| { | |
| "markdown": "## مبرهنة\nأبو الفضل محمد بن ناصر أنا أبو الفضل بن خيرون وأبو الحسين بن الطيوري وأبو الغنائم\n\\prod_{k=1}^{n} (1 \\approx \\theta_k) = 0\n## ملاحظة\nواللفظ له قالوا أنا عبد الوهاب بن محمد زاد ابن\n\\nabla_{j} J(j) = \\frac{1}{m} X^T ( \\sigma(X j) - Y )\n## برهان\nخيرون ومحمد بن الحسن قالا أنا أحمد بن عبدان أنا محمد بن سهل أنا محمد بن إسماعيل (5) قال\nt_{n+1} = t_n - \\alpha \\nabla f(t_n)\n## مبرهنة\nسعيد بن العاص الأموي القرشي سمع عمر بن الخطاب وعثمان وعائشة سمع منه سالم وابنه يحيى وقال سعيد بن يحيى كنية سعيد أبو\n\\frac{\\partial k}{\\partial z} = \\lim_{h \\to 0} \\frac{\\sin(z + h) - \\sin(z)}{h}", | |
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| "hyperlinks": [], | |
| "header": null, | |
| "footer": null, | |
| "dimensions": { | |
| "dpi": 96, | |
| "height": 663, | |
| "width": 573 | |
| }, | |
| "confidence_scores": { | |
| "word_confidence_scores": [ | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 0 | |
| }, | |
| { | |
| "text": "مبرهنة", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "أبو", | |
| "confidence": 1.0, | |
| "start_index": 10 | |
| }, | |
| { | |
| "text": "الفضل", | |
| "confidence": 1.0, | |
| "start_index": 14 | |
| }, | |
| { | |
| "text": "محمد", | |
| "confidence": 1.0, | |
| "start_index": 20 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 25 | |
| }, | |
| { | |
| "text": "ناصر", | |
| "confidence": 1.0, | |
| "start_index": 28 | |
| }, | |
| { | |
| "text": "أنا", | |
| "confidence": 1.0, | |
| "start_index": 33 | |
| }, | |
| { | |
| "text": "أبو", | |
| "confidence": 1.0, | |
| "start_index": 37 | |
| }, | |
| { | |
| "text": "الفضل", | |
| "confidence": 1.0, | |
| "start_index": 41 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 47 | |
| }, | |
| { | |
| "text": "خيرون", | |
| "confidence": 1.0, | |
| "start_index": 50 | |
| }, | |
| { | |
| "text": "وأبو", | |
| "confidence": 1.0, | |
| "start_index": 56 | |
| }, | |
| { | |
| "text": "الحسين", | |
| "confidence": 1.0, | |
| "start_index": 61 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 68 | |
| }, | |
| { | |
| "text": "الطيوري", | |
| "confidence": 1.0, | |
| "start_index": 71 | |
| }, | |
| { | |
| "text": "وأبو", | |
| "confidence": 1.0, | |
| "start_index": 79 | |
| }, | |
| { | |
| "text": "الغنائم", | |
| "confidence": 1.0, | |
| "start_index": 84 | |
| }, | |
| { | |
| "text": "\\prod_{k=1}^{n}", | |
| "confidence": 1.0, | |
| "start_index": 92 | |
| }, | |
| { | |
| "text": "(1", | |
| "confidence": 1.0, | |
| "start_index": 108 | |
| }, | |
| { | |
| "text": "\\approx", | |
| "confidence": 1.0, | |
| "start_index": 111 | |
| }, | |
| { | |
| "text": "\\theta_k)", | |
| "confidence": 1.0, | |
| "start_index": 119 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 129 | |
| }, | |
| { | |
| "text": "0", | |
| "confidence": 1.0, | |
| "start_index": 131 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 133 | |
| }, | |
| { | |
| "text": "ملاحظة", | |
| "confidence": 1.0, | |
| "start_index": 136 | |
| }, | |
| { | |
| "text": "واللفظ", | |
| "confidence": 1.0, | |
| "start_index": 143 | |
| }, | |
| { | |
| "text": "له", | |
| "confidence": 1.0, | |
| "start_index": 150 | |
| }, | |
| { | |
| "text": "قالوا", | |
| "confidence": 1.0, | |
| "start_index": 153 | |
| }, | |
| { | |
| "text": "أنا", | |
| "confidence": 1.0, | |
| "start_index": 159 | |
| }, | |
| { | |
| "text": "عبد", | |
| "confidence": 1.0, | |
| "start_index": 163 | |
| }, | |
| { | |
| "text": "الوهاب", | |
| "confidence": 1.0, | |
| "start_index": 167 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 174 | |
| }, | |
| { | |
| "text": "محمد", | |
| "confidence": 1.0, | |
| "start_index": 177 | |
| }, | |
| { | |
| "text": "زاد", | |
| "confidence": 1.0, | |
| "start_index": 182 | |
| }, | |
| { | |
| "text": "ابن", | |
| "confidence": 1.0, | |
| "start_index": 186 | |
| }, | |
| { | |
| "text": "\\nabla_{j}", | |
| "confidence": 1.0, | |
| "start_index": 190 | |
| }, | |
| { | |
| "text": "J(j)", | |
| "confidence": 1.0, | |
