Which ancient Greek mathematician, known as 'The Father Of Geometry', wrote the hugely influential book 'Elements' that dominated European mathematics until the 19th century?
"History of geometry Geometry (from the ; ""geo-"" ""earth"", ""-metron"" ""measurement"") arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers (arithmetic). Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, ""The Elements"" is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century. In modern times, geometric"
"Elements being the earliest extant documentation of the axioms of plane geometry— though Proclus tells of an earlier axiomatisation by Hippocrates of Chios. Euclid's ""Elements"" (c. 300 BC) is one of the oldest extant Greek mathematical treatises and consisted of 13 books written in Alexandria; collecting theorems proven by other mathematicians, supplemented by some original work. The document is a successful collection of definitions, postulates (axioms), propositions (theorems and constructions), and mathematical proofs of the propositions. Euclid's first theorem is a lemma that possesses properties of prime numbers. The influential thirteen books cover Euclidean geometry, geometric algebra, and the ancient"
"formula_8 Iamblichus goes on to describe how some systems of linear equations that are not in this form can be placed into this form. Euclid (Greek: ) was a Greek mathematician who flourished in Alexandria, Egypt, almost certainly during the reign of Ptolemy I (323–283 BCE). Neither the year nor place of his birth have been established, nor the circumstances of his death. Euclid is regarded as the ""father of geometry"". His ""Elements"" is the most successful textbook in the history of mathematics. Although he is one of the most famous mathematicians in history there are no new discoveries attributed"
"important textbook in mathematics until the 19th century, built upon the work of the Hellenic era Pythagoreans. Euclid developed proofs for the Pythagorean Theorem, for the infinitude of primes, and worked on the five Platonic solids. Eratosthenes used his knowledge of geometry to measure the circumference of the Earth. His calculation was remarkably accurate. He was also the first to calculate the tilt of the Earth's axis (again with remarkable accuracy). Additionally, he may have accurately calculated the distance from the Earth to the Sun and invented the leap day. Known as the ""Father of Geography "", Eratosthenes also created"
"the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof. His textbook ""Elements"" is widely considered the most successful and influential textbook of all time. The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse. He developed formulas for calculating the surface area and volume of solids of revolution and used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, in a manner not too dissimilar from modern calculus. Other notable achievements of Greek mathematics are conic"
"were not tried again for almost two millennia. The mathematician Euclid laid down the foundations of mathematical rigour and introduced the concepts of definition, axiom, theorem and proof still in use today in his ""Elements"", considered the most influential textbook ever written. Archimedes, considered one of the greatest mathematicians of all time, is credited with using the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He is also known in physics for laying the foundations of hydrostatics and the explanation"
"the ""Elements"", provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations, although this would not be realized until mathematics developed in medieval Islam. By the time of Plato, Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them. Diophantus (3rd century AD) was an Alexandrian Greek mathematician and the author of a series of books called ""Arithmetica"". These texts deal with solving algebraic equations, and have led, in"
"the Geometric Elements"" has been traditionally attributed to Hero of Alexandria. It has been studied recently by Wilbur Knorr, who suggested that the attribution to Hero is incorrect, and that the true author is Diophantus. Diophantus' work has had a large influence in history. Editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the 17th and 18th centuries. Diophantus and his works have also influenced Arab mathematics and were of great fame among Arab mathematicians. Diophantus' work created a foundation for work on algebra and in fact much of"
"Elements of Algebra Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German. ""Elements of Algebra"" is one of the earliest books to set out algebra in the modern form we would recognize today (another early book being ""Elements of Algebra"" by Nicholas Saunderson, published in 1740), and is one of Euler's few writings, along with ""Letters to a German Princess"", that are accessible to the general public. Written in numbered paragraphs as was common practice till the 19th century, ""Elements"" begins with the definition of mathematics and builds on"
"not tried again for almost two millennia. In Hellenistic Egypt, the mathematician Euclid laid down the foundations of mathematical rigor and introduced the concepts of definition, axiom, theorem and proof still in use today in his ""Elements"", considered the most influential textbook ever written. Archimedes, considered one of the greatest mathematicians of all time, is credited with using the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He is also known in physics for laying the foundations of hydrostatics, statics,"
