Sâbit bin Kurra bin Marvan el Sabi el Harrani MS 836’da Harran’da doğdu. İsminden de anlaşıldığı üzere, kendisi Sabiilik mezhebindendir. kendisinin diller konusundaki hakimiyeti ve bilimde büyük ilerleme kaydedeceğine dair bir potansiyel oluşturması sebebiyle, Abbasi halifesi tarafından yönetilen Bağdat’ta bulunan bilim takımına büyük müslüman matematikçi Muhammed bin Musa bin Şakir tarafından seçilmiştir. Orada Beni Musa kardeşlerle birlikte bilimsel çalışmalarını yürütmüştür. Sâbit; matematik, astronomi, mekanik gibi alanlardaki çalışmalarının yanında Yunanca’dan Arapça’ya yaptığı birçok tercümeyle de bilime büyük katkılar sunmuştur. Sonra Abbasi Halifesi el M’utadid tarafından himaye edilmiştir. Uzun bir akademik kariyer yolculuğunun ardından 901 yılında Bağdat’ta vefat etmiştir.

Sâbit, çalışmalarıyla ağırlıklı olarak matematik ve astronomiye katkı sağlamıştır. Geleneksel geometrinin geometrik cebire gelişiminde etkili olmuştur ve Öklid dışı geometri, küresel trigonometri, integral hesabı ve gerçek sayılar gibi konuların gelişimine ışık tutan teoriler üretmiştir. Öklid‘in Öğeleri’ni eleştirmiştir ve bunun için önemli gelişme sunacak fikirler önermiştir. Geometrik büyüklüklere aritmetik terminolojiyi uygulayıp özellikle parabol ve elips olmak üzere konik bölümlerin çeşitli yönleri üzerinde çalışmıştır. Farklı cisimlerin hacimleri ve yüzeylerini bulmak amacıyla birçok hesaplama yapmıştır ve aslında bu hesaplamalar, daha sonra geliştirilen integral hesabının da ilerlemesinde pay sahibidir.

Sâbit bin Kurra, Harran’ın yerlisi ve Sabiilik mezhebinin bir üyesiydi. Bu mezhep, Harran’da yıldızlara tapan Mandayelerle karıştırılır. Yıldızlara tapıyor olmak astronomi çalışmaları için güçlü bir motivasyon kaynağı anlamına gelmektedir ve bu mezhep çok iyi matematikçi ve astronom yetiştirmiştir. Güçlü Yunan bağlantıları sayesinde, Sabiiler Yunan kültürünü benimsemiştir. Bu yüzden de Sabiiler’in bölgesi Müslümanlar tarafından fethedilip mezhep üyeleri Arapça konuşmaya başlasa da aralarında Yunanca yaygın bir dildi. Türkiye’nin güneydoğusunda konuşulan ve Edessa’nın Doğu Aramice diyalektiği olan Süryanice de bölgede konuşulan diğer bir dildi. Bu dil, Sâbit bin Kurra’nın ana diliydi ve bununla birlikte Sâbit hem Yunanca’yı hem de Arapça’yı ana dili kadar iyi konuşabiliyordu.

Sâbit’in gençken -bugünün deyişiyle- dövizci olduğu söylenir. Bu mümkündür ama bazı tarihçiler bunu onaylamaz. Kesin olarak söylenebilir ki kendisi büyük bir aile servetini miras almıştır ve toplumda yüksek itibar sahibi bir aileden gelmiş olmalıdır. Harran’ı ziyaret gelen Musa bin Şakir, Sâbit’in diller konusundaki bilgisinden etkilenip bu genç adamın potansiyelini fark ederek onu Bağdat’a gidip kendisinden ve Beni Musa kardeşlerden matematik dersleri almaya ikna etmiştir. Sâbit, dönemin alimleri arasında yaygın olan tıp eğitiminin yanında matematik eğitimi de almıştır. Sonra, Harran’a geri dönmüştür fakat zıt görüşlerinden vazgeçmek zorunda kalınca onun liberal felsefesi farklı bir görünüme yol açmıştır. Daha fazla zulme maruz kalmamak için Harran’ı terk edip Bağdat’a saray astronomu olarak atanmıştır. Sâbit, en iyi Abbasi Halifelerinden olan Halife el Mu’tadid yönetimi altında çalışmalarını sürdürmüştür.

