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- Scientific method — The scientific method, as systematic approach to theory and experimentation, developed during the Middle Ages due to the work of scholars such as Alhazen, Biruni, Bacon, and Robert Grosseteste, who produced a systemized process of scientific enquiry based upon observation, experimentation and verification of hypotheses. Arithmetic and Algebra — the Islamic scholar Al-Khwarizmi was the author of two books that changed the face of both Islamic and European mathematics. His “De numero indorum” (which only exists in Latin translation; no Arabic original is known) introduced the Hindu decimal place value number system first into the Arab world in the 9th Century and then into Europe in the 12th Century. His “al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala” was a compendium of basic algebra, a word taken from the title of the book, drawn from Babylonian, Greek and Indian sources. In it he demonstrates how to solve linear and quadratic equations but only those with positive solutions. Brahmagupta, one of his main sources, was already dealing with negative solutions in the 7th Century. Later Islamic mathematicians extended Al-Khwarizmi’s results to those polynomials of higher degree that could be reduced to quadratics through substitution. His arithmetic was taught as Algorithmus, a corruption of his name, in mediaeval universities as a part of computus. His arithmetic and algebra were popularised in Europe through the publication of the Liber abbaci by Leonardo of Pisa in the 13th century.. Differential calculus — The concepts of tangential lines and infinitesimals were developed by the ancient Greeks including Archimedes; however, it was Medieval scholars, notably Bhaskara, that developed the basic mathematical framework for modern differential calculus. Mechanics — In the 6th Century, John Philoponus in his critique of Aristotle’s theory of motion, introduced the concept of “impressed force” to explain why thrown objects continued to move after losing contact with the thrower. This theory of impetus was modified by Islamic scholars such as Avicenna in the 11th century, who theorized the concept of momentum, as well as by Avempace—who developed the concept of a reaction force— and Abu’l Barakat— who developed the concept that force applied continuously produces acceleration— in the 12th century. These concepts were adopted by various western thinkers, achieving their most developed form in the hands of Jean Buridan in the 14th century. Galileo further developed this into the theory of inertia, which after further modification, through Descartes, became Newton’s First Law of Motion. Optics — the Greeks treated optics as three independent disciplines: theories of philosophical or physical optics; physiological theories of the eye; and geometrical optics. In the 10th Century the Islamic polymath Alhazen became the first thinker to combine all three fields into an integrated science of optics. This was however not just a work of synthesis, as he made original contribution to the field. Whereas the Greeks had merely assumed the linear propagation of light, Alhazen proved it with empirical experiments. In the 13th Century Robert Grosseteste developed a unified theory of light based on the works of Al-Kindi and Ptolemaeus. Roger Bacon adopted Grosseteste's theories and expanded them to include the optics of Alhazen. John Pecham and Witelo expanded on Bacon's work and provided the fundament on which Kepler erected the modern theory of optics. Modern surgery — Although the first known surgical text was written by Sushruta in antiquity, Medieval researchers, especially Abulcasis, developed the techniques and tools that led to modern surgical practices. The 1266 work Chirurgia, (Surgery), by Theodoric Borgognoni advocates antiseptic surgery, in opposition to the Arab belief in "laudable pus. " Alchemy & chemistry — As with other disciplines, alchemy and chemistry in Islam was drawn from multiple sources: Egyptian, Greek, Indian and Chinese, and as with other disciplines the whole was significantly greater than the parts. Islamic culture created a vast corpus of alchemic literature that through transfer into Europe during the High Middle Ages and the Renaissance had a major effect on the development of science. The most influential texts were the so-called Jaberian corpus (much of which was written in the 10th century by the Ism’iliya, or Brotherhood of Purity), the Summa Perfectionis of Paulus de Tarento and the Secret of Secrets of al-Razi. The first two introduced atomism and the sulphur-mercury theory as competitors to Aristotle’s theory of matter. Al-Razi described many of the methods and much of the equipment that formed the basis of work in chemistry, metallurgy and pharmacology up to the middle