"With the exception of Autolycus' ""On the Moving Sphere"", the ""Elements"" is one of the oldest extant Greek mathematical treatises, and it is the oldest extant axiomatic deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science. Euclid's ""Elements"" has been referred to as the most successful and influential textbook ever written. Being first set in type in Venice in 1482, it is one of the very earliest mathematical works to be printed after the invention of the printing press and was estimated by Carl Benjamin Boyer to be second only to the Bible"
"of logic to mathematics. In historical context, it has proven enormously influential in many areas of science. Scientists Nicolaus Copernicus, Johannes Kepler, Galileo Galilei, and Sir Isaac Newton were all influenced by the ""Elements"", and applied their knowledge of it to their work. Mathematicians and philosophers, such as Thomas Hobbes, Baruch Spinoza, Alfred North Whitehead, and Bertrand Russell, have attempted to create their own foundational ""Elements"" for their respective disciplines, by adopting the axiomatized deductive structures that Euclid's work introduced. The austere beauty of Euclidean geometry has been seen by many in western culture as a glimpse of an otherworldly"
"textbooks, did it cease to be considered something all educated people had read. Scholars believe that the ""Elements"" is largely a compilation of propositions based on books by earlier Greek mathematicians. Proclus (412–485 AD), a Greek mathematician who lived around seven centuries after Euclid, wrote in his commentary on the ""Elements"": ""Euclid, who put together the ""Elements"", collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors"". Pythagoras (c. 570–495 BC) was probably the source for most of books I and II, Hippocrates of"
"space, and also the interesting question of how far a rock would fall if a hole were drilled through the Earth and a rock dropped through it, see center of gravity. Campanus of Novara probably had access to Adelard's translation of ""Elements"", and it is Campanus' edition that was first published in Venice in 1482 after the invention of the printing press. It became the chief textbook of the mathematical schools of Western Europe until the 16th century. Adelard of Bath Adelard of Bath (; 1080 1152 AD) was a 12th-century English natural philosopher. He is known both for his"
"as a textbook for about 2,000 years. The ""Elements"" still influences modern geometry books. Further, its logical axiomatic approach and rigorous proofs remain the cornerstone of mathematics. Euclid's axiomatic approach and constructive methods were widely influential. Many of Euclid's propositions were constructive, demonstrating the existence of some figure by detailing the steps he used to construct the object using a compass and straightedge. His constructive approach appears even in his geometry's postulates, as the first and third postulates stating the existence of a line and circle are constructive. Instead of stating that lines and circles exist per his prior definitions,"
"lost. He was brought to the university at Alexandria by Ptolemy I, King of Egypt. ""The Elements"" began with definitions of terms, fundamental geometric principles (called ""axioms"" or ""postulates""), and general quantitative principles (called ""common notions"") from which all the rest of geometry could be logically deduced. Following are his five axioms, somewhat paraphrased to make the English easier to read. Concepts, that are now understood as algebra, were expressed geometrically by Euclid, a method referred to as Greek geometric algebra. Archimedes (287-212 BC), of Syracuse, Sicily, when it was a Greek city-state, is often considered to be the greatest"
"to him, rather he is remembered for his great explanatory skills. The ""Elements"" is not, as is sometimes thought, a collection of all Greek mathematical knowledge to its date, rather, it is an elementary introduction to it. The geometric work of the Greeks, typified in Euclid's ""Elements"", provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations. Book II of the ""Elements"" contains fourteen propositions, which in Euclid's time were extremely significant for doing geometric algebra. These propositions and their results are the geometric equivalents of our modern symbolic"
"although many of the proofs are supposedly his. Euclid's systematic development of his subject, from a small set of axioms to deep results, and the consistency of his approach throughout the ""Elements"", encouraged its use as a textbook for about 2,000 years. The ""Elements"" still influences modern geometry books. Further, its logical axiomatic approach and rigorous proofs remain the cornerstone of mathematics. The standards of mathematical rigor have changed since Euclid wrote the ""Elements"". Modern attitudes towards, and viewpoints of, an axiomatic system can make it appear that Euclid was in some way ""sloppy"" or ""careless"" in his approach to"
"proof. Although most of 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. In addition to the familiar theorems of Euclidean geometry, the ""Elements"" was meant as an introductory textbook to all mathematical subjects of the time, such as number theory, algebra and solid geometry, including proofs that the square root of two is irrational and that there are infinitely many prime numbers. Euclid"
"known simply as ""geometry"", and was considered to be the only geometry possible. Today, however, that system is often referred to as ""Euclidean geometry"" to distinguish it from other so-called ""non-Euclidean geometries"" that mathematicians discovered in the 19th century. The Papyrus Oxyrhynchus 29 (P. Oxy. 29) is a fragment of the second book of the ""Elements"" of Euclid, unearthed by Grenfell and Hunt 1897 in Oxyrhynchus. More recent scholarship suggests a date of 75–125 AD. The classic translation of T. L. Heath, reads: In addition to the ""Elements"", at least five works of Euclid have survived to the present day."