O dönemde, Yunanca-Arapça tercümeleri yapan yetenekli alimler birçok yönetici tarafından değerlendiriliyordu. Sâbit, matematikteki başarılarının yanında dildeki becerileri sayesinde birçok değerli Yunan çalışmasını tercüme etmiştir. Öklid’in Öğeleri’nin en eski iki tercümesi el-Haccâc tarafından yapılmıştır. Ancak, bazı parçalar dışında bunlar kaybolmuştur. Sâbit tarafından revize edilen ve Hunayn bin İshak tarafından Arapça’ya tercüme edilen üçüncü eserin çok sayıda el yazması versiyonu da vardır. Öklid’in Öğeleri’nin Arapça çevirilerinin öyküsünün bugünkü malumatı, daha sonraki tüm Arapça versiyonların Sâbit tarafından yapılan bu düzenlemeden filizlendiğini göstermektedir.

Aslında, Yunanca öğrenmenin Arap dünyasına katkısı sayesinde Yunan metinleri bugün hala ayaktadır. Ancak, Sâbit gibi matematikçilerin Yunan öğretisinin yegâne koruyucuları olduğu fikrine kapılmamalıyız. Bunun dışında Sâbit, önemli matematik keşifleriyle parlak bir alimdir.

Sâbit, birçok farklı alana katkı sağlamış olsa da en önemli katkısı matematik üzerine olmuştur [1]: –

… O, pozitif reel sayılar konusunun genişletilmesi, integral hesabı, küresel trigonometri, analitik geometri ve Öklid dışı geometri gibi teoremlerle önemli matematiksel keşiflerin yapılmasında çok önemli bir rol oynamıştır. Astronomi’de Sâbit, Batlamyus sisteminin ilk yenilikçilerindendir ve mekanikte statitiğin kurucusudur.

Sâbit’in bu alanlardaki çalışmalarını, özellikle de dostane sayılar hakkındaki sayı teorisini daha detaylı olarak inceleyelim. Modern gösterimde S (n)’nin, n’nin alikot kısımlarının toplamını, yani uygun bölümlerinin toplamını gösterdiğini varsayalım. Mükemmel sayılar, eğer S (n) = m ve S (m) = n olduğunda ve m ve n dostane sayılar iken S (n) = n olan n sayılardır. Dostane sayıların belirlenmesi hakkında yazılan kitapta Sâbit, Pisagor’un mükemmel ve dostane sayılar üzerine çalıştığını iddia eder. Pisagor’un MS 3. yüzyılda yazılan biyografisinde dostane sayılar 220 ve 284 olarak -kesinlikle yanlış olsa da- verilmiştir ve bu iddia muhtemelen ilk olarak Iamblikhos tarafından ortaya atılmıştır. Ama sonra Öklid ve Nicomachus mükemmel sayılar üzerinde çalışmış ve Öklid bunları belirlemek için bir kural koymuş olsa da([6],[7]) Sâbit, şöyle ifade eder:

… Bu yazarlardan hiçbiri dostane sayılardan bahsetmemiş ve ilgi duymamıştır.

Sonra şu şekilde devam eder ([6], [7]):

[Dostane sayılar] meselesi benim aklıma geldiğinden ve kanıtı çıkardığım için de kuralı mükemmel bir şekilde kanıtlamadan yazmak istemedim. Çünkü [Öklid ve Nicomachus] kuralı görmezden geldiği için gerekli lemaları tanıtttıktan sonra kanıtlamalıydım.

Dokuz lema verdikten sonra Sâbit, teoremini şu şekilde kanıtlar:

n > 1 için, pn = 3.2n-1 ve qn = 9.2 2n-1 -1 olarak verelim. Eğer pn-1, pn, ve qn asal sayı ise, a = 2npn-1pn ve b = 2nqn dostane sayılardır. Bol bir n sayısının S (n)> n’yi sağladığına ve eksik bir n sayısının S (n) < n’yi sağladığına dikkat edilmelidir. Yazarların Sâbit’in kuralı nasıl keşfettiği hakkındaki varsayımı [9] ‘da daha ayrıntılı olarak verilmiştir. Hogendijk, [13]’te Sâbit’in 17296 ve 18416 dostane sayılarını ilk keşfeden kişi olduğundan bahseder.

Sâbit’in çalışmasının diğer önemli tarafı ise oranların bileşimi üzerine yazdığı kitabıdır. Bu kitapta Sâbit, geometrik büyüklüklerin oranlarına uygulanan aritmetik işlemlerle ilgilenir. Yunanlar geometrik büyüklüklerle ilgilenmiştir fakat onları, aritmetiğin genel kurallarının uygulanabileceği sayılar olarak düşünmemişlerdi. [22] ve [23]’teki yazarlar geometrik ve sayısal olmayan nicelik olarak düşünülen aritmetik işlemleri tanıtarak Sâbit’in sayı konseptinin genelleştirilmesine yol açan bir eğilim başlattığını vurgulamaktadır.

