or geometry with coordinates and equations , by René Descartes (1596–1650) and Pierre de Fermat (1601–1665). This was a necessary precursor to the development of calculus and a precise quantitative science of physics . The second geometric development of this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry studies properties of shapes which are unchanged under projections and sections , especially as they relate to artistic perspective . Two developments in geometry in
14161-519: Was written in 1555, may have more than a little to do with that 2242 (3797–1555) had recently been proposed by his major astrological source Richard Roussat as a possible date for the end of the world. Additionally, scholars have pointed out that almost all English translations of Nostradamus's quatrains are of extremely poor quality: they seem to display little or no knowledge of 16th-century French, are tendentious , and are sometimes intentionally altered in order to make them fit whatever events to which
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