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HUCENDÎ, Hâmid b. Hıdır Skip to content Ebû Mahmûd Hâmid b. el-Hıdr el-Hucendî (ö. 390/1000 [?])
Matematik ve astronomi bilgini.
Hayatı hakkında çok az bilgi bulunmaktadır. Nisbesinden anlaşıldığına göre Hucend’de yetişmiş ve muhtemelen orada doğmuştur. Nasîrüddîn-i Tûsî’nin “han” unvanı taşıdığını belirtmesine bakılırsa (Kitâbü Şekli’l-ḳaṭṭâʿ , s. 108) Hucend hanlarından biri veya onlardan birinin aile mensubu olması gerekir. Hayatının sonlarına doğru Büveyhî hükümdarlarından Fahrüddevle’nin (984-997) himayesine girmiş ve Rey’de özellikle Fahrüddevle’nin hükümdarlık yıllarında ün kazanmıştır. Nitekim Bîrûnî onun bilimdeki dirayeti, matematik ve astronomiye katkılarda bulunması ve yeni rasat aletleri icat etmesi sebebiyle zamanının tek bilgini olduğunu söylemektedir (Taḥdîdü nihâyâti’l-emâkin , s. 107). Hucendî 390 (1000) yılı civarında, muhtemelen Rey şehrinde vefat etmiştir.
Hucendî, çok yönlü kişiliğiyle çeşitli alanlarda eser kaleme almışsa da en çok matematikçi ve astronom olarak tanınmıştır. Mevcut eserlerinin konularına bakıldığında onun astronomik gözlem aletleri yapımına dair verdiği teorik ve pratik bilgilerin yanında cebir, trigonometri ve sayı sistemleriyle de yakından ilgilendiği ve bu alanlara önemli yenilikler getirdiği görülür.
Nasîrüddîn-i Tûsî, matematik tarihinde İskenderiyeli Menelaus’un (ö. I. yüzyıl sonları) adıyla bilinen teoremin yerini alan küresel (sferik) üçgenlerle ilgili sinüs teoreminin, astronomi bilimi için öneminden ve çok kullanılmasından dolayı Hucendî tarafından “Kānûnü’l-hey’e” şeklinde adlandırıldığını söylemektedir (Kitâbü Şekli’l-ḳaṭṭâʿ , s. 108-110). Aynı eserinde Tûsî, bu teoremin ilk defa ortaya konulmasının Hucendî ile birlikte çağdaşları Ebü’l-Vefâ el-Bûzcânî ve Bîrûnî’nin hocası Ebû Nasr İbn Irâk’a atfedildiğini de belirtmektedir. Tûsî’nin bu sözleri tartışmalara yol açmıştır. C. Schoy, sinüs teoremini ortaya atan ve ilk defa ispatlayanın Hucendî olduğunu söylerken (ISIS , VIII [1926], s. 260-263) P. Luckey, Hucendî’nin nazarî meselelerden çok astronominin amelî konularıyla ilgilendiğini öne sürerek bu alanda onun katkısının bulunduğu görüşüne itiraz etmektedir (Deutsche Mathematik , V [1940-1941], s. 413, 416, 418-419). Ancak Luckey’e katılmak mümkün değildir; zira Hucendî’nin matematik bilgisi gerektiren usturlap yapımının nazariyatı ile uğraştığı bilinen bir husustur. Diğer taraftan İbn Irâk’ın sinüs teriminin tanıtımını konu alan bir mektubunda (Arapça metin ve Almanca çevirisi için bk. Suter, X [1910], s. 156-190) hocasından hiç söz etmemesine bakılırsa Tûsî’nin İbn Irâk hakkında söylediğinin doğru olmadığı ve dolayısıyla meselenin sadece Ebü’l-Vefâ el-Bûzcânî veya Hucendî’den birine atfedilmesi gerektiği anlaşılır; bugünkü genel kabul Bûzcânî yönündedir.
