Ilimin lissafi a duniyar Islama ta tsakiya

Lissafi a lokacin Golden Age na Islama, musamman acikin ƙarni na 9 da 10, an gina shi akan Lissafin Girka (Euclid, Archimedes, Apollonius) da Lissafin Indiya (Aryabhata, Brahmagupta). sami cigaba mai mahimmanci, kamar cikakken cigaba na tsarin ƙididdigar ƙididdigal don haɗawa da raguwa na ƙididdiga, binciken farko na algebra, da cigaba acikin lissafi da trigonometry.

Ilimin lissafi a duniyar Islama ta tsakiya
Bayanai
Ƙaramin ɓangare na	Lissafi

Shafin daga Littafin Compendious a kan Ƙididdiga ta hanyar Cikakken da Daidaitawa ta Al-Khwarizmi

Ayyukan Larabci sun taka muhimmiyar rawa wajen watsa lissafi zuwa Turai a cikin ƙarni na 10-12.

Ra'ayoyi

Omar Khayyám's "Cubic equations and intersections of conic sections" shafi na farko na rubutun surori biyu da aka ajiye a Jami'ar Tehran

• 
  Zana bin tafsirinAbu Sahl al-Quhidon zana sassa na zane-zane.
• 
  Tafsirin Ibn Haytham.

Nazarin algebra, wanda sunan ya samo asaline daga kalmar Larabci wanda ke nufin kammalawa ko "haɗin ɓangarorin da suka karye", ya bunƙasa a lokacin zamanin zinariya na Islama. Muhammad ibn Musa al-Khwarizmi, masanin Farisa a cikin House of Wisdom a Bagadaza shine wanda ya kafa Algebra, yana tare da masanin lissafin Girka Diophantus, wanda aka sani da mahaifin algebra. A cikin littafinsa The Compendious Book on Calculation by Completion and Balancing, Al-Khwarizmi yayi magana game da hanyoyin warware Tushen asali na farko da na biyu (layi da quadratic) polynomial equations. gabatar da hanyar raguwa, kuma ba kamar Diophantus ba, ya kuma bada mafita ta gaba ɗaya don daidaitattun da yake hulɗa dasu.

Algebra na Al-Khwarizmi ya kasance na magana ne, wanda ke nufin cewa an rubuta ma'auni cikin cikakkun jimloli. Wannan ya bambanta da aikin algebra na Diophantus, wanda aka daidaita, ma'ana ana amfani da wasu alamomi. Canja wurin algebra na alama, inda ake amfani da alamomi kawai, ana iya gani a cikin aikin Ibn al-Banna' al-Marrakushi da Abū al-Hasan ibn ʿAlī al-Qalasādi.

Akan aikin da Al-Khwarizmi yayi, J. J. O'Connor da Edmund F. Robertson sun ce:

Sauran masana lissafi da yawa a wannan lokacin sun faɗaɗa kan algebra na Al-Khwarizmi. Abu Kamil Shuja' ya rubuta littafi na algebra tare da zane-zane da hujjoji. Ya kuma lissafa duk hanyoyin da za'a iya magance wasu matsalolinsa. Abu al-Jud, Omar Khayyam, tare da Sharaf al-Dīn al-Tūsī, sun sami mafita da yawa na ma'aunin cubic. Omar Khayyam ya sami mafita ta lissafi na lissafin cubic.

Ƙididdigar cubic

Don w'x'">a ³'auni na uku x + a² = 'b' Khay ya gina parabola x2 = ay, da'irar da ke da diamita b / a2, da kuma layin tsaye ta hanyar maɓallin.       Ana ba da mafita ta tsawon ɓangaren layin kwance daga asalin zuwa tsakiya na layin tsaye da x-axis.

  Omar Khayyam (c. 1038/48 a Iran - 1123/24)

[1] ya rubuta rubutun kan Nuna Matsalar Algebra wanda ke dauke da tsarin warware ma'auni na cubic ko na uku, yana wucewa Algebra na al-Khwārizmī. Khayyám ya sami mafita ga waɗannan daidaitattun ta hanyar gano wuraren haɗuwa na sassan conic guda biyu. sun amfani da wannan hanyar, amma basu haɗa hanyar da za ta rufe duk daidaitattun da Tushen tabbatacce ba.

