{"book":"adl0946","page":156,"text":"۱۴۹\n\nاست و چنین لازم می آید که دو زاویه متقارنه ۲ و ۵ مساوی باشند.\n\nهمچنین اگر دو زاویه متناوب خارجی مساوی باشند پس ۱ و ۸ مساوی میگردند.\n\nو بالاخره اگر دو زاویه ۱ و ۵ مکمل یکدیگر باشند زاویه ۸ که متمم زاویه ۵ است با زاویه متقارنه ۱ مساوی است پس می توانیم چهار قضیه ذیل را بیان نمائیم:\n\nقضیه هرگاه دو خط با خط ثالثی: زوایای متناوبه داخله مساوی تشکیل دهند.\nیا زوایای متناوبه خارجه مساوی تشکیل دهند.\nیا زوایای متقارنه مساوی تشکیل دهند.\nیا زوایای داخلی مکمله در یک طرف خط تشکیل دهند آن دو خط با هم موازیند.","chars":502,"image":"https://storage.googleapis.com/adl-page-images/adl0946/00156.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/adl0946/156","canvas":"https://afghanpress.org/iiif/adl0946/canvas/156","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."}}