«FI-L-BAROHIN ILO MASOIL…»

«FI-L-BAROHIN ILO MASOIL…» nomi purraash «Risola fi-l-barohin ilo masoil il-jabr va-l-muqobala», asarest, ki Umari Khayyom soli 1074 talif kardaast. «Fi-l-barohin ilo masoil» risolaest dar bobi matematika, algebra va amalhoi on. Onro ba chunin faslho judo metavon kard: 1) muqaddima; 2) halli muodilahoi darajai yakum va duyum; 3) halli muodilahoi darajai seyum; 4) ba muodilahoi tartibashon poyon tabdil dodani muodilahoe, ki buzurgihoi baraksi nomalum dorand; 5) ilova. Dar muqaddima Khayyom bori nakhustin fanni algebra va tariqati onro hamchun ilm oid ba muodilaho harjoniba manidod namudaast.
Manoi asosii «jabr» va «muqobala» du amali odditarin buda, yake azoi manfii muodilaro az yak tarafi barobari ba tarafi digari on bo alomati aks guzaronidan va digare az har du tarafi barobari azoi yakkhelaro khorij namudan ast. Dar on Khayyom ba Muhammadi Khorazmi payravi namuda, tasnifoti muodilaho va halli muodilahoi na tanho darajai yakumu duyum, balki darajai seyumro niz ovardaast. U bori avval dar tarikhi matematika sobit namudaast, ki muodilahoi darajai seyum ba vositai pargor (sirkul) va khatkashak halnopazirand. Mahz dar hamin asar Khayyom dar khususi risolai digari matematikii khud «Mushkilot-ul-hisob» sukhan ronda, tariqai az tahti reshahoi darajahoi dilkhoh barovardani adadhoro nishon medihad va binomi adadhoi butunro kashf menamoyad. Nuskhahoi khattii asar holo dar kitobkhonahoi Parij (№ 2461; 2458(7), Leyden (L8 14/2), London (№ 7; 34/10) va Votikon (№ 96,/2) mahfuz ast.
Adabiyot: Omar Hayyam, Traktati, Moskva, 1961. X. Abdullozoda.