{"book":"adl0258","page":196,"text":"۱۹۱\n\nمثال ۶ ولاّ+ (اّ+۱) لا+ ۱ را مضروبات تفریق کنید\n\n{ولاّ+ (اّ+۱)لا+۱= ولاّ+ اّ+۱/و لا+۱\n\n= {ولاّ+ اّ+۱/و لا+ (اّ+۱/۲و)٢} - (۱- ۱+اّ٢+اّ٢/۴و٢)}\n\n={ولاّ+ اّ+۱/۲و}٢- ۱+اّ٢-اّ٢/۴و٢}\n\n= {ولاّ+ اّ+۱/۲و+ ۱-اّ/۲و}{ولاّ+ اّ+۱/۲و - ۱-اّ/۲و}\n\n= {ولا+۱}{ولا+اّ/و}\n\n= (لا+۱)(ولا+اّ)\n\nو بطرق فوق نیز ثابت شده میتواند که\n\nولاّ- (اّ+۱)لا+اّ= (ولا-۱)(لا-اّ)\n\nو ولاّ+(اّ-۱)لا-اّ= (ولا+۱)(لا-اّ)\n\nو ولاّ-(اّ-۱)لا-اّ= (ولا-۱)(لا+اّ)\n\nمثال ۷ ۴(لا٢+٣لا+۵)٢+۱۷(لا٢+٣لا+۵)(لا٢+۶لا)+۴(لا٢+۶لا)٢ را\n\nبمضروبات تفریق کنید\n\nفرض کنید که ا=لا٢+٣لا+۵ وب=لا٢+۶لا\n\nپس جمله مفروضه= ۴ا٢+۱۷اب+۴ب٢\n\nوچون ۴ا٢+۱۷اب+۴ب٢= (ا+۴ب)(۴ا+ب) از قرار قاعده فوق\n\nلهذا جمله مفروضه= {(لا٢+٣لا+۵)+۴(لا٢+۶لا)}{۴(لا٢+٣لا+۵)+(لا٢+۶لا)}\n\n= (۵لا٢+٣۶لا+۵)(۵لا٢+۱۲لا+۲۰)\n\n= (۵لا+۱)(لا+۵)۵(لا٢+۱۲لا+۲۰)","chars":743,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00196.jpg","first_page":1,"last_page":309,"title":"Kitāb-i jabr va muqābalah ‏كتاب جبر و مقابله Silsilah-ʼi Mūʼallifāt-i Madrasah-i Mubārakah-i Ḥabībīyah-ʼi Dār al-Salṭanah-ʼi Kābul","permalink":"https://afghanpress.org/book/adl0258/196","canvas":"https://afghanpress.org/iiif/adl0258/canvas/196","source":"https://afghanistandl.nyu.edu/books/adl0258/","source_pdf":"https://afghanistandl.nyu.edu/pdf/adl0258_download.pdf","rights":{"image":{"statement":"Public domain. NYU states: \"All works presented on this website are, unless otherwise indicated, in the public domain. The images available on this website may be freely reproduced, distributed and transmitted by anyone for any purpose, commercial or non-commercial.\"","uri":"http://rightsstatements.org/vocab/NoC-US/1.0/","holder":"New York University Libraries","source":"https://afghanistandl.nyu.edu/about.html","delivery":"Images are served from a copy mirrored by this project, not from NYU's servers, under the reproduction terms above.","endorsement":"This is an independent project. It is not affiliated with, endorsed by, or reviewed by New York University."},"text":{"statement":"Machine-generated transcription, dedicated to the public domain under CC0 1.0. No warranty of accuracy: see the provenance block on every page.","uri":"https://creativecommons.org/publicdomain/zero/1.0/","holder":"Steps Ventures"}},"provenance":{"text_produced_by":"gemini-3.1-pro-preview","thinking_level":"low","read_completed":"2026-08-09","per_page_confidence":null,"per_page_confidence_note":"Not recorded during the corpus run. No calibrated per-page score exists, and none is estimated here.","human_reviewed":false,"accuracy_context":"Roughly two thirds of characters agree with a modern printed edition of the same text. Much of the disagreement is editorial, not misreading. Treat the transcription as a finding aid and read the page image before quoting.","primary_source":"The page image. The text is an index into it."}}