{"book":"adl0131","page":33,"text":"کتاب\n۲۲\nمساحت\n\nکه ارتفاع نها یک اند۔\n۲۹- اگر قاعده و ارتفاع مثلث و سطح قائمه الزاویه یک باشد پس مثلث\nاز سطح قائمه الزاویه نصف خواهد بود. فرض کنید که مثلث الف ب ج وسطح\nقائمه الزاویه الف ب دی بر یک قاعده واقع اند و ارتفاع انها هم یک است\nپس مثلث از سطح قائمه الزاویه\nنصف خواهد بود.\nثبوت- فرض کنید که بر خط الف ب از نقطه ج ف عمود کشیده ام\nپس تصدیق این چندان مشکل نیست که مثلث ب ج ف برابر ست مثلث\nب دج و مثلث الف ف ج برابر ست بمثلث ج ی الف و ازین\nظاهر ست که مثلث الف ب ج نصف است از سطح قائمه الزاویه اب دی\nپس ازین معلوم شد که اگر قاعده و ارتفاع دو مثلث با یک هستند\nپس با هم برابر میباشند۔\n۳۰- مربع وتر مثلث قائمه الزاویه برابر میباشد بجموعه آن مربع ها که برضلاع\n\nاو ساخته","chars":666,"image":"https://storage.googleapis.com/adl-page-images/adl0131/00033.jpg","first_page":1,"last_page":381,"title":"Kitāb-i ʻIlm i masāḥat کتاب عالم ا مساحت","permalink":"https://afghanpress.org/book/adl0131/33","canvas":"https://afghanpress.org/iiif/adl0131/canvas/33","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."}}