{"book":"adl0258","page":254,"text":"۲۴۹\nمثال ۳ ۱-لا ۱+ی و ا+ ی وا+ لا را در یکدیگر ضرب کنید\nلا+لا۲ ۱-لا\nچون ا+ لا = ۱-لا +لا = ۱\n۱-لا ۱-لا ۱-لا\n∴ حاصل ضرب مطلوب = (۱+لا)(۱-لا) x (۱+ی)(۱-ی) x ۱\n۱+ی لا(۱+لا) ۱-لا\n= (۱+لا)(۱-لا)(۱+ی)(۱-ی) = ۱-ی\nلا(۱+ی)x(۱+لا)x(۱-لا) لا\nمسئله (۵۹)\nکسور ذیل را در یکدیگر ضرب کنید :-\n(۱) ۳ا۲ و ۹ب۲ و ۸ج۲ (۲) ۴ا۲ب۳ و ۱ج۳ و ۳د۲\n۴اب ۱۶اج ۹ب ج ۳ج۲ ۱۶د۲ ۲ب\n(۳) لا۳ و ی۲ و ع۳ (۴) ۷ا۲ب۴ج۳ و ۴لا۳ی۲ع۲\nی۶ ع۴ لا۵ ۱۲لاییع۶ ۲۱ا۳ب۴ج۳\n(۵) ۱۲م۲ن۳ و ۳۵لا۴ی۶\n۷لا۴ی۳ ۶۹م۳ن\nمختصر کنید :-\n(۶) لا+۱ x لا۲+لا-۲ (۷) ۱۲-۹ب۲ x ۲۱۳\n۱-لا لا+لا۲ ا۲+۳اب ا۲-۳اب\n(۸) ا۲-ب۲ x (ا + ب)۲ (۹) لا۲+۸لا x لا۲-۴لا+۴لا۲\nا۲+اب ا۲+۲اب+ب۲ لا۲-۴لا لا۲-۴لا+۴لا۲\n(۱۰) لا۲+۴لا+۳ x لا۲-۳لا+۲ (۱۱) لا۲-۷لا+۱۰ x لا۲-۳لا-۱۸\nلا۲-۴ ۹-لا۲ لا۲-۳لا-۱۵ لا۲-۸لا+۱۲\n(۱۲) لا۲-۴لا+۳ x لا۲-۷لا-۱۰ (۱۳) ا۲-ب۲ x ا-ب\nلا۲-۶لا+۵ لا۲-۵لا+۶ ا۲-۲اب+ب۲ ا۲+اب","chars":779,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00254.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/adl0258/254","canvas":"https://afghanpress.org/iiif/adl0258/canvas/254","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."}}