"only reference that historians rely on of Euclid having written the ""Elements"" was from Proclus, who briefly in his ""Commentary on the Elements"" ascribes Euclid as its author. Although best known for its geometric results, the ""Elements"" also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the Euclid–Euler theorem), the infinitude of prime numbers, Euclid's lemma on factorization (which leads to the fundamental theorem of arithmetic on uniqueness of prime factorizations), and the Euclidean algorithm for finding the greatest common divisor of two numbers. The geometrical system described in the ""Elements"" was long"
"in its favor. Although many of the results in ""Elements"" originated with earlier mathematicians, one of Euclid's accomplishments was to present them in a single, logically coherent framework, making it easy to use and easy to reference, including a system of rigorous mathematical proofs that remains the basis of mathematics 23 centuries later. There is no mention of Euclid in the earliest remaining copies of the ""Elements"", and most of the copies say they are ""from the edition of Theon"" or the ""lectures of Theon"", while the text considered to be primary, held by the Vatican, mentions no author. The"
"Euclid (c. 325-265 BC), of Alexandria, probably a student at the Academy founded by Plato, wrote a treatise in 13 books (chapters), titled ""The Elements of Geometry"", in which he presented geometry in an ideal axiomatic form, which came to be known as Euclidean geometry. The treatise is not a compendium of all that the Hellenistic mathematicians knew at the time about geometry; Euclid himself wrote eight more advanced books on geometry. We know from other references that Euclid’s was not the first elementary geometry textbook, but it was so much superior that the others fell into disuse and were"
"center of Pythagorean thinking: Hippocrates has been described as a 'para-Pythagorean', a philosophical 'fellow traveler'. The ""reductio ad absurdum"" argument (or proof by contradiction) has been traced to him. The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometry textbook, called ""Elements"" (Στοιχεῖα, ""Stoicheia""), that is, basic theorems, or building blocks of mathematical theory. From then on, mathematicians from all over the ancient world could, at least in principle, build on a common framework of basic concepts, methods, and theorems, which stimulated the scientific progress of mathematics. Only a single, and famous, fragment"
"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 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"
"the ""father of algebra"". Many parts of modern geometry are based on the work of Euclid, while Eratosthenes was one of the first scientific geographers, calculating the circumference of the earth and conceiving the first maps based on scientific principles. The Hellenistic period, following Alexander's conquests, continued and built upon this knowledge. Hipparchus is considered the pre-eminent astronomical observer of the ancient world, and was probably the first to develop an accurate method for the prediction of solar eclipse, while Aristarchus of Samos was the first known astronomer to propose a heliocentric model of the solar system, though the geocentric"
"Chios (c. 470–410 BC, not the better known Hippocrates of Kos) for book III, and Eudoxus of Cnidus (c. 408–355 BC) for book V, while books IV, VI, XI, and XII probably came from other Pythagorean or Athenian mathematicians. The ""Elements"" may have been based on an earlier textbook by Hippocrates of Chios, who also may have originated the use of letters to refer to figures. In the fourth century AD, Theon of Alexandria produced an edition of Euclid which was so widely used that it became the only surviving source until François Peyrard's 1808 discovery at the Vatican of"
"BCE) said definitions should describe the concept being defined in terms of other concepts already known. Mathematical proofs were revolutionized by Euclid (300 BCE), who introduced the axiomatic method still in use today, starting with undefined terms and axioms (propositions regarding the undefined terms assumed to be self-evidently true from the Greek ""axios"" meaning ""something worthy""), and used these to prove theorems using deductive logic. His book, the ""Elements"", was read by anyone who was considered educated in the West until the middle of the 20th century. In addition to theorems of geometry, such as the Pythagorean theorem, the ""Elements"""
"with Tarquin Publications published a digitized copy based on Hewlett's translation of the first four sections (or Part I) of the book. In 2015, Scott Hecht published both print and Kindle versions of ""Elements of Algebra"" () with Euler's Part I (Containing the Analysis of Determinate Quantities), Part II (Containing the Analysis of Indeterminate Quantities), Lagrange's Additions, and footnotes by Johann Bernoulli and others. Elements of Algebra Elements of Algebra is an elementary mathematics textbook written by mathematician Leonhard Euler and originally published in 1770 in German. ""Elements of Algebra"" is one of the earliest books to set out algebra"
"great strides made in the development of geometry made by Ancient Greeks and surveys in Rome, we were to wait for another thousand years before the first equations of motion arrive. The exposure of Europe to the collected works by the Muslims of the Greeks, the Indians and the Islamic scholars, such as Euclid’s ""Elements"", the works of Archimedes, and Al-Khwārizmī's treatises began in Spain, and scholars from all over Europe went to Spain, read, copied and translated the learning into Latin. The exposure of Europe to Arabic numerals and their ease in computations encouraged first the scholars to learn"
"most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution. Descartes refused to accept the authority of previous philosophers. He frequently set his views apart from those of his predecessors. In the opening section of the ""Passions of the Soul"", an early modern treatise on emotions, Descartes goes so far as to assert"
"would be known too. Only much later was it proven (by Ferdinand von Lindemann, in 1882) that this approach had no chance of success, because the factor pi (π) is transcendental. The number π is the ratio of the circumference to the diameter of a circle, and also the ratio of the area to the square of the radius. In the century after Hippocrates at least four other mathematicians wrote their own ""Elements"", steadily improving terminology and logical structure. In this way Hippocrates' pioneering work laid the foundation for Euclid's ""Elements"" (c. 325 BC) that was to remain the standard"
"of Cnidus. The ""Elements"" is a treatise on geometry, and it has exerted a continuing influence on mathematics. From Archimedes several treatises have come down to the present. Among them are ""Measurement of the Circle"", in which he worked out the value of pi; ""The Method of Mechanical Theorems"", on his work in mechanics; ""The Sand Reckoner""; and ""On Floating Bodies"". A manuscript of his works is currently being studied. Very little has survived of prose fiction from the Hellenistic Era. ""The Milesiaka"" by Aristides of Miletos was probably written during the second century BC. ""The Milesiaka"" itself has not"