{"book":"adl0258","page":116,"text":"یعنی مربع تفاضل دو مقدار جبری مساوی مجموع مربع هر یکی از مقادی\nمذکور ناقص دو چند حاصل ضرب مقادیر مذکور میباشد\nنتیجه ۱- ۲(ا+ب) = (ا۲+ ۲اب+ ب۲) + ۲اب = (ا-ب)۲ + ۴اب\nنتیجه ۲- چون (ا+ب)۲ = ا۲+ ۲اب+ ب۲ و (ا-ب)۲ = ا۲- ۲اب+ ب۲\nلهذا (ا+ب)۲ = (ا-ب)۲ + ۴اب\nو (ا-ب)۲ = (ا+ب)۲ - ۴اب\nمثال ۱ مربع (۳ا - ۴ب) را معلوم کنید.\n(۳ا - ۴ب)۲ = (۳ا)۲ - ۲(۳ا)(۴ب) + (۴ب)۲\n= ۹ا۲ - ۲۴اب + ۱۶ب۲\nمثال ۲ مربع لا - ی - ۶ را معلوم کنید.\n(لا - ی - ۶)۲ = {لا - (ی + ۶)}۲\n= لا۲ - ۲لا(ی + ۶) + (ی + ۶)۲\n= لا۲ - ۲لای - ۱۲لا + ی۲ + ۱۲ی + ۳۶\n= لا۲ + ی۲ + ۳۶ - ۲لای - ۱۲لا + ۱۲ی\nمثال ۳ مربع (۲لا - ۳ی - ۴۶) را معلوم کنید\n(۲لا - ۳ی - ۴۶)۲ = {۲لا - (۳ی + ۴۶)}۲\n= (۲لا)۲ - ۲(۲لا)(۳ی + ۴۶) + (۳ی + ۴۶)۲\n= ۴لا۲ - ۱۲لای - ۱۶لا + ۹ی۲ + ۲۴ی + ۱۶۶۲\n= ۴لا۲ + ۹ی۲ + ۱۶۶۲ - ۱۲لای - ۱۶لا + ۲۴ی","chars":740,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00116.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/adl0258/116","canvas":"https://afghanpress.org/iiif/adl0258/canvas/116","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."}}