📚 Year 10 Cambridge History: Quick Reference Guide to Formulae and Theorems | Year 10 Cambridge 历史：公式定理速查手册
History does not come with equations in the traditional sense, but historians rely on a set of intellectual tools every bit as rigorous as mathematical formulas. These 'theorems' are the frameworks we use to analyse causes, weigh evidence, and construct arguments. This handbook compiles the essential analytical formulae that every Year 10 Cambridge History student should keep at their fingertips.
历史学科并没有传统意义上的数学公式，但历史学家依赖一套与数学定理同样严谨的思维工具。这些“定理”正是我们用来分析原因、权衡证据并构建论证的框架。本手册汇编了每一位 Year 10 剑桥历史学生都应熟记于心的核心分析公式。
1. The Causation Formula | 因果关系公式
To understand why an event happened, apply: Long-term causes + Short-term triggers + Catalysts = Historical Event. Long-term causes are deep-rooted social, economic, or political factors; triggers are immediate sparks; catalysts speed up the process. Never reduce an event to a single cause.
要理解事件为何发生，请应用：长期原因 + 短期导火索 + 催化剂 = 历史事件。长期原因是深层的社会、经济或政治因素；导火索是直接的触发点；催化剂则加速过程。永远不要将事件归结为单一原因。
- liances, Imperialism, Nationalism (long-term) + Assassination of Archduke Franz Ferdinand (trigger) + Blank Cheque (catalyst).
- 例子：第一次世界大战 = 军国主义、同盟体系、帝国主义、民族主义（长期）+ 斐迪南大公遇刺（导火索）+ 空头支票（催化剂）。
2. The Change and Continuity Theorem | 变迁与延续性定理
Historians assess the pace and nature of transformation using: Change = (New conditions – Old conditions) / Time. But always identify what stayed the same: continuity. Real understanding comes from explaining why some things transformed while others persisted.
历史学家运用以下方式评估变迁的速度与性质：变迁 = （新状况 – 旧状况） / 时间。但同时要识别出哪些保持不变：延续性。真正的理解源自解释为何有些事物变化了，而另一些却持久存在。
Rate of Change = Magnitude of Change ÷ Duration
变化速率 = 变化程度 ÷ 持续时间
3. The Evidence Reliability Formula | 证据可靠性公式
Every source must be tested: Reliability = (Nature + Origin + Purpose) − Bias. Nature refers to the type of source (diary, speech, photograph). Origin asks who created it and when. Purpose uncovers why it was made. Subtract the distorting effect of bias to gauge how trustworthy the account is.
每一则史料都需要检验：可靠性 = （性质 + 来源 + 目的） − 偏见。性质指史料的类型（日记、演讲、照片）。来源追问是谁、何时所创。目的揭示其制作意图。减去偏见的扭曲效应，即可判断叙述的可信程度。
| Factor | 因素 | Key Question | 关键问题 |
| Nature | 性质 | What type of source is it? | 这是什么类型的史料？ |
| Origin | 来源 | Who made it and when? | 谁在何时制作了它？ |
| Purpose | 目的 | Why was it produced? | 为何被创作出来？ |
4. The Periodisation Theorem | 历史分期定理
Dividing the past into eras requires criteria: Period = Turning point events + Shared characteristics. A turning point is an event so significant that life afterwards was different. Shared characteristics might be political systems, economic structures, or cultural ideas. Remember, all period labels are later constructions.
将过去划分为时代需要标准：时期 = 转折点事件 + 共享特征。转折点事件是指发生后使生活变得不同的重大事件。共享特征可能是政治制度、经济结构或文化观念。切记，所有时代标签都是后人的构建。
5. Primary vs Secondary Source Equation | 一手与二手资料辨析公式
Classify sources with: Source type = Proximity to event × Nature of information. Primary sources are created at the time of the event or by people directly involved. Secondary sources are interpretations produced later using primary evidence. Some sources can be both depending on the question asked.
用以下公式对史料分类：史料类型 = 与事件的接近程度 × 信息的性质。一手资料是在事件发生时或由直接参与者所创。二手资料是后来利用一手证据做出的诠释。有些史料依据所问问题不同，可以兼具两种属性。
6. The Bias and Objectivity Theorem | 偏见与客观性定理
No source is perfectly objective. Use: Objectivity = 1 − Bias. Bias stems from the creator's background, beliefs, and intentions. Instead of discarding a biased source, ask: what does this bias reveal about the attitudes of the time? Bias becomes evidence itself.
没有任何史料是完全客观的。运用：客观性 = 1 − 偏见。偏见源于创作者的背景、信念和意图。不要抛弃带偏见的史料，而是反问：这种偏见揭示了当时怎样的态度？偏见本身也成了证据。
7. The Historical Significance Formula | 历史重要性公式
Judging significance uses five criteria: = Depth of impact + Number affected + Duration of legacy + Uniqueness + Relevance to today. An event is significant if it changed many people's lives deeply, lasted a long time, was unusual, and still matters now.
判断重要性使用五项标准：重要性 = 影响深度 + 受影响人数 + 遗产持续时间 + 独特性 + 与今天的关联。一个事件若能深刻改变许多人的生活、影响久远、非同寻常且至今仍有关系，则具有重要意义。
8. The Comparative Analysis Formula | 比较分析公式
To compare two cases, use: Similarity = Shared attributes; Difference = Divergent attributes. Identify points of comparison (economic, political, social) and then contrast. A strong comparative essay explains both why similarities and differences exist, linking back to causes.
比较两个案例时，使用：相似性 = 共享属性；差异性 = 分歧属性。确定比较点（经济、政治、社会）而后对照。一篇出色的比较论文既要解释相似性，也要解释差异性存在的原因，并回溯至原因层面。
9. The Interpretation Framework | 历史解释框架
Every historical account is an interpretation governed by: Interpretation = Evidence selection × Historian's perspective. Two historians using the same evidence can reach different conclusions because they emphasise different factors. Recognise historiographical debate as a normal part of the discipline.
每一则历史叙述都是一种诠释，受制于：诠释 = 证据选择 × 历史学家的视角。两位使用相同证据的历史学家可能得出不同结论，因为他们强调不同的因素。认识到史学争论是这门学科的正常组成部分。
10. Glossary of Key Historical Concepts | 核心历史概念词汇表
These are the building blocks of historical reasoning, the 'constants' in our equations.
这些是历史推理的基石，是我们方程式中的“常量”。
| Concept | 概念 | Definition | 定义 |
| Causation | 因果关系 | The relationship between cause and effect in history. | 历史中原因与结果之间的关系。 |
| Change & Continuity | 变迁与延续 | The balance between what changes and what remains the same over time. | 随时间推移，变化之物与保持不变之物间的平衡。 |
| Evidence | 证据 | Information from sources used to build historical claims. | 来自史料、用以构建历史主张的信息。 |
| Interpretation | 诠释 | A way of explaining the past shaped by the historian's viewpoint. | 受史学家观点影响而形成的一种解释过去的方式。 |
| Significance | 重要性 | The importance assigned to a historical event, person, or development. | 赋予某一历史事件、人物或发展过程的重要性。 |
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