Hucendî’nin sinüs teoremiyle ilgili çözümü şöyledir: AC ve AB kenarları çeyrek dairelere tamamlanmış olan küresel bir ABC üçgeni verilsin. RA, RD, RE ve RB birleştirilir ve bunlar birbirini kesen küresel dairelerin yarı çaplarını teşkil eder.
m$RAperp DE$ çemberinin düzlemi; aynı zamanda m$RAperp RE$ ve RD yarı çapları.
DE çemberi düzleminde CF dikeyini yap. FN ve CS dikeyleri de ABE düzleminde yapılmış olsun. CFNS bir dikdörtgendir ve DE \ FN’dir.
m$overset{triangle}{DER}sim overset{triangle}{FNR}$
CT dikeyi AR çemberi düzleminde yapılmıştır ve RS’ye paraleldir.
m$widehat{R}=widehat{T}=90^{o}$ m$CFperp RH$
m$widehat{CFR}=90^{o}$ O halde CFRT,
m$frac{RF=CT=sin AC}{FN=CS=sin C B}=frac{RH=sin 90^{o}}{FE=sin A}$ olan bir dikdörtgen teşkil eder.
Hucendî’nin ayrıca cebir sahasına da katkısı vardır. Bu da geometrik yolla ilk defa x3 + y3 = z3 şeklindeki diofanten eşitlik diye bilinen belirsiz denklemin çözülmesi, yani iki küp sayılar toplamının bir başka küp sayı olamayacağının ispatlanmasıdır. Bu çalışmasıyla Hucendî, Fransız matematikçisi Pierre de Fermat’ya (ö. 1665) atfen “Fermat teoremi” denilen teoremin özel hali x, y, z’nin tam değerleri için çözüm imkânsızlığını ilk defa ispat etmiştir. Dolayısıyla söz konusu teoremin tam (doğal) sayılarla çözülemeyeceğini Fermat’dan yaklaşık 650 yıl önce göstermiştir. Bazı matematik eserlerinin toplandığı bir mecmuada bulunan (Paris, Bibliotèque Nationale, Fonds Arabes, nr. 2457), biri anonim, diğeri rasyonel kenarlı dik açılı üçgen teorisi konusunda ve Ebû Ca‘fer el-Hâzin’e ait olan iki risâlenin muhtevasından Hucendî’nin ilk defa böyle bir teoremi çözümlediği anlaşılmaktadır. Hâzin, Hucendî’nin muhtemelen bu konuda yazdığı bir risâleyi kendi çalışmasında nakletmekte, fakat bu arada ispat şeklinin hatalı ve yanlış olduğunu söyleyerek onu eleştirmektedir. Risâleleri Fransızca’ya çeviren Fr. Woepcke (bk. bibl.) yanılgıya düşmüş ve Hâzin’in Ebû Muhammed Abdullah b. Ali el-Hâsib adlı bir kişiye ithafen yazdığı risâlenin yazarı olarak Ebû Muhammed Ca‘fer b. Hüseyin adlı bir matematikçiyi göstermiştir. Woepcke, ayrıca Hâzin’e ait başka birtakım eserleri de bu hayalî matematikçiye izâfe etmiş ve bu yanlış kanaat son zamanlara kadar sürüp gelmiştir. Halbuki Woepcke’nin sözünü ettiği Ebû Ca‘fer, Ebû Ca‘fer Muhammed b. Muhammed b. Hüseyin el-Hâzin’den başkası olmayıp anılan risâle de Âdil Enbûbâ tarafından neşredilmiştir (aş.bk.).
