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{{about|sejarah sains dalam tamadun Islam di antara abad ke-8 dan ke-16|maklumat pada sains dalam konteks Islam|Islam dan sains}}
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(contracted; show full)metikan]], [[isnad]] atau "sandaran", dan perkembangan [[kaedah saintifik|kaedah saintifik bagi siasatan terbuka]] untuk membuktikan sesuatu dakwaan itu salah, [[ijtihad]] yang dapat digunapakai secara amnya kepada banyak jenis persoalan. Dari kurun ke-12, di sebalik kecanggihan mantik [[al-Ghazali]], kebangkitan mazhab [[Ash'ari]] pada lewat Zaman Pertengahan secara perlahan-lahan membataskan karya asal mengenai ilmu mantik di dunia Islam, meskipun ia berterusan hingga kurun ke-15.

=== Mat
hematics ===
{{Main|Islamic mathematics}}
[[Fail:1983_CPA_5426.jpg|thumb|right|[[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwarizmi]], seorang peneroka [[algebra]] dan [[algoritma]].]]

John J. O'Connor and Edmund F. Robertson wrote in the ''[[MacTutor History of Mathematics archive]]'':
{{quote|"Recent research paints a new picture of the debt that we owe to Islamic [[mathematics]]. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier."<ref>John J. O'Connor and Edmund F. Robertson (1999). [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics: forgotten brilliance?] ''[[MacTutor History of Mathematics archive]]''.</ref>}}

[[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwarizmi]] (780-850), from whose name the word [[algorithm]] derives, contributed significantly to [[algebra]], which is named after his book, ''[[The Compendious Book on Calculation by Completion and Balancing|Kitab al-Jabr]]'', the first book on [[elementary algebra]].<ref>{{Harv|Eglash|1999|p=61}}</ref> He also introduced what is now known as [[Arabic numerals]], which originally came from [[Indian mathematics|India]], though Muslim mathematicians did make several refinements to the number system, such as the introduction of [[Decimal separator|decimal point]] notation. [[Al-Kindi]] (801-873) was a pioneer in [[cryptanalysis]] and [[cryptology]]. He gave the first known recorded explanations of [[cryptanalysis]] and [[Frequency analysis (cryptanalysis)|frequency analysis]] in ''A Manuscript on Deciphering Cryptographic Messages''.<ref>Simon Singh, ''The Code Book'', p. 14-20.</ref><ref>{{cite web |url=http://www.muslimheritage.com/topics/default.cfm?ArticleID=372 |title=Al-Kindi, Cryptgraphy, Codebreaking and Ciphers |accessdate=2007-01-12 |format=HTML}}</ref>

The first known [[Mathematical proof|proof]] by [[mathematical induction]] appears in a book written by [[Al-Karaji]] around 1000 AD, who used it to prove the [[binomial theorem]], [[Pascal's triangle]], and the sum of [[integral]] [[Cube (algebra)|cubes]].<ref>Victor J. Katz (1998). ''History of Mathematics: An Introduction'', p. 255-259. [[Addison-Wesley]]. ISBN 0-321-01618-1.</ref> The [[historian]] of mathematics, F. Woepcke,<ref>F. Woepcke (1853). ''Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi''. [[Paris]].</ref> praised Al-Karaji for being "the first who introduced the [[theory]] of [[algebra]]ic [[calculus]]." [[Ibn al-Haytham]] was the first mathematician to derive the formula for the sum of the [[fourth power]]s, and using the method of induction, he developed a method for determining the general formula for the sum of any integral [[Exponentiation|powers]], which was fundamental to the development of integral calculus.<ref>Victor J. Katz (1995). "Ideas of Calculus in Islam and India", ''Mathematics Magazine'' '''68''' (3), p. 163-174.</ref> The 11th century [[Persian literature|poet]]-mathematician [[Omar Khayyám]] was the first to find general [[geometry|geometric]] solutions of [[cubic equation]]s and laid the foundations for the development of [[analytic geometry]], [[algebraic geometry]] and [[non-Euclidean geometry]]. [[Sharaf al-Din al-Tusi]] (1135-1213) found algebraic and [[Numerical analysis|numerical]] solutions to cubic equations and was the first to discover the [[derivative]] of [[Cubic function|cubic polynomials]], an important result in differential calculus.<ref>J. L. Berggren (1990). "Innovation and Tradition in Sharaf al-Din al-Tusi's Muadalat", ''Journal of the American Oriental Society'' '''110''' (2), p. 304-309.</ref>