of the 19th century. Trigonometry — developed in ancient times by Hipparchus, Menelaus and Ptolemaeus in order to facilitate their astronomical calculations. In Greek trigonometry, angles were represented by the chords of a circle. Menelaus laid the foundations for spherical trigonometry in his Sphaerica whilst Ptolemaeus produced the most extensive ancient trigonometry text as part of his Syntaxis Mathematike. Hindu mathematicians, who may have borrowed much from Greek astronomy, replaced the Greek chordal trigonometry with half-chords producing the equivalent of our sine and cosine. The most important Hindu trigonometry texts are the Surya Siddhanta (4th Century), the Aryabhatiya (5th Century) and the Siddhanta Shiromani (12th Century); as with the Greeks, all of these are astronomy texts. The Islamic mathematicians and astronomers took over the mathematical astronomy of Ptolemaeus, Aryabhata and Brahmagupta, and introduced the secant, cosecant, tangent and cotangent. In the 13th century, al-Tusi produced the first complete work on planar and spherical trigonometry, treating it as a discrete mathematical discipline independent of astronomy. Trigonometry was introduced to Western Europe during the Latin translations of the 12th century, and later came into wider use due to Peurbach and Regiomontanus in the middle of the 15th century. Like the Islamic astronomers, they replaced the Ptolemaic chordal trigonometry with Hindu-Arabic half-chord trigonometry. Technologies for navigation — Although primitive versions of the technologies were known in antiquity, it was during the Middle Ages that key technologies such as the latitude-independent astrolabe and the portable compass were developed as practical tools for navigation, especially on the open seas. In the thirteenth century Peter of Maricourt made two major innovations to improve the accuracy and practicality of the magnetic compass by adding a calibrated scale and placing the magnet on a pivot. Accurate lunar models — The motions of the moon and planets had been studied for millennia. The Middle Ages produced the first model of lunar motion which matched physical observations. This and other developments in planetary models are believed to have been used by the Renaissance astronomer Copernicus. Incendiary weapons and bombs — The use of fire and flammable materials in warfare are as old as mankind itself but the Middle Ages took the science from simple recipes and brute force approaches to sophisticated formulae and devices. These included everything from flamethrowers to land/sea mines and solid-fuel rockets. Because of the decline of the Byzantine Empire and the medieval Muslim empires much of the scientific progress of the medieval period slowed significantly during the late Middle Ages. Progress was finally re-ignited by the European Scientific Revolution which followed its Renaissance period.
- Na vzdělanost ve středověku obecně nebyl kladen přílišný důraz. Především v raném středověku byla snaha získat jinou než čistě praktickou, například řemeslnou či válečnickou dovednost značně okrajovým jevem. Vzdělání se realizovalo nejprve prostřednictvím klášterů, později v městském prostředí také prostřednictvím neklášterních škol včetně prvních univerzit. Nárůst vzdělanosti byl jednou z příčin vedoucí k postupné přeměně středověké společnosti ve společnost novověkou.
- La expresión ciencia medieval se refiere a los descubrimientos en el campo de la filosofía natural que ocurrieron en el periodo de la Edad Media —el periodo intermedio, en una división esquemática de la Historia de Europa. Europa Occidental entró en la Edad Media con grandes dificultades que minaron la producción intelectual del continente. Los tiempos eran confusos y se había perdido el acceso a los tratados científicos de la antigüedad clásica, manteniéndose sólo las compilaciones resumidas y hasta desvirtuadas, por las sucesivas traducciones que los romanos habían hecho al latín. Sin embargo, con el inicio de la llamada Revolución del siglo XII, se reavivó el interés por la investigación de la naturaleza. La ciencia que se desarrolló en ese periodo dorado de la filosofía escolástica daba énfasis a la lógica y abogaba por el empirismo, entendiendo la naturaleza como un sistema coherente de leyes que podrían ser explicadas por la razón. Fue con esa visión con la que sabios medievales se lanzaron en busca de explicaciones para los fenómenos del universo y consiguieron importantes avances en áreas como la metodología científica y la física. Esos avances fueron repentinamente interrumpidos por la Peste negra y son virtualmente desconocidos por el público contemporáneo, en parte porque la mayoría de las teorías avanzadas del periodo medieval están hoy obsoletas, y en parte por el estereotipo de que la Edad Media fue una supuesta "Edad de las Tinieblas".