Ebû Ca‘fer’e atfedilen bir risâlede (Bodleian Library, Thurston, nr. 3), söz konusu diofanten belirsiz denklemle ilk uğraşan ve çözümleyen kişinin Ebû Ca‘fer olduğu söylenmektedir. Bu risâle muhteva bakımından, Woepcke’nin Fransızca’ya çevirdiği Hâzin’in Risâletü Ebî Caʿfer el-Ḫâzin fi’l-müs̱elles̱âti’l-ḳāʾimeti’z-zevâya ve’l-münteḳati’l-eḍlâʿ adlı (nşr. Âdil Enbûbâ, MTUA , III/1 [1979], s. 134-178) risâlesiyle tamamen aynıdır; ancak onun Hucendî’nin ispatından söz ettiği cümleler metinde yer almamaktadır. Bu durumda söz konusu risâleye, Hâzin’in eserinin bir başkası tarafından yapılmış eksik bir kopyası şeklinde bakmak gerekmektedir. Dolayısıyla buradan hareketle söz konusu denklemle ilk uğraşan ve ilk çözümleyen kişinin Hâzin olduğu sonucu çıkarılamaz. Esasen Hâzin kendi eserinde, bu meseleyle ilk uğraşanın ve çözümünü yapanın Hucendî olduğunu belirtmekte, ancak onun ispat şeklini hatalı bulmaktadır. Fakat Hâzin’in Hucendî’nin ispatı hakkındaki bu yargısı yerinde değildir. Öte yandan Hâzin’in değerlendirmesine dayanan bazı matematik tarihçileri Hucendî’nin ispatının mükemmel olmadığını söylemektedirler (Cantor, I, 752-753; Dilgan, s. 36). Bu meseleler, Fermat ve Euker’e gelinceye kadar Hucendî ve Hâzin’den sonra da İbn Sînâ, İbnü’l-Hevvâm ve Kemâleddin el-Fârisî gibi birçok matematikçiyi uğraştırmıştır.
Hucendî’nin bilime katkısı matematikle sınırlı değildir; astronomi alanında da bazı yeni rasat aletleri icat etmiştir. Bunların en önemlisi, güneşin meridyen yüksekliğiyle ekliptik eğimini tayin için geliştirdiği ve Fahrüddevle’ye ithafen “es-südsü’l-Fahrî” adını verdiği bir tür sekstanttır (Sâlih Zeki, I, 165). Hucendî, bir bina boyutlarında tasarladığı bu yeni sekstantını 384 (994) yılında Rey yakınındaki Cebel Tebrûk adlı bir tepeye kurmuştur. İslâm astronomi tarihinde meşhur olan bu aletten Bîrûnî (Taḥdîdü nihâyâti’l-emâkin , s. 101-108), Gıyâseddin Cemşîd el-Kâşî (Risâle der Şerḥ-i Âlât-ı Raṣad , s. 2) ve Hasan b. Ali el-Merrâküşî (Câmiʿu’l-mebâdîʾ ve’l-ġāyât fî ʿilmi’l-mîḳāt , I, 201 vd.) gibi âlimler övgüyle bahsetmektedirler. Bîrûnî, bu konuda verdiği bilgileri Hucendî’nin Maḳāle fî taṣḥîḥi’l-meyl adlı bir eserinden aktardığını söylemektedir ki bu onun Risâle fî taṣḥîḥi’l-meyl ve ʿarżi’l-beled baʿde ḥuṣûli irtifâʿâti nıṣfi’n-nehâri’l-muḥaḳḳaḳa ʿinde’l-inḳılâbeyn adlı çalışmasından başkası değildir. Hucendî söz konusu risâlede bu aleti kendisinin icat ettiğini ve daha öncekilerden farklı yönünün saniyeleri de göstermesi olduğunu söylemektedir (s. 62, 67). Alet, toprağın üstünde 10 m. yüksekliğe varan meridyene paralel iki duvardan oluşmaktadır. İki duvarın arasındaki açıklığı kapatan üst örtüsünün güney yönündeki duvara yakın kısmında çapı 3 şibr (7,62 cm.; Bîrûnî’ye göre 1 şibr; bk. Taḥdîdü nihâyâti’l-emâkin , s. 93) olan ortası delik küçük bir kubbecik vardır. Tam deliğin altında tabana 10 m. derinliğinde bir çukur açılmıştır. Toprak üstündeki duvar yüksekliğiyle birlikte toplam 20 metreye varan yükseklik, aynı zamanda merkezini kubbe deliğinin teşkil ettiği bir dairenin de yarı çapına eşittir. Anılan dairenin 1/6’sına (süds) tekabül eden, ahşaptan mâmul ve üzeri bakır levhalarla kaplı 60°’lik bir yay bu çukura yerleştirilmiş, yayın her derecesi 60 dakikaya ve her dakika da 10 saniyeye bölünmüştür.
