{"book":"adl0946","page":216,"text":"۲۰۹\n\nمساوی است بچهار قائمه -\n۲۴۵ - مسئله - میخواهیم مجموع زوایای\nکثیرالاضلاعی را معلوم کنیم -\nدر ۱۸۲ زاویۀ x را ملاحظه می کنیم که با زاویۀ\ny مکمل یک دیگرند و همچنین هر زاویۀ داخلی با زاویۀ\nخارجیش مکمل همدیگر میباشند -\nهرگاه تمام زوایای داخلی و خارجی را بر هم بیفزائیم\nحاصل جمع بقدر دو برابر عدۀ اضلاع یا رئوس زاویه قائمه\nخواهد شد و چون مجموع تمام زوایای خارجی مساوی چهار\nقائمه است - پس مجموع زوایای داخلی هر کثیرالاضلاع\nمحدّب مساوی است با دو برابر عدۀ رئوس منهای\nچهار قائمه -\nفرض می کنیم ن عدۀ رئوس باشد مجموع زوایای\nداخلی از این تساوی بدست می آید -\n(ن × ۲) - ۴ = ۲ ن - ۴","chars":571,"image":"https://storage.googleapis.com/adl-page-images/adl0946/00216.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/adl0946/216","canvas":"https://afghanpress.org/iiif/adl0946/canvas/216","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."}}