{"book":"adl0131","page":34,"text":"کتاب ۲۳ مساحت\n\nاو ساخته شوند در این شکل یک مثلث قائم الزاویه ساخته بر وتر و ضلاع\nجدا جدا مربعها ساخته شده‌اند. پس مربع کلان که وتر ساخته شده است برابر است\nبه باقی مربع ها. و این شکل در علم هندسه بسیار مفید است ثبوت این را ظاهر\nمی‌نمائیم.\n\nثبوت - فرض کنید که الف ب ج د ی غ ه یک شکل است که او\nاز ساختن چند مربع ها تیار شده است\nغ ه را برابر ب ج بسازید و خطوط ف ه\nو ج ه را باهم یکجا کنید و این همه شکل را\nاز کاغذ ساخته ببرید. و از او حصه را مثلاً ۱ و ۲ و ۳ بسازید و باز\nاین حصه ها را با یک دیگر اینطور یکجا کرده بمانید که همچنان بشکل ج ا ف ه\nمانده شده اند و از این ظاهر میشود که یک همچین مربع ساخته شده است\nکه ضلاع او برابر ف ه است که بر ف غ و غ ه ساخته شده‌اند.\n\n۳۱- اگر خط مستقیم دائره را مس کند پس آن نصف قطر که از نقطه تماس","chars":723,"image":"https://storage.googleapis.com/adl-page-images/adl0131/00034.jpg","first_page":1,"last_page":381,"title":"Kitāb-i ʻIlm i masāḥat کتاب عالم ا مساحت","permalink":"https://afghanpress.org/book/adl0131/34","canvas":"https://afghanpress.org/iiif/adl0131/canvas/34","source":"https://afghanistandl.nyu.edu/books/adl0131/","source_pdf":"https://afghanistandl.nyu.edu/pdf/adl0131_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."}}