{ "markdown": "\\frac{\\partial y}{\\partial n} = \\lim_{h \\to 0} \\frac{\\cos(n + h) - \\cos(n)}{h}\n## مبرهنة\nذلك، فمن زاد على صوم داود، فقد ترك الأفضل، فتبصّر، والله تعالى أعلم. (قَالَ عَبْدُ اللهِ بْنُ عَمْرٍو رضي\n\\sum_{i=0}^{\\infty} \\frac{y^i}{i!} = e^{y}\n## مبرهنة\nالله عنه: لَأَنْ أَكُونَ قَبِلْتُ الثَّلَاثَةَ أَيَّامَ الَّتِي قَالَ رَسُولُ اللهِ صلى الله عليه وسلم) أي:\n\\sigma_{n+1} = \\sigma_n - \\alpha \\nabla f(\\sigma_n) + \\frac{i}{\\sigma^2}\n\\iint_{D} i^2 \\leq \\theta^2 \\, dx \\, dy", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 481, "width": 756 }, "confidence_scores": { "word_confidence_scores": [ { "text": "\\frac{\\partial", "confidence": 1.0, "start_index": 0 }, { "text": "y}{\\partial", "confidence": 1.0, "start_index": 15 }, { "text": "n}", "confidence": 1.0, "start_index": 27 }, { "text": "=", "confidence": 1.0, "start_index": 30 }, { "text": "\\lim_{h", "confidence": 1.0, "start_index": 32 }, { "text": "\\to", "confidence": 1.0, "start_index": 40 }, { "text": "0}", "confidence": 1.0, "start_index": 44 }, { "text": "\\frac{\\cos(n", "confidence": 1.0, "start_index": 47 }, { "text": "+", "confidence": 1.0, "start_index": 60 }, { "text": "h)", "confidence": 1.0, "start_index": 62 }, { "text": "-", "confidence": 1.0, "start_index": 65 }, { "text": "\\cos(n)}{h}", "confidence": 1.0, "start_index": 67 }, { "text": "##", "confidence": 1.0, "start_index": 79 }, { "text": "مبرهنة", "confidence": 1.0, "start_index": 82 }, { "text": "ذلك،", "confidence": 1.0, "start_index": 89 }, { "text": "فمن", "confidence": 1.0, "start_index": 94 }, { "text": "زاد", "confidence": 1.0, "start_index": 98 }, { "text": "على", "confidence": 1.0, "start_index": 102 }, { "text": "صوم", "confidence": 1.0, "start_index": 106 }, { "text": "داود،", "confidence": 1.0, "start_index": 110 }, { "text": "فقد", "confidence": 1.0, "start_index": 116 }, { "text": "ترك", "confidence": 1.0, "start_index": 120 }, { "text": "الأفضل،", "confidence": 1.0, "start_index": 124 }, { "text": "فتبصّر،", "confidence": 1.0, "start_index": 132 }, { "text": "والله", "confidence": 1.0, "start_index": 140 }, { "text": "تعالى", "confidence": 1.0, "start_index": 146 }, { "text": "أعلم.", "confidence": 1.0, "start_index": 152 }, { "text": "(قَالَ", "confidence": 1.0, "start_index": 158 }, { "text": "عَبْدُ", "confidence": 1.0, "start_index": 165 }, { "text": "اللهِ", "confidence": 1.0, "start_index": 172 }, { "text": "بْنُ", "confidence": 1.0, "start_index": 178 }, { "text": "عَمْرٍو", "confidence": 1.0, "start_index": 183 }, { "text": "رضي", "confidence": 1.0, "start_index": 191 }, { "text": "\\sum_{i=0}^{\\infty}", "confidence": 1.0, "start_index": 195 }, { "text": "\\frac{y^i}{i!}", "confidence": 1.0, "start_index": 215 }, { "text": "=", "confidence": 1.0, "start_index": 230 }, { "text": "e^{y}", "confidence": 1.0, "start_index": 232 }, { "text": "##", "confidence": 1.0, "start_index": 238 }, { "text": "مبرهنة", "confidence": 1.0, "start_index": 241 }, { "text": "الله", "confidence": 1.0, "start_index": 248 }, { "text": "عنه:", "confidence": 1.0, "start_index": 253 }, { "text": "لَأَنْ", "confidence": 1.0, "start_index": 258 }, { "text": "أَكُونَ", "confidence": 1.0, "start_index": 265 }, { "text": "قَبِلْتُ", "confidence": 1.0, "start_index": 273 }, { "text": "الثَّلَاثَةَ", "confidence": 1.0, "start_index": 282 }, { "text": "أَيَّامَ", "confidence": 1.0, "start_index": 295 }, { "text": "الَّتِي", "confidence": 1.0, "start_index": 