- Keskiajan tieteellä tarkoitetaan Euroopassa ja Lähi-idän alueella noin vuosien 500–1500 aikana harjoitettua tiedettä. Keskiaika on historiankirjoituksessa pitkään nähty lasku- ja suvantovaiheena eurooppalaisen tieteen historiassa. Nykytutkimus on kuitenkin paljastanut, ettei tilanne ollut aivan niin lohduton Euroopan osalta kuin on luultu. Islaminuskoisessa Lähi-idässä eri tieteenalojen tutkimiseen kuitenkin panostettiin selvästi Eurooppaa enemmän. Luonnontieteiden osalta taso Lähi-idässä ja Persian alueilla oli Eurooppaan verrattuna hyvin korkealla. Islaminuskoisten alueiden osalta keskiajan tieteen yhteydessä puhutaan islamilaisesta renessanssista. Karolingisen renessanssin aikana Euroopan tieteet ja taiteet osittain elpyivät Länsi-Rooman hajoamisen aiheuttamasta taantumasta. 1000-luvulta lähtien kulttuuria ja myös tieteitä rikastuttivat yhteydet islamilaiseen maailmaan. Sydänkeskiajalla läntiseen Eurooppaan syntyi yliopistolaitos. Vanhoja antiikin auktoreiden laatimia tekstejä alettiin kääntää kreikasta tai arabiasta latinaksi, koska kreikan kieltä ei läntisessä Euroopassa yleisesti osattu. Keskiaika oli myös skolastisen filosofian kulta-aikaa, mikä tarkoittaa sitä, että oppineet uskoivat kaiken totuuden löytyvän antiikin lähteistä. Skolastikkojen tehtävänä oli myös sovittaa uskonnon ja järjen väliset ristiriitaisuudet. Aristoteles nousi merkittävimmäksi auktoriteetiksi tieteen harjoittamisessa sydänkeskiajalta lähtien. Hänen oppejaan sovellettiin ja muokattiin niin teologian, filosofian, tähtitieteen kuin fysiikan saroilla. Aristoteleella oli johtavan auktoriteetin asema aina uuden ajan tieteelliseen vallankumoukseen saakka, joskin myös muiden antiikin ajattelijoiden suosio kasvoi.
- La science du Moyen Âge se réfère à l'étude de la nature durant le Moyen Âge. Cette science comprend les disciplines pratiques, les sciences mathématiques et la philosophie naturelle, encore appelée philosophie première, dans le vocabulaire du Moyen Âge. Le contenu et la classification des sciences ont beaucoup évolué par rapport à notre contexte contemporain, de sorte que l'on précise dans le premier paragraphe le contexte historique et culturel dans lequel les sciences et la philosophie se sont développées au Moyen Âge en occident. Bien que cette période s'apparente généralement à l'histoire européenne, les avancées technologiques du monde oriental sont également évoquées dans ce présent article. Par contre, pour les sciences et techniques dans l'empire byzantin, se reporter à cet article. D'autre part, la période couverte dans cet article recoupe la période décrite dans l'article Renaissance. Ceci est dû au fait que, artistiquement, scientifiquement, et techniquement, l'Italie avait au moins un siècle d'avance dans la Renaissance, par rapport au reste de l'Europe, et particulièrement de la France. Les premières caractéristiques de la Renaissance en art se manifestèrent au XIII siècle en Italie, en sculpture (voir par exemple Niccolo Pisano), et en littérature.
