{"book":"adl0258","page":204,"text":"۱۹۹\nمثال ۳ لا۳+۷ لا۲+۱۴لا+۸ را لمضروبات تفریق کنید\nاگر در مثال فوق بنظر دقت ملاحظه کنیم واضح میگردد که جمله مفروضه با نچنین\nدو حصه تقسیم کرده میتوانیم که هر یک از انها بر لا+۲ بدون باقی تقسیم میشود\n(۱) (لا۲+۸)+۷ لا(لا+۳) (۲) لا(لا+۳)+۵ لا(لا+۳)+۴(لا+۴)\nپس بقرار طریق دوم لا۳+۷ لا۲+۱۴لا+۸=(لا+۳)(لا۲+۵لا+۴)\n=(لا+۳)(لا+۱)(لا+۴)\nتنبیه ـ باید دانست که اگر لا= -۱ یا -۲ یا -۴ باشد\nقیمت جمله مفروضه در هر حالت صفر خواهد بود\nمثال ۳ لا۳+۶ لا۲+۱۱لا+۶ را بمضروبات تفریق کنید\nبعد از تحقیق معلوم میشود که جمله مفروضه باینچنین دو حصه منقسم شده میتواند\nکه هر حصه برلا+۳ بدو طریق ذیل بدون باقی تقسیم میشود : ـ\n(۱) لا(لا+۳)+۳لا(لا+۳)+۲(لا+۳) و (۲) لا(لا۲+۶لا+۹)+۲(لا+۳)\nپس بموجب طریق دوم لا۳+۶ لا۲+۱۱لا+۶=لا(لا+۳)۲+۲(لا+۳)\n=(لا+۳){لا(لا+۳)+۲}\n=(لا+۳)(لا۲+۳لا+۲)\n=(لا+۳)(لا+۱)(لا+۲)\nتنبیه درین مثال نیز ظاهر است که اگر لا= -۳ یا -۱ یا -۲ باشم\nدر هر حالت قیمت جمله مفروضه صفر خواهد بود\nمثال ۴ لا۳-۳ لا۲-۵لا+۶ را بمضروبات تفریق کنید","chars":913,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00204.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/adl0258/204","canvas":"https://afghanpress.org/iiif/adl0258/canvas/204","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."}}