1 line
114 KiB
JSON
1 line
114 KiB
JSON
|
{"embedding_dim": 1024, "data": [{"__id__": "rel-ae3f638be76012d98393202f750542b3", "__created_at__": 1753235760, "src_id": "三角不等式", "tgt_id": "欧几里得第五公理", "content": "三角不等式\t欧几里得第五公理\nangle comparison,mathematical foundation\nEuclid's fifth postulate is applied in the proof to establish angle relationships supporting the triangle inequality.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-e3c9f606eb2d48c5e37f2c2d8bff69ed", "__created_at__": 1753235760, "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 |AB|+|BC|>|AC|.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-039ba025f89bcd6d36103f7ef75d76ca", "__created_at__": 1753235766, "src_id": "三角不等式", "tgt_id": "几何原本", "content": "三角不等式\t几何原本\ngeometric principles,historical reference\nThe proof references Proposition 19 from Euclid's Elements to justify the relationship between angles and sides.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-6144c8f85132b7365b9799eef55d09c1", "__created_at__": 1753235766, "src_id": "三角形ABC", "tgt_id": "点P", "content": "三角形ABC\t点P\nangle proof,internal point\nPoint P is an arbitrary internal point used to prove that ∠BPC > ∠A, demonstrating angle relationships within the triangle.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-37e6f8ce2b52adfdbedbf5458829145f", "__created_at__": 1753235766, "src_id": "三角形ABC", "tgt_id": "点D", "content": "三角形ABC\t点D\nconstruction,geometric manipulation\nPoint D is constructed within the proof to extend AB and create an isosceles triangle, aiding in the demonstration of the triangle inequality.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-0690c6c3dffa43e58c067410c23810f1", "__created_at__": 1753235766, "src_id": "角∠BCD", "tgt_id": "角∠BDC", "content": "角∠BCD\t角∠BDC\nangle equality,isosceles properties\nThese angles are equal in measure due to the isosceles property of triangle BCD.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-34d0503289f0ce6c719fad737c47ac3a", "__created_at__": 1753235766, "src_id": "三角形BCD", "tgt_id": "线段DC", "content": "三角形BCD\t线段DC\nauxiliary construction,geometric formation\nSegment DC forms one side of the constructed isosceles triangle BCD.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-d4bf6ded658d08c34b9ab19a92ecc42a", "__created_at__": 1753235766, "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\nThe fifth postulate is one of the foundational elements in Euclid's Elements.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-67bf295529ac8beed8a2efee8a5258dd", "__created_at__": 1753235766, "src_id": "点D", "tgt_id": "直线AB", "content": "点D\t直线AB\ngeometric construction,proof technique\nPoint D is constructed by extending line AB to create the proof's geometric configuration.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-815c9e7f8e7a204e1f24036fe6acc705", "__created_at__": 1753235771, "src_id": "角∠ACD", "tgt_id": "角∠ADC", "content": "角∠ACD\t角∠ADC\nEuclidean principles,angle comparison\nEuclid's fifth postulate establishes that ∠ACD > ∠ADC in this configuration.", "source_id": "chunk-4ed981658aa2a32c616f4cf86c4efbaa", "file_path": "JiHe.docx"}, {"__id__": "rel-2bea8cd56f2052300952cb213e2b39c0", "__created_at__": 1753235772, "src_id": "边AC", "tgt_id": "边AD", "content": "边AC\t边AD
|