Sâbit, Pisagor teoremini Pappus’un yaptığı gibi diğer sıradan üçgenler için de genelleştirmiştir. Ayrıca parabolleri, açı üçlemeyi ve sihirli kareleri de ele almıştır. Sâbit’in paraboller ve paraboloidler üzerine yaptığı çalışmanın ayrı bir önemi vardır. Çünkü bu, integral hesabının keşfi için atılan önemli adımlardan biridir. Burada düşünülmesi gereken önemli bir nokta ise Sâbit’in Arşimet’in metotlarına aşina olup olmamasıdır. Çoğu yazar inanıyor ki Arşimet’in parabolün karesel yapısı üzerine bulduğu sonuçlara Sâbit aşina olsa da; Arşimet’in konuyla ilgili iki incelemesine de sahip değildi. ([29]) Aslında Sâbit √𝑥’in integralini başarılı bir şekilde hesaplamıştır [1]: –

Hesaplama temel olarak üst ve alt integral toplamlarının uygulamasını esas almıştır ve kanıt da tüketme yöntemiyle şu şekilde bulunmuştur: orada, ilk defa entegrasyon segmenti eşit olmayan parçalara bölünmüştür.

Sâbit, Sekizinci Küre’nin Hareketi Üzerine’yi de astronomi için yazmıştır. O -yanlış bir şekilde- ekinoksların hareketinin salınımla olduğuna inanmıştır. Güneş için yaptığı gözlemleri de yayımlamıştır. Aslında Sâbit’in astronomi üzerine yazdığı tamamlanmış sekiz tezi günümüze ulaşmıştır ve makale [20]’de şöyle anlatılır:

9. yüzyıl Bağdat’ında bilimsel hareketin başlamasını düşündüğümüzde; Sâbit’in; astronominin yöntem, konu ve program olarak tam bir bilim olarak kuruluşunda çok önemli bir rol oynadığını görüyoruz. Bu bilim gözlem ve teori arasındaki ilişkinin teorileşmesi, astronominin “matematikleşmesi” ve matematiksel ve fiziksel astronominin çelişkili ilişkisi üzerindeki odaklanma olarak üç çizgide gelişme göstermiştir.

Sâbit’in kiriş dengesi için yazdığı kitabı Kitab fi’l Karastun mekanik üzerinedir. Gherard of Cremona tarafından Latince’ye çevrilen bu kitap mekanik çalışmalarında popülerleşmiştir. Bu çalışmada Sâbit, kaldıraçların denge ilkesini kanıtlamaktadır. Üçte birini dengeleyen iki eşit yükün, dengeyi bozmadan ikisi arasında bir noktaya yerleştirilen toplamları ile değiştirilebileceğini göstermektedir. Genelleme yaptıktan sonra Sâbit, eşit bir şekilde dağılan devamlı yüklerin durumunu ele alır ve kirişin dengesi için gerekli koşulları bulur. Elbette Arşimet yerçekimi merkezi için bir teori düşünmüştür fakat [14]’te yazar Sâbit’in çalışmalarının Arşimet’in teorilerine dayanmadığını ileri sürer.

Son olarak Sâbit, felsefe ve diğer alanlarda da çalışmalarını yürütmüştür. Sâbit’in Iraklı bir Hristiyan olan Ebu Musa İsa İbni Üseyyid adında bir öğrencisi vardı. İbni Üseyyid, hocası Sâbit’e çeşitli sorular sormuştur ve Sâbit’in verdiği cevapların bir el yazması vardır, bu el yazması [21] ‘de ele alınmıştır. Sâbit’in sayı kavramı Plato’nunkini izler ve Sâbit, birinin bunu bilmesinden bağımsız olarak sayıların var olduğunu ve sayılabilir şeylerden ayrı olduğunu savunur. Diğer yönlerden ise Sâbit, Plato ve Aristo’nun fikirlerini özellikle de hareketle ilgili olanları eleştirir. Görünüşe göre buradaki fikirleri, geometrik argümanlarındaki devinimle ilgili iddiaları kullanmanın kabulüne dayanıyor.

Son olarak Sâbit şunlar üzerine de yazmıştır [1]: –

… mantık, psikoloji, etik, bilimin sınıflandırılması, Süryani dillerinin dil bilgisi, siyaset, Plato’nun sembolizmi… din ve Sabiiliğin gelenekleri.

Hem oğlu Sinan bin Sâbit hem torunu İbrahim bin Sinan bin Sâbit matematiğin gelişimine katkı sunan seçkin alimlerdir. Ancak ikisi de Sâbit’in matematik seviyesine ulaşamamıştır.

