{"book":"adl0258","page":171,"text":"١٦٦\nتنبیه بعض اوقات مقسوم بر مقسوم علیه بدون باقی تقسیم میشود\nمثلا اگر در مثال فوق مقسوم ٦لا٤ + ٣٦لا٣ + ٦لا٢ + ٨٦ باشد حاصل تفریق\nدوم ٣٦لا٣ + ٦لا٢ + ٨٦ میشود وحاصل تفریق اخير ٦لا٢ + ٥ وچون ٦لا٢ +٥\nبر ٣لا٢ + ٦لا + ٩ کامل تقسیم نمیشود لہذا در تقسیم درینصورت باقی میماند\nوبقرار قواعد علم حساب قرار ذیل نوشته میشود یعنی\n١٦لا٤ + ٣٦لا٣ + ٦لا٢ + ٨٦ = ٤لا٢ - ٦لا + ٩ + ٦لا٢ + ٥ / ٣لا٢ + ٦لا + ٩\nو آن حصہ مقسوم را کہ بر مقسوم علیه تقسیم شده نمیتواند باقی میگویند\nپس اگر از مقسوم بحرف م و از مقسوم علیه بحرف ع واز خارج قسمت بحرف خ\nو از باقی بحرف ب تعبیر شود نتیجه ذیل دائما صحیح خواهد بود۔\nم = ع × خ + ب\nمثال ٣لا - ٤لا٢ - ٢لا٣ + ٣لا٤ + ٨لا - ١٢ را بر لا٤ - ٤ تقسیم کنید\nتنبیه این امر ضروری نیست که مقسوم ومقسوم علیہ محض بلحاظ قوای\nمتناقصہ یک حصی مشترکہ ترتیب داده شوند بلکہ اینقدر لازم است که یک تربیتی خاص\nداشته باشند خواه بلحاظ قوای متناقصه و خواه بلحاظ قوای متزائده یک حصہ مشترکہ\nچنانچہ حل این مثال بعد از ترتیب مقسوم و مقسوم علیہ بلحاظ قوای متزائده لا کرده میشود\n- ٤ + لا٢) - ١٢ + ٨لا + ٣لا - ٤لا٢ - ٢لا٣ + ٣لا٤ ( ٣ - ٢لا + لا٢\n- ١٢         + ٣لا٢\n+ ٨لا       - ٣لا٢\n+ ٨لا       - ٣لا٢\n+ ٤لا٣ + لا٤\n+ ٤لا٣ + لا٤\n×","chars":1107,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00171.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/adl0258/171","canvas":"https://afghanpress.org/iiif/adl0258/canvas/171","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."}}