Sharaf al-Dīn al-Ṭūsī (? a Tus, Iran - 1213/4) ya haɓɓaka sabon hanyar bincike kan ƙididdigar cubic - hanyar da ta haɗada gano ma'anar da cubic polynomial ke samun matsakaicin darajarta. Mis'a', don warware daidaitattun

 

x

3

+ a = b x

{\displaystyle \ x^{3}+a=bx}

, tare da a da b tabbatacce, zai lura cewa matsakaicin ma'anar layin

y = b x −

x

3

{\displaystyle \ y=bx-x^{3}}

ya faru a

x =

b 3

{\displaystyle x=\textstyle {\sqrt {\frac {b}{3}}}}

, kuma cewa daidaitattun ba zai sami mafita ba, mafita ɗaya ko mafita biyu, dangane da ko tsawo na layin a wannan lokacin ya kasance ƙasa da, dai-dai da, ko mafi girma. Ayyukansa da suka tsira basu bada alamar yadda ya gano tsarinsa don mafi girman waɗannan layin ba. gabatar da ra'ayoyi daban-daban don yin la'akari da bincikensa.  

Ƙaddamarwa

Za'a iya samun alamun farko na ƙididdigar lissafi a cikin hujjar Euclid cewa yawan firam ɗin ba shi da iyaka (c. 300 KZ). Pascal ne ya bada cikakkiyar tsari na farko game da ka'idar shigarwa a cikin Traité du triangle arithmétique (1665).

A tsakanin, al-Karaji (c. 1000) ya gabatar da hujja ta hanyar shigarwa don jerin lissafi kuma al-Samaw'al ya ci gaba, wanda yayi amfani da shi don lokuta na musamman na binomial theorem da kaddarorin Triangle na Pascal.

Lambobin da ba su da ma'ana

Helenawa sun gano lambobi marasa ma'ana, amma basu gamsu da su ba kuma kawai suna iya jimrewa ta hanyar zana bambanci tsakanin girmansa da adadi. A cikin ra'ayi na Girkanci, girman ya bambanta a kai a kai kuma ana iya amfani dashi ga ƙungiyoyi kamar sassan layi, yayin da lambobi sun kasance masu rarrabe. Saboda haka, ana iya sarrafa irrationals ne kawai ta hanyar lissafi; kuma haƙiƙa lissafin Girka yafi na lissafi. lissafin Islama ciki har Abū Kāmil Shujāʿ ibn Aslam da Ibn Tahir al-Baghdadi sannu a hankali sun cire bambancin tsakanin girman da adadi, suna bada damar adadi mara ma'ana ya bayyana a matsayin ma'auni a cikin daidaitattun kuma ya zama mafita na daidaitattun algebraic. Sun aiki da yardar rai tare da rashin ma'ana a matsayin abubuwa na lissafi, amma basu bincika yanayin suba.

A cikin ƙarni na goma sha biyu, fassarar Latin na Al-Khwarizmi's Arithmetic akan lambobin Indiya sun gabatar da tsarin lamba na lamba ga yammacin duniya. Littafinsa Mai Daraja akan Ƙididdigar Ƙirar ta Ƙarshe da Daidaitawa ya gabatar da tsarin tsari na farko na daidaitattun layi da ma'auni. A cikin Renaissance Turai, an ɗauke shi asalin wanda ya kirkiro algebra, kodayake yanzu an san cewa aikinsa ya dogara ne akan tsoffin tushen Indiya ko Girkanci. Yayi bitar labarin Geography na Ptolemy kuma ya yi rubutu akan ilmin taurari da taurari. Duk da haka, CA Nallino ya nuna cewa ainihin aikin al-Khwarizmi bai dogara da Ptolemy ba amma akan taswirar duniya, mai yiwuwa a cikin Syriac ko Larabci.

Spherical trigonometry

  An gano ka'idar sines mai sassauƙa a ƙarni na 10: an danganta ta daban-daban ga Abu-Mahmud Khojandi, Nasir al-Din al-Tusi da Abu Nasr Mansur, tare da Abu al-Wafa' Buzjani a matsayin mai ba da gudummawa. Littafin Ibn Mu'ādh al-Jayyanī 's Littafin baka da ba'a san shi ba a cikin ƙarni na 11 ya gabatar da ƙa'idar sines gaba ɗaya. Nasīr al-Dīn al-Tūsi ya bayyana dokar jirgin sama na sines a ƙarni na 13. A cikin Siffar Sashinsa, ya bayyana ƙa'idar sines don jirgin sama da triangles mai siffar zobe kuma ya bada hujjoji ga wannan doka.

