{"book":"adl0258","page":242,"text":"۲۳۷\nفرض کنید که ا/ب = ا/ب :. ا/ب x ب = ا/ب x ب = ا.... (بحکم تعریف فقره ۹۱)\n:. ا/ب x م x ب = ا x م یا ا/ب x ب م = ام لہذا ا/ب = ام ÷ ب م یعنی ا/ب = ام/ب م\nو نیز بر عکس آن چون ام/ب م = ا/ب :. ام/ب م = ام ÷ م/ب م ÷ م و هو المراد\nنتیجه = ا/ب = ا x (-۱) / ب x (-۱) = -ا/-ب\nیعنے اگر علامات صورت و مخرج یک کسر جبری تبدیل شود قیمیت کسر\nهیچ فرق واقع نمیشود :-\n۹۳ طریق اختصار کسور جبریه\nکسر مختصر آنست که صورت و مخرج آن هیچ مضروب مشترک نداشته باشد\nپس مفهوم اختصار یک کسر جبری اینست که یک کسر دیگر مساوی کسر\nمفروض انقسم معلوم شود که صورت و مخرج آن هیچ مضروب مشترک نداشته با\nظاهر است که اگر صورت و مخرج کسر بر قاسم مشترک اعظم آنها تقسیم شود\nکسر مذکور مختصر میشود :-\nتنبیه اگر مضروبات صورت و مخرج ظاهر باشند پس برای اختصا کسر\nهمینقدر کافیست که مضروبات مشترک صورت و مخرج برداشته شود -\nمثال ۱ ۴ ا۲ ب۲ ج۳ / ۱۰ ا ب۲ ج۳ را مختصر کنید :-\n۴ ا۲ ب۲ ج۳ / ۱۰ ا ب۲ ج۲ = ۲ x ۲ x ا۲ x ب۲ x ج۳ / ۲ x ۵ x ا x ب۲ x ج۲\n= ۲ ا ج / ۵ ب","chars":902,"image":"https://storage.googleapis.com/adl-page-images/adl0258/00242.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/adl0258/242","canvas":"https://afghanpress.org/iiif/adl0258/canvas/242","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."}}