Delikten giren güneş ışınları tabana doğru tepesi yukarıda, tabanı yay üzerinde olan bir koni teşkil etmektedir. Koninin merkezini ölçmek için de yay üzerinde kaydırılabilen bir alete ihtiyaç vardır. Bu alet dik açıda birbirini kesen iki çemberden oluşur. Güneşin hareketiyle koni şeklindeki ışınlar kaydıkça bu aletin gölgesi de merkezi meridyen üzerine gelinceye kadar kaydırılır. Şakul sicimiyle güneşin yüksekliği arasındaki yay güneş yüksekliğinin kosinüsüne eşit olur; böylece güneşin meridyen yüksekliğiyle ekliptik eğimi hesaplanır (DSB , VII, 353). Hucendî bu aletle, 16 ve 17 Haziran 994 günlerinde (yaz dönencesi) güneşin meridyen yüksekliğini 77° 57′ 40″, 14 ve 15 Aralık 994 günlerinde ise (kış dönencesi) 30° 53′ 35″ ve 30° 53′ 32″ olarak bulmuş ve kış ölçümlerindeki 3 saniyelik fark sebebiyle ortak ölçümü 30° 57′ 2,30″ şeklinde belirlemiştir. Güneşin maksimum ve minimum yüksekliği arasındaki ½ derecelik farkın ekliptik eğimine eşit olacağı fikrinden hareketle de bunun hesabını ½ (77° 57′ 40″ – 30° 53′ 2″) = 23° 32′ 19″ (Bîrûnî’ye göre 21″; bk. el-Ḳānûnü’l-Mesʿûdî , I, 364) olarak yapmıştır. Hucendî bu değerin, Hintliler’in 24° ve Batlamyus’un 23° 51′ 20″ hesapladığı değerden farklı olduğunu biliyordu ve ekliptik eğiminin bugün de tesbit edildiği gibi azalan bir değişken değer olduğunun farkındaydı. Bîrûnî ise bu değerin sabitliğine inandığı için Hucendî’nin bulduğu sonucun o zamanki hesaplamalardan 1′ 35″ eksik olduğunu söylemekte, bunun sebebini de bizzat Hucendî ile yaptığı bir görüşmeden aktararak sekstantın üst kısmında meydana gelen bir kaymanın yayın merkezini hafifçe yerinden oynatmasına bağlamaktadır. Esasen farklı zamanlardaki ölçümlerde bu gibi farklılıklar tabiidir. Bîrûnî’ye göre Hucendî Rey’in enlemini de 35° 34′ 39″ olarak tayin etmiştir (Taḥdîdü nihâyâti’l-emâkin , s. 86-87, 99, 238; ayrıca bk. el-Ḳānûnü’l-Mesʿûdî , II, 612). Bîrûnî, Hucendî’nin sekstantına benzer bir aletin 998 yılında faaliyete geçen Şerefüddevle Rasathânesi’nde Ebû Sehl el-Kûhî tarafından kurulduğunu haber vermektedir (Taḥdîdü nihâyâti’l-emâkin , s. 92). Onun bu icadının, daha sonraki asırlarda Merâga Rasathânesi (1261) ve Semerkant Rasathânesi (1420) gibi müesseselerde daha büyük çaptaki aletlerin yapılmasına öncülük ettiği de bilinmektedir.
