{"book":"adl0290","page":105,"text":"علم حساب ۱\n۹۸\nاگر باقی آخری برابر آن باقی باشد که بعد از تقسیم مجموعه هندسه های حاصل ضرب مضروب و مضروب فیه بر ۹ حاصل شده است غالباً عمل ضرب صحیح است و اگر در باقیات اختلاف باشد عمل ضرب حکماً غلط است میزان صحت ضرب بر این اصول مبنی میباشد که اگر کدام عدد را بر ۹ تقسیم کنیم باقی همان می برآید که کل هندسه های عدد مذکور را جمع نموده بر ۹ تقسیم کرده شود و ثبوت این حسب ذیل است :-\n۳۵۴ = ۳۹ × ۹ + ۳\nدر این صورت خواه ۳۵۴ را بر ۹ تقسیم کنید و خواه مجموعه هندسه ها یعنی ۴ + ۵ + ۳ = ۱۲ را بر ۹ تقسیم کنید در هر صورت باقی یکی میباشد\nتوضیح قاعده صحت حاصل ضرب از مثال ذیل میشود :-\n۵۳۳   مجموعه هندسه های مضروب = ۳+۳+۵= ۱۱\n۵۷\n۳۷۳۱      ۹ ) ۱۱ (\n۲۶۶۵      ۹\n۳۰۳۸۱      ۲ باقی\n\n   ۲\n۶    ۶\n   ۳","chars":678,"image":"https://storage.googleapis.com/adl-page-images/adl0290/00105.jpg","first_page":1,"last_page":1089,"title":"ʻIlm-i ḥisābعالم حساب","permalink":"https://afghanpress.org/book/adl0290/105","canvas":"https://afghanpress.org/iiif/adl0290/canvas/105","source":"https://afghanistandl.nyu.edu/books/adl0290/","source_pdf":"https://afghanistandl.nyu.edu/pdf/adl0290_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."}}