quod erat demonstrandum

简明释义

被论证过

英英释义

例句

1.The lawyer presented her evidence clearly and ended her argument with quod erat demonstrandum, 这就是要证明的.

律师清晰地呈现了她的证据，并以quod erat demonstrandum结束了她的论点，这就是要证明的.

2.The physicist derived the equation and confidently wrote quod erat demonstrandum at the bottom, 这就是要证明的.

物理学家推导出这个方程，自信地在底部写下quod erat demonstrandum，这就是要证明的.

3.After proving the theorem, the mathematician concluded with a satisfied smile, quod erat demonstrandum, 这就是要证明的.

在证明完这个定理后，数学家满意地微笑着说，quod erat demonstrandum，这就是要证明的.

4.After demonstrating the principle through experiments, she said quod erat demonstrandum, 这就是要证明的.

在通过实验展示原理后，她说quod erat demonstrandum，这就是要证明的.

5.In his final remarks, he stated, quod erat demonstrandum, 这就是要证明的, leaving no doubt about his findings.

在他的最后发言中，他表示，quod erat demonstrandum，这就是要证明的，毫无疑问他所发现的结果.

作文

In the realm of mathematics and logic, the phrase quod erat demonstrandum serves as a powerful conclusion to a proof or argument. This Latin expression translates to 'which was to be demonstrated' in English and is often abbreviated as Q.E.D. The use of this phrase can be traced back to ancient Greek philosophers, but it became widely popularized during the Renaissance, particularly in the works of mathematicians and scientists. Understanding the significance of quod erat demonstrandum not only enriches our appreciation for mathematical proofs but also enhances our critical thinking skills in various fields.Mathematics is fundamentally about establishing truths through logical reasoning. When a mathematician presents a theorem, they do not simply state it; they provide a rigorous proof that demonstrates its validity. This process often involves a series of logical steps, each building upon the previous one. Once the proof reaches its conclusion, the mathematician may write quod erat demonstrandum to signify that they have successfully demonstrated the theorem's truth. This practice is not merely a formality; it reinforces the importance of evidence and rationale in the pursuit of knowledge.Beyond mathematics, the concept encapsulated by quod erat demonstrandum extends to various disciplines, including science, philosophy, and even everyday decision-making. In science, for instance, researchers formulate hypotheses and conduct experiments to gather data. The results must then be analyzed and interpreted to draw conclusions. When a hypothesis is supported by substantial evidence, scientists often conclude their findings with a statement that echoes the sentiment of quod erat demonstrandum. They are essentially saying that the evidence provided confirms their initial assertion.Philosophically, the idea of demonstrating a claim is central to rational discourse. When engaging in debates or discussions, individuals are expected to support their arguments with logical reasoning and empirical evidence. The ability to substantiate one's claims is crucial in persuading others and advancing knowledge. In this context, quod erat demonstrandum serves as a reminder of the responsibility we bear to provide proof for our assertions, encouraging a culture of inquiry and skepticism.In everyday life, the principles behind quod erat demonstrandum can be observed in decision-making processes. Whether we are evaluating the credibility of a news article or choosing a product based on reviews, we often seek evidence to support our choices. By applying the mindset of quod erat demonstrandum, we become more discerning consumers of information, less likely to accept claims at face value without seeking justification.In conclusion, the phrase quod erat demonstrandum embodies a fundamental principle of reasoning: the necessity of evidence and demonstration in validating claims. Its roots in mathematics highlight the importance of logical proof, while its relevance in science, philosophy, and daily life underscores its broader significance. By embracing the spirit of quod erat demonstrandum, we cultivate a culture of critical thinking and intellectual rigor, empowering ourselves to navigate an increasingly complex world with clarity and confidence.

在数学和逻辑的领域中，短语quod erat demonstrandum作为证明或论证的有力结论。这句拉丁语表达翻译成英语是“这就是要证明的”，通常缩写为Q.E.D。这个短语的使用可以追溯到古希腊哲学家，但在文艺复兴时期，尤其是在数学家和科学家的著作中，它变得广为人知。理解quod erat demonstrandum的意义不仅丰富了我们对数学证明的欣赏，也增强了我们在各个领域的批判性思维能力。数学根本上是通过逻辑推理来建立真理。当一个数学家提出一个定理时，他们不仅仅是陈述它；他们提供一个严谨的证明来证明其有效性。这个过程通常涉及一系列逻辑步骤，每一步都建立在前一步的基础上。一旦证明达到结论，数学家可能会写下quod erat demonstrandum，以表明他们成功地证明了定理的真实性。这一做法不仅仅是形式上的，它强调了在追求知识过程中证据和推理的重要性。超越数学，quod erat demonstrandum所包含的概念扩展到各种学科，包括科学、哲学，甚至日常决策。在科学中，例如，研究人员制定假设并进行实验以收集数据。然后必须分析和解释结果，以得出结论。当一个假设得到实质性证据的支持时，科学家们常常会以一种呼应quod erat demonstrandum的声明结束他们的发现。他们基本上是在说，所提供的证据证实了他们最初的主张。在哲学上，证明一个主张的思想是理性论述的核心。当参与辩论或讨论时，个人被期望用逻辑推理和实证证据来支持他们的论点。证实自己主张的能力在说服他人和推进知识方面至关重要。在这个背景下，quod erat demonstrandum提醒我们提供主张证明的责任，鼓励一种探究和怀疑的文化。在日常生活中，quod erat demonstrandum背后的原则可以在决策过程中观察到。无论我们是在评估新闻文章的可信度还是根据评论选择产品，我们通常都会寻求证据来支持我们的选择。通过应用quod erat demonstrandum的思维方式，我们成为了更具鉴别力的信息消费者，不容易在没有寻求证明的情况下接受声称。总之，短语quod erat demonstrandum体现了推理的基本原则：验证主张的必要性和证明。它在数学中的根源强调了逻辑证明的重要性，而在科学、哲学和日常生活中的相关性则突显了它的更广泛意义。通过拥抱quod erat demonstrandum的精神，我们培养了批判性思维和智力严谨的文化，使我们能够以清晰和信心应对日益复杂的世界。