| "start_index": 201 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 206 | |
| }, | |
| { | |
| "text": "\\frac{1}{m}", | |
| "confidence": 1.0, | |
| "start_index": 208 | |
| }, | |
| { | |
| "text": "X^T", | |
| "confidence": 1.0, | |
| "start_index": 220 | |
| }, | |
| { | |
| "text": "(", | |
| "confidence": 1.0, | |
| "start_index": 224 | |
| }, | |
| { | |
| "text": "\\sigma(X", | |
| "confidence": 1.0, | |
| "start_index": 226 | |
| }, | |
| { | |
| "text": "j)", | |
| "confidence": 1.0, | |
| "start_index": 235 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 238 | |
| }, | |
| { | |
| "text": "Y", | |
| "confidence": 1.0, | |
| "start_index": 240 | |
| }, | |
| { | |
| "text": ")", | |
| "confidence": 1.0, | |
| "start_index": 242 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 244 | |
| }, | |
| { | |
| "text": "برهان", | |
| "confidence": 1.0, | |
| "start_index": 247 | |
| }, | |
| { | |
| "text": "خيرون", | |
| "confidence": 1.0, | |
| "start_index": 253 | |
| }, | |
| { | |
| "text": "ومحمد", | |
| "confidence": 1.0, | |
| "start_index": 259 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 265 | |
| }, | |
| { | |
| "text": "الحسن", | |
| "confidence": 1.0, | |
| "start_index": 268 | |
| }, | |
| { | |
| "text": "قالا", | |
| "confidence": 1.0, | |
| "start_index": 274 | |
| }, | |
| { | |
| "text": "أنا", | |
| "confidence": 1.0, | |
| "start_index": 279 | |
| }, | |
| { | |
| "text": "أحمد", | |
| "confidence": 1.0, | |
| "start_index": 283 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 288 | |
| }, | |
| { | |
| "text": "عبدان", | |
| "confidence": 1.0, | |
| "start_index": 291 | |
| }, | |
| { | |
| "text": "أنا", | |
| "confidence": 1.0, | |
| "start_index": 297 | |
| }, | |
| { | |
| "text": "محمد", | |
| "confidence": 1.0, | |
| "start_index": 301 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 306 | |
| }, | |
| { | |
| "text": "سهل", | |
| "confidence": 1.0, | |
| "start_index": 309 | |
| }, | |
| { | |
| "text": "أنا", | |
| "confidence": 1.0, | |
| "start_index": 313 | |
| }, | |
| { | |
| "text": "محمد", | |
| "confidence": 1.0, | |
| "start_index": 317 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 322 | |
| }, | |
| { | |
| "text": "إسماعيل", | |
| "confidence": 1.0, | |
| "start_index": 325 | |
| }, | |
| { | |
| "text": "(5)", | |
| "confidence": 1.0, | |
| "start_index": 333 | |
| }, | |
| { | |
| "text": "قال", | |
| "confidence": 1.0, | |
| "start_index": 337 | |
| }, | |
| { | |
| "text": "t_{n+1}", | |
| "confidence": 1.0, | |
| "start_index": 341 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
| "start_index": 349 | |
| }, | |
| { | |
| "text": "t_n", | |
| "confidence": 1.0, | |
| "start_index": 351 | |
| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 355 | |
| }, | |
| { | |
| "text": "\\alpha", | |
| "confidence": 1.0, | |
| "start_index": 357 | |
| }, | |
| { | |
| "text": "\\nabla", | |
| "confidence": 1.0, | |
| "start_index": 364 | |
| }, | |
| { | |
| "text": "f(t_n)", | |
| "confidence": 1.0, | |
| "start_index": 371 | |
| }, | |
| { | |
| "text": "##", | |
| "confidence": 1.0, | |
| "start_index": 378 | |
| }, | |
| { | |
| "text": "مبرهنة", | |
| "confidence": 1.0, | |
| "start_index": 381 | |
| }, | |
| { | |
| "text": "سعيد", | |
| "confidence": 1.0, | |
| "start_index": 388 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 393 | |
| }, | |
| { | |
| "text": "العاص", | |
| "confidence": 1.0, | |
| "start_index": 396 | |
| }, | |
| { | |
| "text": "الأموي", | |
| "confidence": 1.0, | |
| "start_index": 402 | |
| }, | |
| { | |
| "text": "القرشي", | |
| "confidence": 1.0, | |
| "start_index": 409 | |
| }, | |
| { | |
| "text": "سمع", | |
| "confidence": 1.0, | |
| "start_index": 416 | |
| }, | |
| { | |
| "text": "عمر", | |
| "confidence": 1.0, | |
| "start_index": 420 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 424 | |
| }, | |
| { | |
| "text": "الخطاب", | |
| "confidence": 1.0, | |
| "start_index": 427 | |
| }, | |
| { | |
| "text": "وعثمان", | |
| "confidence": 1.0, | |
| "start_index": 434 | |