çeviri kaynak: Biography – Muslim Scholars and Scientists (ed. W. Hazmy C.H., Zainurashid Z., Hussaini R.) s. 21-28

Kaynakça:

1. Biography in Dictionary of Scientific Biography (New York 1970-1990).

2. Biography in Encyclopaedia Britannica.

3. F J Carmody, The Astronomical Works of Thabit b. Qurra (Berkeley-Los Angeles, 1960).

4. F J Carmody, Thabit b. Qurra, Four Astronomical Tracts in Latin (Berkeley, Calif., 1941).

5. E A Moody and M Clagett (eds.), The medieval science of weights, Treatises ascribed to Euclid, Archimedes, Thabit ibn Qurra, Jordanus de Nemore, and Blasius of Parma (Madison, Wis., 1952).

6. R Rashed, The development of Arabic mathematics : between arithmetic and algebra (London, 1994).

7. R Rashed, Entre arithmétique et algèbre: Recherches sur l’histoire des math-ématiques arabes (Paris, 1984).

8. C B Boyer, Clairaut le Cadet and a theorem of Thabit ibn Qurra, Isis 55 (1964), 68-70.

9. S Brentjes and J P Hogendijk, Notes on Thabit ibn Qurra and his rule for amicable numbers, Historia Math. 16 (4) (1989), 373-378.

10. F J Carmody, Notes on the astronomical works of Thabit b. Qurra, Isis 46 (1955), 235-242.

11. Y Dold-Samplonius, The ‘Book of assumptions’, by Thabit ibn Qurra (836-901), in History of mathematics (San Diego, CA, 1996), 207-222.

12. H Hadifi, Thabit ibn Qurra’s ‘al-Mafrudat’ (Arabic), Deuxième Colloque Maghrebin sur l’Histoire des Mathématiques Arabes (Tunis, 1990), A163- A164, 197-198.

13. J P Hogendijk, Thabit ibn Qurra and the pair of amicable numbers 17296, 18416, Historia Math. 12 (3) (1985), 269-273.

14. K Jaouiche, Le livre du qarastun de Tabit ibn Qurra. étude sur l’origine de la notion de travail et du calcul du moment statique d’une barre homogène, Arch. History Exact Sci. 13 (1974), 325-347.

15. L M Karpova and B A Rosenfeld, The treatise of Thabit ibn Qurra on sections of a cylinder, and on its surface, Arch. Internat. Hist. Sci. 24 (94) (1974), 66-72.

16. L M Karpova and B A Rozenfel’d, A treatise of Thabit ibn Qurra on composite ratios (Russian), in History Methodology Natur. Sci. V (Moscow, 1966), 126-130.

17. G E Kurtik, The theory of accession and recession of Thabit ibn Qurra (Russian), Istor.-Astronom. Issled. 18 (1986), 111-150.

18. G E Kurtik and B A Rozenfel’d, Astronomical manuscripts of Thabit ibn Qurra in the library of the USSR Academy of Sciences (Russian), Voprosy Istor. Estestvoznan. i Tekhn. (4) (1983), 79-80. 27Muslim Scholars and Scientists

19. K P Moesgaard, Thabit ibn Qurra between Ptolemy and Copernicus : an analysis of Thabit’s solar theory, Arch. History Exact Sci. 12 (1974), 199-216.

20. R Morelon, Tabit b. Qurra and Arab astronomy in the 9th century, Arabic Sci. Philos. 4 (1) (1994), 6; 111-139.

21. S Pines, Thabit Qurra’s conception of number and theory of the mathematical infinite, in 1968 Actes du Onzième Congrès International d’Histoire des Sciences Sect. III : Histoire des Sciences Exactes (Astronomie, Mathématiques, Physique) (Wroclaw, 1963), 160-166.

22. B A Rozenfel’d and L M Karpova, Remarks on the treatise of Thabit ibn Qurra (Russian), in Phys. Math. Sci. in the East ‘Nauka’ (Moscow, 1966), 40-41.

23. B A Rozenfel’d and L M Karpova, A treatise of Thabit ibn Qurra on composite ratios (Russian), in Phys. Math. Sci. in the East ‘Nauka’ (Moscow, 1966), 5-8.

24. A I Sabra, Thabit ibn Qurra on the infinite and other puzzles : edition and translation of his discussions with Ibn Usayyid, Z. Gesch. Arab.-Islam. Wiss. 11 (1997), 1-33

25. A Sayili, Thabit ibn Qurra’s generalization of the Pythagorean theorem, Isis 51 (1960), 35-37.

26. J Sesiano, Un complément de Tabit ibn Qurra au ‘Per“ diairéseon’ d’Euclide, Z. Gesch. Arab.-Islam. Wiss. 4 (1987/88), 149-159.