- Met de wetenschap in de middeleeuwen wordt de wetenschap bedoeld in de traditionele "middenperiode" in de schematische indeling van de Europese geschiedenis. De bestudering van de wetenschap in deze periode door wetenschapshistorici richtte zich vooral op de praktische disciplines, zoals de wiskunde en natuurfilosofie. Tegenwoordig zijn een aantal wetenschapshistorici, zoals Pierre Duhem, tegen het grote belang dat vaak werd en wordt gelegd bij een 17 eeuwse anti-aristotelische en anti-kerkse Wetenschappelijke Revolutie tijdens de Verlichting. Zij benadrukken juist de vooruitgang die in de middeleeuwse wetenschap werd geboekt door geleerden als Thomas van Aquino en Johannes Buridan. Dit was volgens hen de opmaat voor de latere ontdekkingen en paradigmaverschuivingen tijdens de Wetenschappelijke Revolutie. Hoewel de term "middeleeuwen" voornamelijk wordt gebruikt voor een periode in de geschiedenis van Europa, wordt de term vaak ook voor andere delen van de wereld gebruikt. Hieronder zal daarom ook de vooruitgang in het Oosten aan de orde komen.
- Ciência medieval se refere às descobertas no campo da filosofia natural que ocorreram no período da Idade Média - o período intermédio, numa divisão esquemática da História da Europa. A Europa Ocidental entrou na Idade Média em grandes dificuldades que minaram a produção intelectual do continente. Os tempos eram confusos e havia-se perdido o acesso aos tratados científicos da antiguidade clássica, ficando apenas as compilações resumidas e até deturpadas que os romanos tinham traduzido para o latim. Entretanto, com o início do chamado Renascimento do Século XII, renovou-se o interesse pela investigação da natureza. A ciência que se desenvolveu nesse período áureo da filosofia escolástica dava ênfase à lógica e advogava o empirismo, entendendo a natureza como um sistema coerente de leis que poderiam ser explicadas pela razão.
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- Scientific method — The scientific method, as systematic approach to theory and experimentation, developed during the Middle Ages due to the work of scholars such as Alhazen, Biruni, Bacon, and Robert Grosseteste, who produced a systemized process of scientific enquiry based upon observation, experimentation and verification of hypotheses.
- Na vzdělanost ve středověku obecně nebyl kladen přílišný důraz. Především v raném středověku byla snaha získat jinou než čistě praktickou, například řemeslnou či válečnickou dovednost značně okrajovým jevem. Vzdělání se realizovalo nejprve prostřednictvím klášterů, později v městském prostředí také prostřednictvím neklášterních škol včetně prvních univerzit.
- La expresión ciencia medieval se refiere a los descubrimientos en el campo de la filosofía natural que ocurrieron en el periodo de la Edad Media —el periodo intermedio, en una división esquemática de la Historia de Europa. Europa Occidental entró en la Edad Media con grandes dificultades que minaron la producción intelectual del continente.
- Keskiajan tieteellä tarkoitetaan Euroopassa ja Lähi-idän alueella noin vuosien 500–1500 aikana harjoitettua tiedettä. Keskiaika on historiankirjoituksessa pitkään nähty lasku- ja suvantovaiheena eurooppalaisen tieteen historiassa. Nykytutkimus on kuitenkin paljastanut, ettei tilanne ollut aivan niin lohduton Euroopan osalta kuin on luultu. Islaminuskoisessa Lähi-idässä eri tieteenalojen tutkimiseen kuitenkin panostettiin selvästi Eurooppaa enemmän.
- La science du Moyen Âge se réfère à l'étude de la nature durant le Moyen Âge. Cette science comprend les disciplines pratiques, les sciences mathématiques et la philosophie naturelle, encore appelée philosophie première, dans le vocabulaire du Moyen Âge.
- Met de wetenschap in de middeleeuwen wordt de wetenschap bedoeld in de traditionele "middenperiode" in de schematische indeling van de Europese geschiedenis. De bestudering van de wetenschap in deze periode door wetenschapshistorici richtte zich vooral op de praktische disciplines, zoals de wiskunde en natuurfilosofie.
- Ciência medieval se refere às descobertas no campo da filosofia natural que ocorreram no período da Idade Média - o período intermédio, numa divisão esquemática da História da Europa. A Europa Ocidental entrou na Idade Média em grandes dificuldades que minaram a produção intelectual do continente.
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