304 }, { "text": "قَالَ", "confidence": 1.0, "start_index": 312 }, { "text": "رَسُولُ", "confidence": 1.0, "start_index": 318 }, { "text": "اللهِ", "confidence": 1.0, "start_index": 326 }, { "text": "صلى", "confidence": 1.0, "start_index": 332 }, { "text": "الله", "confidence": 1.0, "start_index": 336 }, { "text": "عليه", "confidence": 1.0, "start_index": 341 }, { "text": "وسلم)", "confidence": 1.0, "start_index": 346 }, { "text": "أي:", "confidence": 1.0, "start_index": 352 }, { "text": "\\sigma_{n+1}", "confidence": 1.0, "start_index": 356 }, { "text": "=", "confidence": 1.0, "start_index": 369 }, { "text": "\\sigma_n", "confidence": 1.0, "start_index": 371 }, { "text": "-", "confidence": 1.0, "start_index": 380 }, { "text": "\\alpha", "confidence": 1.0, "start_index": 382 }, { "text": "\\nabla", "confidence": 1.0, "start_index": 389 }, { "text": "f(\\sigma_n)", "confidence": 1.0, "start_index": 396 }, { "text": "+", "confidence": 1.0, "start_index": 408 }, { "text": "\\frac{i}{\\sigma^2}", "confidence": 1.0, "start_index": 410 }, { "text": "\\iint_{D}", "confidence": 1.0, "start_index": 429 }, { "text": "i^2", "confidence": 1.0, "start_index": 439 }, { "text": "\\leq", "confidence": 1.0, "start_index": 443 }, { "text": "\\theta^2", "confidence": 1.0, "start_index": 448 }, { "text": "\\,", "confidence": 1.0, "start_index": 457 }, { "text": "dx", "confidence": 1.0, "start_index": 460 }, { "text": "\\,", "confidence": 1.0, "start_index": 463 }, { "text": "dy", "confidence": 1.0, "start_index": 466 } ], "average_page_confidence_score": 1.0, "minimum_page_confidence_score": 1.0 }, "blocks": [ { "top_left_x": 20, "top_left_y": 26, "bottom_right_x": 736, "bottom_right_y": 80, "content": "\\frac{\\partial y}{\\partial n} = \\lim_{h \\to 0} \\frac{\\cos(n + h) - \\cos(n)}{h}", "type": "text", "confidence_scores": null, "reading_index": 1 }, { "top_left_x": 32, "top_left_y": 98, "bottom_right_x": 720, "bottom_right_y": 110, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 115, "bottom_right_x": 720, "bottom_right_y": 137, "content": "ذلك، فمن زاد على صوم داود، فقد ترك الأفضل، فتبصّر، والله تعالى أعلم. (قَالَ عَبْدُ اللهِ بْنُ عَمْرٍو رضي", "type": "text", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 32, "top_left_y": 143, "bottom_right_x": 720, "bottom_right_y": 207, "content": "\\sum_{i=0}^{\\infty} \\frac{y^i}{i!} = e^{y}", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 32, "top_left_y": 251, "bottom_right_x": 720, "bottom_right_y": 263, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 5 }, { "top_left_x": 32, "top_left_y": 268, "bottom_right_x": 720, "bottom_right_y": 291, "content": "الله عنه: لَأَنْ أَكُونَ قَبِلْتُ الثَّلَاثَةَ أَيَّامَ الَّتِي قَالَ رَسُولُ اللهِ صلى الله عليه وسلم) أي:", "type": "text", "confidence_scores": null, "reading_index": 6 }, { "top_left_x": 32, "top_left_y": 297, "bottom_right_x": 720, "bottom_right_y": 348, "content": "\\sigma_{n+1} = \\sigma_n - \\alpha \\nabla f(\\sigma_n) + \\frac{i}{\\sigma^2}", "type": "text", "confidence_scores": null, "reading_index": 7 }, { "top_left_x": 20, "top_left_y": 380, "bottom_right_x": 736, "bottom_right_y": 434, "content": "\\iint_{D} i^2 \\leq \\theta^2 \\, dx \\, dy", "type": "text", "confidence_scores": null, "reading_index": 8 } ], "meta": { "template": "math_proof", "hybrid": null, "page_font": "nazli.ttf", "title_font": "almudid.ttf", "language": "ar", "script": "arabic", "direction": "rtl", "augmentation": null } }