{ "markdown": "## مبرهنة\nثَنَا النَّضْرُ بْنُ إِسْمَاعِيلَ الْبَجَلِيُّ، ثَنَا أَبُو حَمْزَةَ الثُّمَالِيُّ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ، عَنْ عِمْرَانَ بْنِ حُصَيْنٍ رضي الله عنه أَنَّ\n\\iint_{D} \\lambda^2 \\leq k^2 \\, dx \\, dy\nt_{n+1} = t_n - \\alpha \\nabla f(t_n) + \\frac{\\beta}{k^2}", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 291, "width": 684 }, "confidence_scores": { "word_confidence_scores": [ { "text": "##", "confidence": 1.0, "start_index": 0 }, { "text": "مبرهنة", "confidence": 1.0, "start_index": 3 }, { "text": "ثَنَا", "confidence": 1.0, "start_index": 10 }, { "text": "النَّضْرُ", "confidence": 1.0, "start_index": 16 }, { "text": "بْنُ", "confidence": 1.0, "start_index": 26 }, { "text": "إِسْمَاعِيلَ", "confidence": 1.0, "start_index": 31 }, { "text": "الْبَجَلِيُّ،", "confidence": 1.0, "start_index": 44 }, { "text": "ثَنَا", "confidence": 1.0, "start_index": 58 }, { "text": "أَبُو", "confidence": 1.0, "start_index": 64 }, { "text": "حَمْزَةَ", "confidence": 1.0, "start_index": 70 }, { "text": "الثُّمَالِيُّ،", "confidence": 1.0, "start_index": 79 }, { "text": "عَنْ", "confidence": 1.0, "start_index": 94 }, { "text": "سَعِيدِ", "confidence": 1.0, "start_index": 99 }, { "text": "بْنِ", "confidence": 1.0, "start_index": 107 }, { "text": "جُبَيْرٍ،", "confidence": 1.0, "start_index": 112 }, { "text": "عَنْ", "confidence": 1.0, "start_index": 122 }, { "text": "عِمْرَانَ", "confidence": 1.0, "start_index": 127 }, { "text": "بْنِ", "confidence": 1.0, "start_index": 137 }, { "text": "حُصَيْنٍ", "confidence": 1.0, "start_index": 142 }, { "text": "رضي", "confidence": 1.0, "start_index": 151 }, { "text": "الله", "confidence": 1.0, "start_index": 155 }, { "text": "عنه", "confidence": 1.0, "start_index": 160 }, { "text": "أَنَّ", "confidence": 1.0, "start_index": 164 }, { "text": "\\iint_{D}", "confidence": 1.0, "start_index": 170 }, { "text": "\\lambda^2", "confidence": 1.0, "start_index": 180 }, { "text": "\\leq", "confidence": 1.0, "start_index": 190 }, { "text": "k^2", "confidence": 1.0, "start_index": 195 }, { "text": "\\,", "confidence": 1.0, "start_index": 199 }, { "text": "dx", "confidence": 1.0, "start_index": 202 }, { "text": "\\,", "confidence": 1.0, "start_index": 205 }, { "text": "dy", "confidence": 1.0, "start_index": 208 }, { "text": "t_{n+1}", "confidence": 1.0, "start_index": 211 }, { "text": "=", "confidence": 1.0, "start_index": 219 }, { "text": "t_n", "confidence": 1.0, "start_index": 221 }, { "text": "-", "confidence": 1.0, "start_index": 225 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 227 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 234 }, { "text": "f(t_n)", "confidence": 1.0, "start_index": 241 }, { "text": "+", "confidence": 1.0, "start_index": 248 }, { "text": "\\frac{\\beta}{k^2}", "confidence": 1.0, "start_index": 250 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 32, "top_left_y": 32, "bottom_right_x": 648, "bottom_right_y": 53, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 32, "top_left_y": 58, "bottom_right_x": 648, "bottom_right_y": 103, "content": "ثَنَا النَّضْرُ بْنُ إِسْمَاعِيلَ الْبَجَلِيُّ، ثَنَا أَبُو حَمْزَةَ الثُّمَالِيُّ، عَنْ سَعِيدِ بْنِ جُبَيْرٍ، عَنْ عِمْرَانَ بْنِ حُصَيْنٍ رضي الله عنه أَنَّ", "type": "text", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 109, "bottom_right_x": 648, "bottom_right_y": 163, "content": "\\iint_{D} \\lambda^2 \\leq k^2 \\, dx \\, dy", "type": "text", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 20, "top_left_y": 195, "bottom_right_x": 664, "bottom_right_y": 245, "content": "t_{n+1} = t_n - \\alpha \\nabla f(t_n) + \\frac{\\beta}{k^2}", "type": "text", "confidence_scores": null, "reading_index": 4 } ], "meta": { "template": "math_proof", "hybrid": null, "page_font": "all-exp02-mema.otf", "title_font": "khat-e-musarat.ttf", "language": "ar", "script": "arabic", "direction": "rtl", "augmentation": null } }