Hucendî bir de “el-âletü’l-âmme” (el-âletü’ş-şâmile) adını verdiği, kadran ve usturlap yerine kullanılabilecek çok fonksiyonlu bir rasat aleti icat etmiştir. el-Âletü’l-âmme önceleri tek bir genişlik için kullanılıyordu; daha sonra onu Bedî‘ el-Usturlâbî bütün genişlikler için kullanılır hale getirmiştir (İbnü’l-Kıftî, s. 222). Hucendî ayrıca usturlap imaliyle ilgili teorik çalışmalar da yapmış ve bu aletin üzerinde azimut dairelerinin durumunu tayin etmeye yarayan yöntemler geliştirmiştir.
Eserleri. 1. Geometri Risâlesi . Asıl adı bilinmeyen eser, sinüs teoremiyle ilgili çalışmalarının yer aldığı matematiğe dair günümüze ulaşmış yegâne eseri olup Kahire’de bulunan (Dârü’l-kütübi’l-Mısriyye, Riyâza, nr. 40) Mesâʾil müteferriḳa hendesiyye li-baʿżi’l-ʿulemâʾ adlı bir mecmuanın içinde tesbit edilmiştir.
2. Risâle fî taṣḥîḥi’l-meyl ve ʿarżi’l-beled baʿde ḥuṣûli irtifâʿâti nıṣfi’n-nehâri’l-muḥaḳḳaḳa ʿinde’l-inḳılâbeyn . Hucendî’nin kendi icadı sekstantı tanıttığı astronomiyle ilgili en önemli eseri olup Luvîs Şeyho tarafından neşredilmiştir (bk. bibl.).
3. Kitâbü’l-Âleti’l-ʿâmme (Kitâbü’l-Âleti’ş-şâmile) . Yine kendi icat ettiği çok fonksiyonlu rasat aletini tanıttığı çalışmasıdır ve çeşitli kütüphanelerde birçok yazma nüshası bulunmaktadır (meselâ bk. Bursa Eski Yazma ve Basma Eserler Ktp., Haraççıoğlu, nr. 1217; Oxford, Bodleian Library, Hunt., nr. 566; Dârü’l-kütübi’l-Mısriyye, Mîkāt, nr. 970).
4. İstiḫrâcü mecâzi devâʾiri’s-sümût bi’ṣ-ṣınâʿa . Usturlapla ilgili teorik bir risâle olup hakkındaki bilgiler Bîrûnî’nin hocası Ebû Nasr İbn Irâk’ın Risâle fî mecâzâti devâʾiri’s-sümût fi’l-usṭurlâb adlı eserinden elde edilmektedir (s. 3-9).
5. Kitâbü Semti’l-ḳıble . Varlığı yine Ebû Nasr İbn Irâk ile (a.g.e. , s. 3-9) Bîrûnî’den (Tasṭîḥu’ṣ-ṣuver , vr. 11) öğrenilmektedir.
6. Kitâb fî sâʿâti’l-mâżiye mine’l-leyl . Câmiʿu ḳavânîni ʿilmi’l-heyʾe adlı bir eser içinde (TSMK, III. Ahmed, nr. 3342) Hucendî’ye nisbet edilmektedir.
7. Risâlâtü ṣafîḥati’l-âfâḳıyye . Kâtib Çelebi’ye göre altmış babdan oluşmaktadır (Keşfü’ẓ-ẓunûn , I, 875).
8. ez-Zîcü’l-Faḫrî . Hucendî’nin Fahrüddevle adına yaptığı astronomi gözlemlerinden (Bîrûnî, Taḥdîdü nihâyâti’l-emâkin , s. 238) yararlanarak hazırlayıp yine ona ithaf ettiği bu zîc de günümüze ulaşmamıştır. Tahran Meclis Kütüphanesi’nde bulunan Farsça düzenlenmiş bir zîc parçasının (nr. 181) Hucendî’nin gözlemlerine dayanmış olması muhtemeldir.
