{"book":"adl0258","page":88,"text":"۸۳\n\nپس ظاهر است که اگر عمل بقرار فوق نموده شود مفهوم آن همانست که آحاد را\nدر خطوط عرضی ب نوشته شود پس همگی آحاد را که بطریق فوق نوشته شدند شمار کنید\nچون تعداد همه سطور عرضی ا است و در هر سطر ب احاد است\nلهذا کل تعداد احاد = (تعداد احاد در سطر عرضی اول) + (تعداد احاد در سطر\nعرضی دوم) + (تعداد احاد در سطر عرضی سوم) + . . . . . . . . .\n(تعداد احاد در سطر عرضی اخیر) که بالف ازان تعبیر شده است = ب\n+ ب + ب . . . . تا ا = ا × ب (۱)\n\nو نیز چون تعداد همه قطارهای عمودی ب است و در هر قطار ا احاد هستند\nلهذا کل تعداد احاد = (احاد در سطر عمودی اول) + (احاد در سطر عمودی دوم)\n+ (احاد در سطر عمودی سوم) . . . . . . . . . + (احاد در سطر عمودی اخیر)\nکه به ب ازان تعبیر شده است = ا + ا + ا + . . . . تا ب = ب ا (۲)\nبنا برین از (۱) و (۲) چنین اخذ میکنیم که ا × ب = ب × ا (۱)\nیعنی ب دفعه ا = ا دفعه ب و همچنین در کسور نیز قاعده مذکوره جاری میباشد\nنتیجه ا در فقره ۴ ثابت شده است که لا × (-ی) = - (لای) و (-ی)\n× لا = - (ی لا) لیکن چون لای = ی لا ∴ لا × (-ی) = (-ی) × لا (ب)","chars":955,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00088.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/adl0258/88","canvas":"https://afghanpress.org/iiif/adl0258/canvas/88","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."}}