{ "markdown": "## ملاحظة\nالأحنف بن قيس 120/ 130/ كتاب المختار إلى ابن الزبير 121/ 131/ كتاب\n\\frac{\\partial n}{\\partial k} = \\lim_{h \\to 0} \\frac{\\log(k + h) - \\log(k)}{h}\n\\frac{\\partial \\alpha}{\\partial \\beta} = \\lim_{h \\to 0} \\frac{\\max(\\beta + h) - \\max(\\beta)}{h} + \\frac{i}{\\sigma^2}\n## مبرهنة\nالمختار إلى ابن الزبير 122/ 132/ كتاب المختار إلى ابن الزبير 122/ 133/ رد ابن الزبير\nk_{n+1} = k_n - \\alpha \\nabla f(k_n)", "images": [], "tables": [], "hyperlinks": [], "header": null, "footer": null, "dimensions": { "dpi": 96, "height": 432, "width": 565 }, "confidence_scores": { "word_confidence_scores": [ { "text": "##", "confidence": 1.0, "start_index": 0 }, { "text": "ملاحظة", "confidence": 1.0, "start_index": 3 }, { "text": "الأحنف", "confidence": 1.0, "start_index": 10 }, { "text": "بن", "confidence": 1.0, "start_index": 17 }, { "text": "قيس", "confidence": 1.0, "start_index": 20 }, { "text": "120/", "confidence": 1.0, "start_index": 24 }, { "text": 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"الأحنف بن قيس 120/ 130/ كتاب المختار إلى ابن الزبير 121/ 131/ كتاب", "type": "text", "confidence_scores": null, "reading_index": 2 }, { "top_left_x": 32, "top_left_y": 84, "bottom_right_x": 529, "bottom_right_y": 138, "content": "\\frac{\\partial n}{\\partial k} = \\lim_{h \\to 0} \\frac{\\log(k + h) - \\log(k)}{h}", "type": "text", "confidence_scores": null, "reading_index": 3 }, { "top_left_x": 20, "top_left_y": 170, "bottom_right_x": 545, "bottom_right_y": 229, "content": "\\frac{\\partial \\alpha}{\\partial \\beta} = \\lim_{h \\to 0} \\frac{\\max(\\beta + h) - \\max(\\beta)}{h} + \\frac{i}{\\sigma^2}", "type": "text", "confidence_scores": null, "reading_index": 4 }, { "top_left_x": 32, "top_left_y": 247, "bottom_right_x": 529, "bottom_right_y": 266, "content": "مبرهنة", "type": "title", "confidence_scores": null, "reading_index": 5 }, { "top_left_x": 32, "top_left_y": 271, "bottom_right_x": 529, "bottom_right_y": 316, "content": "المختار إلى ابن الزبير 122/ 132/ كتاب المختار إلى ابن الزبير 122/ 133/ رد ابن الزبير", "type": "text", "confidence_scores": null, "reading_index": 6 }, { "top_left_x": 32, "top_left_y": 322, "bottom_right_x": 529, "bottom_right_y": 360, "content": "k_{n+1} = k_n - \\alpha \\nabla f(k_n)", "type": "text", "confidence_scores": null, "reading_index": 7 } ], "meta": { "template": "math_proof", "hybrid": null, "page_font": "ae-hor.ttf", "title_font": "ae-hor.ttf", "language": "ar", "script": "arabic", "direction": "rtl", "augmentation": null } }