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{"embedding_dim": 1024, "data": [{"__id__": "rel-e3c9f606eb2d48c5e37f2c2d8bff69ed", "__created_at__": 1752656860, "src_id": "三角不等式", "tgt_id": "三角形ABC", "content": "三角不等式\t三角形ABC\ngeometric proof,inequality\nThe triangle ABC is used to demonstrate the triangle inequality, showing that the sum of two sides is greater than the third.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-d4bf6ded658d08c34b9ab19a92ecc42a", "__created_at__": 1752656860, "src_id": "几何原本", "tgt_id": "欧几里得第五公理", "content": "几何原本\t欧几里得第五公理\naxiomatic system,mathematical foundation\nEuclid's Fifth Postulate is a key component of the 'Elements of Geometry,' which forms the basis for many geometric proofs.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-312e9fb6cd882487fc5723b488ac9b9e", "__created_at__": 1752656860, "src_id": "三角形ABC", "tgt_id": "几何原本", "content": "三角形ABC\t几何原本\nclassical text,geometric principles\nThe proof involving triangle ABC relies on propositions from Euclid's 'Elements,' such as the relationship between angles and sides.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-37e6f8ce2b52adfdbedbf5458829145f", "__created_at__": 1752656860, "src_id": "三角形ABC", "tgt_id": "点D", "content": "三角形ABC\t点D\ngeometric construction,proof technique\nPoint D is constructed by extending side AB of triangle ABC to demonstrate the triangle inequality.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-76b371b136495f3d9f2aba0524d5cc68", "__created_at__": 1752656860, "src_id": "点D", "tgt_id": "等腰三角形BCD", "content": "点D\t等腰三角形BCD\ngeometric construction,isosceles properties\nPoint D is connected to C to form the isosceles triangle BCD, where |BD|=|BC|.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-d7472c102dc691ce25efee0384d64ebb", "__created_at__": 1752656860, "src_id": "欧几里得第五公理", "tgt_id": "等腰三角形BCD", "content": "欧几里得第五公理\t等腰三角形BCD\naxiomatic application,proof logic\nThe properties of isosceles triangle BCD are used in conjunction with Euclid's Fifth Postulate to prove the triangle inequality.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-6144c8f85132b7365b9799eef55d09c1", "__created_at__": 1752656860, "src_id": "三角形ABC", "tgt_id": "点P", "content": "三角形ABC\t点P\ngeometric proof,interior angle\nPoint P is an arbitrary interior point of triangle ABC used to prove that ∠BPC > ∠A.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-54cd96c45458db594af46354860512a2", "__created_at__": 1752656860, "src_id": "命题19", "tgt_id": "点P", "content": "命题19\t点P\nangle comparison,geometric proposition\nThe proof involving point P uses Proposition 19 from Euclid's Elements to compare angles and sides.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-67bf295529ac8beed8a2efee8a5258dd", "__created_at__": 1752656860, "src_id": "点D", "tgt_id": "直线AB", "content": "点D\t直线AB\nline extension,proof construction\nLine AB is extended to create point D, which is essential for constructing the proof of the triangle inequality.", "source_id": "chunk-d4c4f366a47f3e13da193e0b600addae", "file_path": "unknown_source"}, {"__id__": "rel-c1933338c2519d138024b54332ba34fa", "__created_at__": 1752656860, "src_id": "AC", "tgt_id": "BP", "content": "AC\tBP\ngeometric intersection,line segments\nBP intersects AC at point D in the geometric figure.", "source_id": "chunk-618195be0ad6c05ea189e352a4c2e7bb", "file_path": "unknown_source"}, {"__id__": "rel-a0120be6d72710158ad1d7314522045b", "__created_at__": 1752656860, "
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