هندسه: تفاوت میان نسخه‌ها

در [[قرون وسطی]]، [[ریاضیات در جهان اسلام|ریاضیات جهان اسلام]] به توسعه هندسه، به‌خصوص [[هندسه جبری]] کمک نمود.<ref>R. Rashed (1994), ''The development of Arabic mathematics: between arithmetic and algebra'', p. 35 [[London]]</ref><ref>{{Harv|Boyer|1991|loc="The Arabic Hegemony" pp. 241–242}} "Omar Khayyam (c. 1050–1123), the "tent-maker," wrote an ''Algebra'' that went beyond that of al-Khwarizmi to include equations of third degree. Like his Arab predecessors, Omar Khayyam provided for quadratic equations both arithmetic and geometric solutions; for general cubic equations, he believed (mistakenly, as the 16th century later showed), arithmetic solutions were impossible; hence he gave only geometric solutions. The scheme of using intersecting conics to solve cubics had been used earlier by Menaechmus, Archimedes, and Alhazan, but Omar Khayyam took the praiseworthy step of generalizing the method to cover all third-degree equations (having positive roots). .. For equations of higher degree than three, Omar Khayyam evidently did not envision similar geometric methods, for space does not contain more than three dimensions, … One of the most fruitful contributions of Arabic eclecticism was the tendency to close the gap between numerical and geometric algebra. The decisive step in this direction came much later with Descartes, but Omar Khayyam was moving in this direction when he wrote, "Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras are geometric facts which are proved."".</ref> [[ابوعبدالله محمد بن عیسی ماهانی|الماهانی]] (مرگ در ۸۵۳ میلادی)، ایده تقلیل مسائل هندسی چون [[تضعیف مکعب]] به مسائلی در [[جبر]] را درک نموده بود.<ref>{{MacTutor Biography|id=Al-Mahani|title=Al-Mahani|mode=cs1}}</ref> [[ثابت بن قره]] (در لاتین به Thebit شناخته می‌شود) (۸۳۶–۹۰۱ میلادی) با کاربردهای اعمال [[حساب|حسابی]] در [[نسبت (ریاضیات)|نسبت‌های]] کمیت‌های هندسی درگیر بود و به توسعه [[هندسه تحلیلی]] کمک نمود.<ref name="ReferenceA">{{MacTutor Biography|id=Thabit|title=Al-Sabi Thabit ibn Qurra al-Harrani|mode=cs1}}</ref> [[عمر خیام]] (۱۰۴۸–۱۱۳۱ میلادی)، راه حل‌هایی را برای معادلات مکعبی پیدا نمود.<ref>{{MacTutor Biography|id=Khayyam|title=Omar Khayyam|mode=cs1}}</ref> قضایای [[ابن هیثم]] (Alhazen)، عمر خیام و [[خواجه نصیرالدین طوسی]] در ارتباط با [[چهارضلعی|چهارضلعی‌ها]]، شامل چهارضلعی‌های لامبرت و [[چهارضلعی ساکری|ساکری]]، جزو اولین نتایج [[هندسه هذلولوی]] بودند که به همراه فرضیات جایگزینشان همچون [[اصل توازی هیلبرت|اصل پلیفیر]]، در میان هندسه‌دانان اروپایی شامل ویتلو (حدود ۱۲۳۰ تا ۱۳۱۴ میلادی)، [[ابن گرشوم]] (۱۲۸۸ تا ۱۳۴۴ میلادی)، آلفونسو، [[جان والیس]]، و [[جیرولامو ساکری]]، تأثیر قابل توجهی جهت توسعه هندسه نااقلیدسی داشتند.<ref>Boris A. Rosenfeld and Adolf P. Youschkevitch (1996), "Geometry", in Roshdi Rashed, ed. , ''[[Encyclopedia of the History of Arabic Science]]'', Vol. 2, pp. 447–494 [470], [[Routledge]], London and New York: {{quote|"Three scientists, Ibn al-Haytham, Khayyam, and al-Tusi, had made the most considerable contribution to this branch of geometry whose importance came to be completely recognized only in the 19th century. In essence, their propositions concerning the properties of quadrangles which they considered, assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries. Their other proposals showed that various geometric statements were equivalent to the Euclidean postulate V. It is extremely important that these scholars established the mutual connection between this postulate and the sum of the angles of a triangle and a quadrangle. By their works on the theory of parallel lines Arab mathematicians directly influenced the relevant investigations of their European counterparts. The first European attempt to prove the postulate on parallel lines – made by Witelo, the Polish scientists of the 13th century, while revising Ibn al-Haytham's ''[[Book of Optics]]'' (''Kitab al-Manazir'') – was undoubtedly prompted by Arabic sources. The proofs put forward in the 14th century by the Jewish scholar Levi ben Gerson, who lived in southern France, and by the above-mentioned Alfonso from Spain directly border on Ibn al-Haytham's demonstration. Above, we have demonstrated that ''Pseudo-Tusi's Exposition of Euclid'' had stimulated both J. Wallis's and G. Saccheri's studies of the theory of parallel lines."}}</ref>

 

 

 

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