Other achievements of Muslim mathematicians include the invention of [[spherical trigonometry]],<ref>{{cite book |last=Syed |first=M. H. |title=Islam and Science |year=2005 |publisher=Anmol Publications PVT. LTD. |isbn=8-1261-1345-6 |pages=71}}</ref> the discovery of all the [[trigonometric function]]s besides sine and cosine, early inquiry which aided the development of [[analytic geometry]] by [[Ibn al-Haytham]], the first refutations of [[Euclidean geometry]] and the [[parallel postulate]] by [[Nasīr al-Dīn al-Tūsī]], the first attempt at a [[non-Euclidean geometry]] by Sadr al-Din, the development of [[Mathematical notation|symbolic algebra]] by [[Abū al-Hasan ibn Alī al-Qalasādī]],<ref>{{MacTutor Biography|id=Al-Qalasadi|title=Abu'l Hasan ibn Ali al Qalasadi}}</ref> and numerous other advances in algebra, [[arithmetic]], calculus, [[cryptography]], [[geometry]], [[number theory]] and [[trigonometryematik ===
{{Main|Matematik Islam}}
[[Fail:1983_CPA_5426.jpg|thumb|right|[[Muhammad ibn Mūsā al-Khwārizmī|Al-Khwarizmi]], seorang perintis [[algebra]] dan [[algoritma]].]]

John J. O'Connor and Edmund F. Robertson menulis di dalam ''[[MacTutor History of Mathematics archive]]'':
{{quote|"Kajian terkini melakarkan gambaran baru hutang kita terhadap [[matematik]] Islam. Tidak syak lagi banyak idea yang sebelumnya dianggap menjadi tanggapan baru yang bijak disebabkan oleh ahli-ahli matematik Eropah kurun ke-16, 17 dan 18 kini diketahui dikembangkan oleh ahli-ahli matematik Arab/Islam kira-kira empat kurun lebih awal."<ref>John J. O'Connor and Edmund F. Robertson (1999). [http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Arabic_mathematics.html Arabic mathematics: forgotten brilliance?] ''[[MacTutor History of Mathematics archive]]''.</ref>}}

[[Al-Khawarizmi]] (780-850), yang terbit daripada namanya perkataan [[algoritma]], banyak menyumbang pada [[algebra]], yang dinamakan menurut bukunya, ''[[Buku Ringkasan pada Pengiraan dengan Penyelesaian dan Keseimbangan|Kitab al-Jabr]]'', buku pertama mengenai [[algebra permulaan]].<ref>{{Harv|Eglash|1999|p=61}}</ref> Beliau juga memperkenalkan apa yang kini dikenali sebagai [[angka Arab]], yang pada asalnya datang dari [[matematik India|India]], meskipun ahli-ahli matematik Muslim membuat beberapa perbaikan bagi sistem nombor itu, seperti pengenalan notasi [[titik perpuluhan]]. [[Al-Kindi]] (801-873) merupakan seorang perintis dalam [[pemecahan tulisan rahsia]] dan [[kriptologi]]. Beliau memberi penjelasan bercatatan yang pertama diketahui mengenai pemecahan tulisan rahsia dan [[analisis kekerapan]] di dalam ''A Manuscript on Deciphering Cryptographic Messages''.<ref>Simon Singh, ''The Code Book'', p. 14-20.</ref><ref>{{cite web |url=http://www.muslimheritage.com/topics/default.cfm?ArticleID=372 |title=Al-Kindi, Cryptgraphy, Codebreaking and Ciphers |accessdate=2007-01-12 |format=HTML}}</ref>