Lambobi mara kyau

  A cikin ƙarni na 9, masana lissafin Islama sun sabada lambobi mara ƙyau daga ayyukan masana lissafin Indiya, amma ganewa da amfani da lambobi marasa ƙyau a wannan lokacin ya kasance mai kunya. Al-Khwarizmi baiyi amfani da lambobi marasa kyau ba ko ƙididdiga marasa kyau. Amma a cikin shekaru hamsin, Abu Kamil ya misalta ƙa'idojin alamomi na faɗaɗa yawan $(a\pm b)(c\pm d)$. Al-Karaji ya rubuta a cikin littafinsa al-Fakhrī cewa "dole ne a lissafta ma'auni mara ƙyau a matsayin sharuddan". A cikin karni na 10, Abū al-Wafā' al-Būzjānī ya ɗauki basussuka a matsayin lambobi mara kyau a cikin Littafin Abin da Ya Kamata Daga Kimiyyar Lissafi don Marubuta da 'Yan kasuwa.

A karni na 12, magadan al-Karaji za su bayyana ka'idojin alamomi da amfani da su wajen warware rarrabuwar kawuna . Kamar yadda al-Samaw’al ya rubuta:

samfurin mummunan lamba - al-nāqiṣ - ta tabbataccen lamba - al-zāʾid - mara kyau ne, kuma ta mummunan lamba yana da kyau. Idan muka cire lambar mara kyau daga mafi girma mara kyau, saura shine mummunan bambancin su. Bambancin ya kasance tabbatacce idan muka cire lamba mara kyau daga ƙaramin mara kyau. Idan muka cire korau lamba daga tabbataccen lamba, saura shine tabbataccen jimlar su. Idan muka cire tabbataccen lamba daga iko mara kyau ( martaba khāliyya ), saura mara kyau iri ɗaya ne, kuma idan muka cire wani lamba mara kyau daga iko mara kyau, saura shine tabbataccen lamba ɗaya.

Matsayin karya sau biyu

  Between the 9th and 10th centuries, the Egyptian mathematician Abu Kamil wrote a now-lost treatise on the use of double false position, known as the Book of the Two Errors (Kitāb al-khaṭāʾayn). The oldest surviving writing on double false position from the Middle East is that of Qusta ibn Luqa (10th century), an Arab mathematician from Baalbek, Lebanon. He justified the technique by a formal, Euclidean-style geometric proof. Within the tradition of Golden Age Muslim mathematics, double false position was known as hisāb al-khaṭāʾayn ("reckoning by two errors"). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of Quranic inheritance), as well as purely recreational problems. The algorithm was often memorized with the aid of mnemonics, such as a verse attributed to Ibn al-Yasamin and balance-scale diagrams explained by al-Hassar and Ibn al-Banna, who were each mathematicians of Moroccan origin.

Sauran manyan adadi

Sally P. Ragep, masanin tarihin kimiyya a Islama, ya ƙiyasta a cikin 2019 cewa "dubun dubatar" rubuce-rubucen Larabci a cikin kimiyya lissafi da falsafa ba'a karanta su ba, wanda ke bada nazarin "yana nuna son kai da iyakancewar mayar da hankali kan taƙaitaccen rubutun malamai". </link>

• 'Abd al-Hamid bn Turk (fl. 830) (quadratics)
• Thabit bin Qurra (826-901)
• Sind bn Ali (ra) bayan shekara ta 864.
• Ismail al-Jazari (1136-1206)
• Abu Sahl al-Qūhi (c. 940-1000) (cibiyoyin nauyi)
• Abu'l-Hasan al-Uqlidisi (952-953) (ilithmetic)
• 'Abd al-Aziz al-Qabisi (d. 967).
• Ibn al-Haytham (c. 965-1040)
• Abu al-Rayhan al-Bīrunī (973-1048) (Trigonometry)
• Ibn Maɗa' (c. 1116-1196)
• Jamshīd al-Kāshi (c. 1380-1429)

Gallery

• 
  Zana bin tafsirinAbu Sahl al-Quhidon zana sassa na zane-zane.
• 
  Tafsirin Ibn Haytham.

Duba kuma

• Lambobin Larabci
• Tasirin Indiya akan ilimin lissafi na Islama a cikin Islama ta Tsakiya
• Tarihin lissafi
• Tarihin ilimin lissafi
• Kimiyya a duniyar Musulunci ta tsakiya
• Zamanin kimiyya da injiniyanci a duniyar musulmi

 

 

Hanyoyin haɗi na waje

• O'Connor, John J.; Robertson, Edmund F., "Arabic mathematics: forgotten brilliance?", MacTutor History of Mathematics archive, University of St Andrews.
• Richard Covington, Rediscovering Arabic Science, 2007, Saudi Aramco World Archived 2014-10-30 at the Wayback Machine
• List of Inventions and Discoveries in Mathematics During the Islamic Golden Age Archived 2020-02-14 at the Wayback Machine