{"book":"adl0258","page":138,"text":"و همین قاعده در معلوم کردن مربع هر جمله ذوحدود کثیره جاری میباشد\nمثلاً فرض کنید که مربع ا + ب + ج + د + ی مطلوب است\n(ا + ب + ج + د + ی)٢ = {(ا + ب + ج) + (د + ی)}٢\n= (ا + ب + ج)٢ + ٢(ا + ب + ج)(د + ی) + (د + ی)٢\n= {ا٢ + ب٢ + ج٢ + ٢ا(ب + ج) + ٢ب ج} + {٢ا(د + ی)\n+ ٢ب(د + ی) + ٢ج(د + ی)} + (د٢ + ی٢ + ٢دی)\n= ا٢ + ب٢ + ج٢ + د٢ + ی٢ + ٢ا(ب + ج + د + ی) + ٢ب\n(ج + د + ی) + ٢ج(د + ی) + ٢دی\nپس ظاهر است که مربع یک جمله مرکب مساوی مجموع مربع‌های هر حد جمله مذکور\nبا دو چند حاصل ضرب هر حد در هر یکی از ان حدودیکه بعد از حد مذکور می‌آیند میباشد\nتنبیه چون (ا + ب + ج)٢ = ا٢ + ب٢ + ج٢ + ٢(ا ب + ا ج + ب ج)\nپس ٢(ا ب + ا ج + ب ج) = {(ا + ب + ج)٢ + ٢(ا ب + ا ج + ب ج)}\n- (ا٢ + ب٢ + ج٢)\n= (ا + ب + ج)٢ - (ا٢ + ب٢ + ج٢)\nو بهمین طریق (ا٢ + ب٢ + ج٢) = (ا + ب + ج)٢ - ٢(ا ب + ا ج + ب ج)\nمثال مربع لا - ی + ء - د را دریافت کنید.\n(لا - ی + ء - د)٢ = لا٢ + ی٢ + ء٢ + د٢ + ٢لا(- ی + ء - د) + ٢(- ی)(ء - د) + ٢ء(- د)\n= لا٢ + ی٢ + ء٢ + د٢ - ٢لای + ٢لا ء - ٢لاد - ٢ی ء + ٢ی د - ٢ء د","chars":955,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00138.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/adl0258/138","canvas":"https://afghanpress.org/iiif/adl0258/canvas/138","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."}}