[[Pembuktian]] oleh [[aruhan bermatematikaan]] yang pertama diketahui muncul di dalam sebuah buku yang ditulis [[Al-Karaji]] sekitar tahun 1000 M, yang menggunakannya membuktikan [[teorem binomial]], [[segitiga Pascal]] dan hasil tambah [[kubus]] [[kamiran]].<ref>Victor J. Katz (1998). ''History of Mathematics: An Introduction'', p. 255-259. [[Addison-Wesley]]. ISBN 0-321-01618-1.</ref> [[Sejarawan]] matematik, F. Woepcke,<ref>F. Woepcke (1853). ''Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi''. [[Paris]].</ref> memuji al-Karaji sebagai "orang pertama memperkenalkan [[teori]] [[kalkulus]] [[algebra]]." [[Ibn al-Haitham]] merupakan ahli matematik pertama yang menerbitkan formula bagi hasil tambah [[kuasa empat]], dan menggunakan kaedah aruhan, beliau mengembangkan kaedah untuk menentukan formula am bagi hasil tambah sebarang [[pengeksponenan|kuasa]] kamiran, yang merupakan asas kepada perkembangan kalkulus kamiran.<ref>Victor J. Katz (1995). "Ideas of Calculus in Islam and India", ''Mathematics Magazine'' '''68''' (3), p. 163-174.</ref> Ahli matematik dan [[penyair]] kurun ke-11 [[Omar Khayyám]] merupakan orang pertama yang mencari penyelesaian [[geometri]] am bagi [[persamaan kuasatiga]] dan meletakkan batu asas bagi perkembangan [[geometri analisaan]], [[geometri aljabar]] dan [[geometri bukan Euclid]]. [[Sharaf al-Din al-Tusi]] (1135-1213) menemui penyelesaian aljabar dan [[analisis berangka|berangka]] bagi persamaan kuasatiga dan merupakan orang pertama yang menjumpai [[terbitan]] [[fungsi kuasatiga|polinomial kubus]], satu hasil penting dalam kalkulus pembezaan.<ref>J. L. Berggren (1990). "Innovation and Tradition in Sharaf al-Din al-Tusi's Muadalat", ''Journal of the American Oriental Society'' '''110''' (2), p. 304-309.</ref>

Pencapaian lain ahli-ahli matematik Muslim termasuklah ciptaan [[trigonometri sfera]],<ref>{{cite book |last=Syed |first=M. H. |title=Islam and Science |year=2005 |publisher=Anmol Publications PVT. LTD. |isbn=8-1261-1345-6 |pages=71}}</ref> penemuan semua [[fungsi trigonometri]] selain [[sinus]] dan [[kosinus]], siasatan terawal yang membantu perkembangan [[geometri analisaan]] oleh [[Ibn al-Haitham]], sangkalan pertama terhadap [[geometri Euclid]] dan [[postulat selari]] oleh [[Nasīr al-Dīn al-Tūsī]], cubaan pertama pada [[geometri bukan Euclid]] oleh Sadr al-Din, perkembangan [[notasi matematik|algebra simbolik]] oleh [[Abū al-Hasan ibn Alī al-Qalasādī]],<ref>{{MacTutor Biography|id=Al-Qalasadi|title=Abu'l Hasan ibn Ali al Qalasadi}}</ref> dan banyak lagi kemajuan lain dalam algebra, [[aritmetik]], [[kalkulus]], [[pemecahan tulisan rahsia]], [[geometri]], [[teori nombor]] dan [[trigonometri]].

== Natural sciences ==
=== Astrology ===
{{Main|Islamic astrology}}

Islamic astrology, in [[Arabic language|Arabic]] ''ilm al-nujum'' is the study of the heavens by early [[Muslim]]s. In early Arabic sources, ''ilm al-nujum'' was used to refer to both [[astronomy]] and [[astrology]]. In [[medieval]] sources, however, a clear distinction was made between ''ilm al-nujum'' (science of the stars) or ''ilm al-falak'' (science o(contracted; show full)
*[http://www.smi.uib.no/paj/Stenberg.html The Islamization of science or the marginalization of Islam]
*[http://www.muslimheritage.com/ Muslimheritage]
*[http://www.1001inventions.com/index.cfm?fuseaction=main.viewSection&intSectionID=309 1001inventions]
*[http://www.science-islam.net/sommaire.php3?lang=en Science and religion in Islam]
*Keith L. Moore, {{YouTube|id=Rb0uZefwQnc|title=The Developing Human}}

[[Kategori:Sains Islam]]
[[Kategori:Zaman Kegemilangan Islam]]