quod erat demonstrandum

简明释义

证完

英英释义

例句

1.The lawyer presented all the evidence and concluded with quod erat demonstrandum to emphasize the validity of his case.

律师展示了所有证据，并以quod erat demonstrandum结束，以强调他案件的有效性。

2.In her dissertation, she included the phrase quod erat demonstrandum after proving her main hypothesis.

在她的论文中，她在证明了她的主要假设后包含了短语quod erat demonstrandum。

3.The mathematician concluded his proof with the statement that the triangle's angles equal 180 degrees, thus he wrote quod erat demonstrandum to signify that this was what he set out to prove.

这位数学家在他的证明中以三角形的角度总和为180度作为结论，因此他写下了quod erat demonstrandum，以表明这是他所要证明的内容。

4.In his lecture on logic, the professor used quod erat demonstrandum to indicate the conclusion of his argument.

在他的逻辑讲座中，教授使用quod erat demonstrandum来表示他论证的结论。

5.After demonstrating the theory of relativity through various experiments, the physicist confidently stated quod erat demonstrandum to mark the completion of his argument.

在通过各种实验证明相对论后，这位物理学家自信地说quod erat demonstrandum，以标志着他论证的完成。

作文

In the realm of mathematics and logic, the phrase quod erat demonstrandum is often used to conclude a proof or argument. This Latin expression translates to 'which was to be demonstrated' and serves as a formal way to indicate that the desired conclusion has been reached. The use of this phrase can be traced back to ancient mathematicians and philosophers who sought to provide clear and definitive evidence for their claims. Understanding the significance of quod erat demonstrandum is essential not only for students of mathematics but also for anyone engaged in logical reasoning or critical thinking.To illustrate the importance of quod erat demonstrandum, consider a simple mathematical theorem. Suppose we want to prove that the sum of two even numbers is always even. We start by defining what an even number is: an integer that can be expressed in the form 2n, where n is an integer. Let’s take two even numbers, say 2a and 2b, where a and b are integers. When we add these two even numbers together, we get:2a + 2b = 2(a + b).Since a + b is also an integer, we can express the result as 2 times some integer, which means that the sum is even. Therefore, we have successfully demonstrated our claim. We can conclude this proof with the phrase quod erat demonstrandum, signifying that we have shown what we set out to prove.The elegance of quod erat demonstrandum lies in its ability to encapsulate the essence of logical deduction. It is a reminder that every argument must be supported by evidence and that conclusions must follow logically from premises. In a world filled with misinformation and unfounded claims, the principles behind quod erat demonstrandum become increasingly relevant. It encourages us to seek out proof and to question assertions that lack substantiation.Beyond mathematics, the concept of quod erat demonstrandum can be applied in various fields, including science, philosophy, and law. In scientific research, for example, hypotheses must be tested and validated through rigorous experimentation. Once sufficient evidence is gathered to support a hypothesis, researchers can confidently assert their findings, effectively saying quod erat demonstrandum to the scientific community.In philosophy, arguments are structured in a way that requires each premise to lead logically to the conclusion. Philosophers often engage in debates where they must defend their positions with sound reasoning. At the end of a well-structured argument, one might declare quod erat demonstrandum to emphasize that they have fulfilled their obligation to demonstrate the truth of their assertions.In legal contexts, the principle of quod erat demonstrandum is also applicable. Lawyers must present evidence and build a case that leads to a clear conclusion of guilt or innocence. The jury's verdict is the ultimate demonstration of whether the prosecution or defense has successfully proven their case. In this sense, quod erat demonstrandum serves as a powerful reminder of the necessity for clarity and proof in matters of justice.In conclusion, the phrase quod erat demonstrandum embodies the fundamental principles of logic, proof, and evidence. Its application extends beyond mathematics into various domains of human thought and discourse. By embracing the spirit of quod erat demonstrandum, we can cultivate a culture of inquiry, skepticism, and rationality, ensuring that our conclusions are well-founded and demonstrably true. As we navigate the complexities of information in the modern world, let us remember the importance of proving our claims, for it is through demonstration that we attain knowledge and understanding.

在数学和逻辑的领域中，短语quod erat demonstrandum常常用于结束一个证明或论证。这个拉丁表达的意思是“这是要证明的”，并作为一种正式的方式来表明所希望的结论已经达到。这个短语的使用可以追溯到古代的数学家和哲学家，他们试图为自己的主张提供清晰而明确的证据。理解quod erat demonstrandum的重要性不仅对数学学生至关重要，对任何参与逻辑推理或批判性思维的人来说也是如此。为了说明quod erat demonstrandum的重要性，考虑一个简单的数学定理。假设我们想证明两个偶数的和总是偶数。我们首先定义什么是偶数：一个可以用2n的形式表示的整数，其中n是一个整数。让我们取两个偶数，例如2a和2b，其中a和b是整数。当我们将这两个偶数相加时，我们得到：2a + 2b = 2(a + b)。由于a + b也是一个整数，我们可以将结果表示为2乘以某个整数，这意味着和是偶数。因此，我们成功地证明了我们的主张。我们可以用短语quod erat demonstrandum来结束这个证明，表明我们已经展示了我们所要证明的内容。quod erat demonstrandum的优雅之处在于它能够概括逻辑推理的本质。它提醒我们，每一个论点都必须有证据支持，结论必须合乎逻辑地从前提中得出。在充满错误信息和没有根据的主张的世界中，quod erat demonstrandum背后的原则变得越来越相关。它鼓励我们寻找证据，并质疑缺乏证实的主张。除了数学之外，quod erat demonstrandum的概念还可以应用于多个领域，包括科学、哲学和法律。例如，在科学研究中，假设必须通过严格的实验进行测试和验证。一旦收集到足够的证据来支持一个假设，研究人员就可以自信地断言他们的发现，有效地对科学界说quod erat demonstrandum。在哲学中，论证的结构要求每个前提逻辑地引导到结论。哲学家们经常参与辩论，他们必须用合理的推理来捍卫自己的立场。在一个结构良好的论证结束时，人们可能会宣称quod erat demonstrandum，以强调他们已经履行了证明其主张真实性的义务。在法律背景下，quod erat demonstrandum的原则同样适用。律师必须提出证据并建立一个明确的案情，以得出有罪或无罪的结论。陪审团的裁决是最终证明检方或辩方是否成功证明其案件的演示。从这个意义上说，quod erat demonstrandum作为一个强有力的提醒，强调了在司法事务中清晰和证据的必要性。总之，短语quod erat demonstrandum体现了逻辑、证明和证据的基本原则。它的应用超越了数学，延伸到人类思想和话语的各个领域。通过拥抱quod erat demonstrandum的精神，我们可以培养一种探究、怀疑和理性的文化，确保我们的结论是有根据的且可证明的。在我们在现代世界中应对信息的复杂性时，让我们记住证明我们的主张的重要性，因为正是通过证明我们才能获得知识和理解。