9. Leṭâfetnâme . Hucendî’ye nisbet edilen edebî bir eserdir (Bodroligeti, IJMES , XII [1980], s. 101-109).
BİBLİYOGRAFYA
Bîrûnî, Taḥdîdü nihâyâti’l-emâkin (nşr. Muhammed b. Tâvît et-Tancî), Kahire 1962, s. 86-87, 92-93, 99, 101-108, 238.
a.mlf., el-Ḳānûnü’l-Mesʿûdî , Haydarâbâd 1954, I, 364; II, 612.
a.mlf., Tasṭîḥu’ṣ-ṣuver ve tebṭîḥu’l-küver , Kitâbhâne-i Merkezî-i Dânişgâh-i Tahrân, nr. 5469, vr. 11.
Ebû Nasr İbn Irâk, Devâʾirü’s-sümût fi’l-usṭurlâb (Resâʾilü’l-Bîrûnî içinde), Haydarâbâd 1948, s. 3-9.
İbnü’l-Kıftî, İḫbârü’l-ʿulemâʾ , s. 222.
Hasan b. Ali el-Merrâküşî, Câmiʿu’l-mebâdîʾ ve’l-ġāyât fî ʿilmi’l-mîḳāt (nşr. J.-J. Sédillot), Paris 1834, I, 201 vd.
Nasîrüddîn-i Tûsî, Kitâbü Şekli’l-ḳaṭṭâʿ: Traite du quadrilatere (nşr. ve trc. Alexandre Pacha Caratheodory), İstanbul 1309/1891, s. 108-110.
Gıyâseddin el-Kâşî, Risâle der Şerḥ-i Âlât-ı Raṣad (nşr. W. Barthold, Ulugbek i ego vremya içinde), Petrograd 1918, s. 2.
Keşfü’ẓ-ẓunûn , I, 875.
M. Cantor, Vorlesungen über Geschichte der Mathematik , Leipzig 1880, I, 752-753.
Sâlih Zeki, Âsâr-ı Bâkıye , İstanbul 1911, I, 165.
Hamit Dilgan, Büyük Matematikci Ömer Hayyâm , İstanbul 1959, s. 36.
Aydın Sayılı, The Observatory in Islam , Ankara 1960, s. 118-121, 198-199, 277, 283-286.
Sarton, Introduction , I, 667-668.
Sezgin, GAS , V, 305-308; VI, 220-222.
S. Tekeli, “Al-K̲h̲ujandī”, DSB , VII, 352-354.
Ebü’l-Kāsım Kurbânî, Zindegînâme-i Riyâżîdânân-ı Devre-i İslâmî , Tahran 1365, s. 63-65, 231-236.
Fr. Woepcke, “Recherches sur plusieurs ouvrages de Léonard de Pise”, Atti dell’ Accademia Pontificia de’ Nuovi Lincei , XIV, Roma 1861, s. 301-324, 345-356.
L. Cheikho, “Traité arabe de Khodjandi sur le sextant appelé Fakhri suivi de l’épître de Bîrouni sur le sujet”, el-Meşriḳ , XI, Beyrut 1908, s. 60-69.
H. Suter, “Zur Trigonometrie der Araber”, Bibliotheca Mathematica , X, Leipzig 1910, s. 156-190.
C. Schoy, “Behandlung einiger geometrischen Fragepunkte durch muslimische mathematiker”, ISIS , VIII (1926), s. 260-263.
P. Luckey, “Zur Entstehung der Kugeldreiecksrechnung”, Deutsche Mathematik , V, Leipzig 1940-41, s. 413, 416, 418-419.
E. Wiedemann, “Über den Sextant des al-Chogendī”, Archiv für Geschichte der Naturwissenschaften , II, Leipzig 1969, s. 148-151.
A. J. E. Bodroligeti, “Fazylov’s Edition of Khujandi’s Latafat-nama: A Review Article”, IJMES , XII (1980), s. 101-109.
a.mlf., “Hucendî”, İA , V/1, s. 575.
J. Samsó, “Al-K̲h̲ud̲j̲andī”, EI2 (İng.) , V, 46-47.
Bu madde TDV İslâm Ansiklopedisi’nin 1998 yılında İstanbul’da basılan 18. cildinde, 273-275 numaralı sayfalarda yer almıştır.