{"book":"adl0946","page":159,"text":"۱۵۲\n\nواقعه در يك طرف خط وغير مكمل تشکیل دهد\nآن دو خط همدیگر را قطع میکنند .\nقضیه ـ در حالت سابقه محل تقاطع آنها\nدر طرفے است که مجموع دو زاویه از دو قائمه\nکمتر باشد .\n۱۵۹ ـ مطلب اقلیدس یکی از مسائلی است که\nنمیتوان اثبات نمود از زمان یونانیان قدیم اقلیدس\nمهندس مشهور آن را سوال کرده علاوه بر آنکه تا حال\nحال کسی نتوانسته است آن را اثبات کند بالاخره در\nاین دوره ثابت کرده اند که هرگز ممکن نیست اثبات نمود.\nما فقط بملاحظه این مطلب اکتفا نموده همین قدر میگوئیم\nکه هرگاه نقطه تقاطع آن دو خط خارج از صفحه کاغذ باشد\nهرگونه اثبات تجربیه هم محال است .\n۱۶۰ـ نتیجه مطلب اقلیدس ـ از مطلب اقلیدس\nچنین نتیجه مے شود که از نقطه واقعه در خارج خطی ممکن","chars":633,"image":"https://storage.googleapis.com/adl-page-images/adl0946/00159.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/adl0946/159","canvas":"https://afghanpress.org/iiif/adl0946/canvas/159","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."}}