27. K Taleb and R Bebouchi, Les infiniment grands de Thabit Ibn Qurra, in Histoire des mathématiques arabes (Algiers, 1988), 125-131.

28. A P Yushkevich, Note sur les déterminations infinitésimales chez Thabit ibn Qurra, Arch. Internat. Histoire Sci. 17 (66) (1964), 37-45.

29. A P Yushkevich, Quadrature of the parabola of ibn Qurra (Russian), in History Methodology Natur. Sci. V (Moscow, 1966), 118-125.

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    be upgraded routinely to make certain that all URLs are listed.
    You can also utilize a totally free XML sitemap generator to generate a sitemap.

    The XML Sitemap Index need to be a file listing all of the Links on your website.
    The XML Sitemap Index should comply with the very same XML requirement as the equivalent websites.
    The XML Sitemap index should be labelled with a/ sitemapindex > extension.

    To add an XML Sitemap to your website, go to the Google Search Console and also add an URL to your sitemap.
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    Utilizing the XML Sitemap Index, you need to have more than one sitemap.
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  202. Producing an XML Sitemap Index is a terrific way to draw
    in search engine traffic as well as improve your ranking.
    For finest outcomes, the XML sitemap should be structured as a tree.

    For more info, see a sample XML Sitemap.

    XML Sitemap Index files have certain formatting policies.
    Using this technique, the XML Sitemap Index will be noticeable on search engines.

    XML Sitemaps are complimentary as well as simple to develop.
    All that is required is a message file, which have to
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    be in UTF-8 encoding. It must be a single page and also has to remain in the root directory site of your site.
    It is likewise crucial to keep in mind that all URLs in an XML Sitemap need to be from the exact same host.

    You can easily create XML Sitemap Index files. To include an XML
    Sitemap to your website, go to the Google Look Console and
    include an URL to your sitemap.

    A sitemap should include a list of Links. The URLs need to remain in the proper order.
    There have to be no replicate URLs in an XML Sitemap.
    It should be in UTF-8 encoding. If you have greater than fifty
    thousand Links, damage them up into smaller sized XML
    maps. The XML Sitemap Index ought to have the URLs of all
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    Using the XML Sitemap Index, you ought to have even more than one sitemap.
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    The XML Sitemap Index ought to be a data noting all of the Links
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    The XML Sitemap index ought to be tagged with a/ sitemapindex >
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    To include an XML Sitemap to your site, go to the Google Search Console and also add an URL to your
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    mapped URLs. Using the XML Sitemap Index, you ought to have more than one sitemap.
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  205. Developing an XML Sitemap Index is a great way to draw in search engine website traffic and improve your position. For best outcomes, the XML sitemap ought to be structured as a tree.
    For more details, see an example XML Sitemap.

    XML Sitemap Index documents have details formatting rules.
    Using this method, the XML Sitemap Index will certainly be
    visible on search engines.

    XML Sitemaps are totally free and very easy to create.
    It is additionally essential to remember that all Links in an XML Sitemap need to be from the same host.

    You can quickly produce XML Sitemap Index files.

    To include an XML Sitemap to your website, most likely to the Google
    Browse Console and also add a link to your sitemap.
    Then, examine the number of URLs indexed by Google.

    If there is a large void between sent and also indexed numbers, your sitemap might have an error.
    You may require to include more links to your sitemap
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    A sitemap must consist of a list of Links. There should be no duplicate URLs in an XML Sitemap.

    The XML Sitemap Index should consist of the Links of all mapped Links.

    XML Sitemap Index files are files that list all the URLs
    on your web site. The URLs need to be a minimum of 50k as well as must be in UTF-8 encoding.
    Making Use Of the XML Sitemap Index, you should
    have more than one sitemap. The XML Sitemap Index need to be updated consistently to ensure that all URLs
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    The XML Sitemap Index ought to be a documents listing all of the URLs on your website.
    The XML Sitemap Index need to comply with the same XML requirement as the matching websites.
    The XML Sitemap index need to be identified with a/ sitemapindex > extension.

    To add an XML Sitemap to your site, go to the Google Browse Console as well as add a
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    XML Sitemap Index, you need to have even more
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    Informacje o cookies

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    Zamówienia Publiczne

    Informacje o cookies

    Deklaracja dostępności

    Inspektor Ochrony Danych

    SARS-CoV-2
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