{"book":"adl0258","page":191,"text":"١٨٦\n\nمثال ١٢لا٢ + ٧لا - ١٠ را بمضروبات تفریق کنید -\n١٢ لا٢ + ٧لا - ١٠ = ١/١٢ (١٢ × ١٢لا٢ + ٧× ١٢لا - ١٠ × ١٢)\n= ١/١٢ (لا١ ٢ + ٧لا١ - ١٢٠) (بشرط اینکه لا١ = ١٢لا)\nو چون لا١ ٢ + ٧لا١ - ١٢٠ = (لا١ + ١٥) (لا١ - ٨)\nلہٰذا جملہ مفروضہ = ١/١٢ (١٢لا + ١٥) (١٢لا - ٨)\n= ١/١٢ { ٣ (٤لا + ٥) × ٤ (٣لا - ٢)}\n= (٤لا + ٥) (٣لا - ٢)\nمسئله (٤٢)\nجملہای ذیل را بمضروبات تفریق کنید :-\n(١) لا٢ + ٤لا + ٣ (٢) لا٢ + ٥لا + ٦ (٣) لا٢ + ٧لا + ١٢\n(٤) لا٢ + ٩لا + ٢٠ (٥) لا٢ + ٩لا + ١٨ (٦) لا٢ + ١١لا + ٢٨\n(٧) لا٢ - ١٠لا + ٢٤ (٨) لا٢ - ٨لا + ١٥ (٩) لا٢ - ١١لا + ٣٠\n(١٠) لا٢ - ١٢لا + ٣٢ (١١) لا٢ - ١٢لا + ٢٤ (١٢) لا٢ - ٢٢لا + ٤٠\n(١٣) لا٢ + ٧لا - ٣٠ (١٤) لا٢ + ٢لا - ٤٨ (١٥) لا٢ + ١٦لا - ٣٦\n(١٦) لا٢ + ٩لا - ٣٦ (١٧) لا٢ + ١١لا - ٤٢ (١٨) لا٢ + ٤لا - ٧٢\n(١٩) لا٢ - ٣لا - ٤٠ (٢٠) لا٢ - ١١لا - ٨٠ (٢١) لا٢ - ٢٩لا - ٩٦\n(٢٢) لا٢ - ١٠لا - ٥٦ (٢٣) لا٢ - لا - ٤٢ (٢٤) لا٢ - لا - ٧٢\n(٢٥) لا٢ + ٢٢لا + ١٢٠ (٢٦) لا٢ + ١٦لا - ٨٠ (٢٧) لا٢ - ٢١لا - ٧٢\n(٢٨) لا٢ + ٥لا - ٨٤ (٢٩) لا٢ - ٢٠لا + ٩٦ (٣٠) لا٢ + ٢٣لا - ٧٨","chars":967,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00191.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/adl0258/191","canvas":"https://afghanpress.org/iiif/adl0258/canvas/191","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."}}