{"book":"adl0946","page":135,"text":"۱۲۸\n\nنیز بسهولت میگردد.\n۱۶۶ - مثلاً وقتیکه خطی دائره را قطع کند فاصلهٔ مرکز\nدائره تا آن خط همواره کوچک تر است از شعاع دائره\nو این مسئله لازم است بالعکس هرگاه خطی طوری واقع\nشده باشد که فاصله مرکز دائره تا آن خط کوچک تر از شعاع\nدائره باشد (س۱۲۳) نقطهٔ ا در درون دائره است و آن خط\nمجبور است از دائره خارج شود پس آن را قطع می نماید\nو فرض مسئله برای اثبات این امر کافی است.\nپس دو خاصیّت فوق را با هم جمع کرده چنین بیان\nمی کنیم:\nشرط لازم و کافی برای آنکه دائره و خطی\nیکدیگر را قطع کنند آن است که فاصلهٔ مرکز\nدائره از ان خط کوچک تر باشد از شعاع دائره\n۱۶۷ - مسئله - می خواهیم دو مائل را که مواقع\nآنها بيك فاصله از مواقع عمود نیستند مقایسه","chars":630,"image":"https://storage.googleapis.com/adl-page-images/adl0946/00135.jpg","first_page":1,"last_page":327,"title":"Handasah-ʼi musaṭṭaḥah barā-yi ṣinf-i haftum-i makātib-i rushdīyah, bi-qarār-i prūghram-i Vizārat-i Jalīlah-ʼi Muʻārif-i Afghānistān هندسۀ مسطحه :هندسۀ مسطحه","permalink":"https://afghanpress.org/book/adl0946/135","canvas":"https://afghanpress.org/iiif/adl0946/canvas/135","source":"https://afghanistandl.nyu.edu/books/adl0946/","source_pdf":"https://afghanistandl.nyu.edu/pdf/adl0946_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."}}