{"book":"adl0258","page":251,"text":"۲۴۶\nمثال ۵ ۱/ا+ب - ۱/ا+۲ب + ۱/ا+۳ب - ۱/ا+۴ب را مختصر کنید\nجمله مفروضه = {۱/ا+ب - ۱/ا+۲ب} - {۱/ا+۳ب - ۱/ا+۴ب}\nو چون ۱/ا+ب - ۱/ا+۲ب = (ا+۲ب)-(ا+ب)/(ا+ب)(ا+۲ب) = ب/(ا+ب)(ا+۲ب)\nو ۱/ا+۳ب - ۱/ا+۴ب = (ا+۴ب)-(ا+۳ب)/(ا+۳ب)(ا+۴ب) = ب/(ا+۳ب)(ا+۴ب)\nلهذا ب/(ا+ب)(ا+۲ب) - ب/(ا+۳ب)(ا+۴ب) = ب(ا+۳ب)(ا+۴ب)-ب(ا+ب)(ا+۲ب)/(ا+ب)(ا+۲ب)(ا+۳ب)(ا+۴ب)\nو صورت کسر مذکور = ب(ا۲+۷اب+۱۲ب۲)-ب(ا۲+۳اب+۲ب۲)\n= ب(۴اب+۱۰ب۲) = ۲ب۲(۲ا+۵ب)\nپس قیمت مطلوب = ۲ب۲(۲ا+۵ب)/(ا+ب)(ا+۲ب)(ا+۳ب)(ا+۴ب)\nمسئله (۵۸)\nقیمت کسور ذیل معلوم کنید :-\n(۱) ا+ب/ا - ا-ب/ب (۲) لا-ی/لای - ی-ع/ی‌ع - ع-لا/ع‌لا (۳) ۱/ا-لا + لا/ا۲-لا۲\n(۴) ا+ب/ا-ب - ا-ب/ا+ب (۵) ۱/ا+ب - ۱-ب/۲(ا+ب) (۶) ۴لا+۹ی/۴لا۲-۹ی۲ - ۲لا-۳ی/۲لا+۳ی\n(۷) ا/(ا+ب)۲ - ب/(ا-ب)۲ (۸) ا۲+اب+ب۲/ا+ب - ا۲-اب+ب۲/ا-ب (۹) ۱/(ا-ب)(ا-ج) + ۱/(ا-ج)(ب-ج)\n(۱۰) ۱/لا۲-۳لا+۲ + ۱/لا۲-۵لا+۶ (۱۱) ۱/لا۲+۷لا+۱۰ + ۱/لا۲+۱۳لا+۴۰ (۱۲) ۱/(۲لا-۳ی) - ۱/۴لا۲+۳ی۲-۱۲لای","chars":835,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00251.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/adl0258/251","canvas":"https://afghanpress.org/iiif/adl0258/canvas/251","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."}}