{"book":"adl0258","page":143,"text":"۱۳۸\nکه امثال چهار حد اول میباشند بنابراین حد و باقیمانده این حاصل بسط\n۳۵ ا۳ ب۴ و۲۱ ا۲ ب۵ و ۷ اب۶ و ب۷ میباشند پس (ا+ب)۷\n=ا۷+ ۷ ا۶ ب+ ۲۱ ا۵ ب۲+ ۳۵ ا۴ ب۳+ ۳۵ ا۳ ب۴+ ۲۱ ا۲ ب۵+۷ اب۶+ ب۷\nمثال ۲ حاصل بسط (لا-ی)۷ را معلوم کنید :-\nکل تعداد حدود درین حاصل بسط = ۹\nحد اول = لا۸\nحد دوم = ۸ لا۷ ی\nحد سوم = ۸×۷÷۲ لا۶ ی۲ = ۲۸ لا۶ ی۲\nحد چهارم = - ۲۸×۶÷۳ لا۵ ی۳ = - ۵۶ لا۵ ی۳ بموجب قاعده (۲) و(۳) و(۴)\nحد پنجم = ۵۶×۵÷۴ لا۴ ی۴ = ۷۰ لا۴ ی۴\nو حدود باقیمانده را بقرار قاعده پنجم بنویسید :-\nپس (لا-ی)۸ = لا۸ - ۸ لا۷ ی+ ۲۸ لا۶ ی۲ - ۵۶ لا۵ ی۳+ ۷۰ لا۴ ی۴ - ۵۶ لا۳ ی۵+ ۲۸ لا۲ ی۶\n- ۸ لا ی۷+ ی۸\nمثال ۳ حاصل بسط (۲لا- ۳ی)۷ را معلوم کنید:-\nکل تعداد حدود = ۸\nحد اول = (۲لا)۷\nحد دوم = - ۷ (۲لا)۶ (۳ی)\nحد سوم = ۷×۶÷۲ (۲لا)۵ (۳ی)۲ = ۲۱ (۲لا)۵ (۳ی)۲\nحد چهارم = - ۲۱×۵÷۳ (۲لا)۴ (۳ی)۳ = - ۳۵ (۲لا)۴ (۳ی)۳","chars":768,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00143.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/adl0258/143","canvas":"https://afghanpress.org/iiif/adl0258/canvas/143","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."}}