| }, | |
| { | |
| "text": "وعائشة", | |
| "confidence": 1.0, | |
| "start_index": 441 | |
| }, | |
| { | |
| "text": "سمع", | |
| "confidence": 1.0, | |
| "start_index": 448 | |
| }, | |
| { | |
| "text": "منه", | |
| "confidence": 1.0, | |
| "start_index": 452 | |
| }, | |
| { | |
| "text": "سالم", | |
| "confidence": 1.0, | |
| "start_index": 456 | |
| }, | |
| { | |
| "text": "وابنه", | |
| "confidence": 1.0, | |
| "start_index": 461 | |
| }, | |
| { | |
| "text": "يحيى", | |
| "confidence": 1.0, | |
| "start_index": 467 | |
| }, | |
| { | |
| "text": "وقال", | |
| "confidence": 1.0, | |
| "start_index": 472 | |
| }, | |
| { | |
| "text": "سعيد", | |
| "confidence": 1.0, | |
| "start_index": 477 | |
| }, | |
| { | |
| "text": "بن", | |
| "confidence": 1.0, | |
| "start_index": 482 | |
| }, | |
| { | |
| "text": "يحيى", | |
| "confidence": 1.0, | |
| "start_index": 485 | |
| }, | |
| { | |
| "text": "كنية", | |
| "confidence": 1.0, | |
| "start_index": 490 | |
| }, | |
| { | |
| "text": "سعيد", | |
| "confidence": 1.0, | |
| "start_index": 495 | |
| }, | |
| { | |
| "text": "أبو", | |
| "confidence": 1.0, | |
| "start_index": 500 | |
| }, | |
| { | |
| "text": "\\frac{\\partial", | |
| "confidence": 1.0, | |
| "start_index": 504 | |
| }, | |
| { | |
| "text": "k}{\\partial", | |
| "confidence": 1.0, | |
| "start_index": 519 | |
| }, | |
| { | |
| "text": "z}", | |
| "confidence": 1.0, | |
| "start_index": 531 | |
| }, | |
| { | |
| "text": "=", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\lim_{h", | |
| "confidence": 1.0, | |
| "start_index": 536 | |
| }, | |
| { | |
| "text": "\\to", | |
| "confidence": 1.0, | |
| "start_index": 544 | |
| }, | |
| { | |
| "text": "0}", | |
| "confidence": 1.0, | |
| "start_index": 548 | |
| }, | |
| { | |
| "text": "\\frac{\\sin(z", | |
| "confidence": 1.0, | |
| "start_index": 551 | |
| }, | |
| { | |
| "text": "+", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "h)", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 569 | |
| }, | |
| { | |
| "text": "\\sin(z)}{h}", | |
| "confidence": 1.0, | |
| "start_index": 571 | |
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| ], | |
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| "minimum_page_confidence_score": 1.0 | |
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| "top_left_y": 32, | |
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| "bottom_right_y": 48, | |
| "content": "مبرهنة", | |
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| "content": "أبو الفضل محمد بن ناصر أنا أبو الفضل بن خيرون وأبو الحسين بن الطيوري وأبو الغنائم", | |
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| "bottom_right_y": 234, | |
| "content": "واللفظ له قالوا أنا عبد الوهاب بن محمد زاد ابن", | |
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| "content": "\\nabla_{j} J(j) = \\frac{1}{m} X^T ( \\sigma(X j) - Y )", | |
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| "bottom_right_y": 378, | |
| "content": "خيرون ومحمد بن الحسن قالا أنا أحمد بن عبدان أنا محمد بن سهل أنا محمد بن إسماعيل (5) قال", | |
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| "content": "t_{n+1} = t_n - \\alpha \\nabla f(t_n)", | |
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| "top_left_x": 32, | |
| "top_left_y": 487, | |
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| "bottom_right_y": 532, | |
| "content": "سعيد بن العاص الأموي القرشي سمع عمر بن الخطاب وعثمان وعائشة سمع منه سالم وابنه يحيى وقال سعيد بن يحيى كنية سعيد أبو", | |
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| "top_left_x": 32, | |
| "top_left_y": 538, | |
| "bottom_right_x": 537, | |
| "bottom_right_y": 591, | |
| "content": "\\frac{\\partial k}{\\partial z} = \\lim_{h \\to 0} \\frac{\\sin(z + h) - \\sin(z)}{h}", | |
| "type": "text", | |
| "confidence_scores": null, | |
| "reading_index": 12 | |
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| "language": "ar", | |
| "script": "arabic", | |
| "direction": "rtl", | |
| "augmentation": null | |
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