Legal Definitions - Quod erat demonstrandum

Quod erat demonstrandum, often abbreviated as Q.E.D., is a Latin phrase meaning "which was to be demonstrated." It is traditionally placed at the end of a mathematical proof or a logical argument to signify that the initial proposition or argument has been conclusively proven or established.

Here are some examples illustrating its application:

• Imagine a mathematician working through a complex geometric proof. After several pages of axioms, postulates, and logical deductions, they arrive at the final statement that directly confirms the theorem they set out to prove. Concluding with Q.E.D. would signal that the entire process has successfully demonstrated the truth of the theorem.

  This illustrates the term in its classic academic context, where a series of logical steps leads to an undeniable conclusion, fulfilling the initial goal of the demonstration.

• Consider a lawyer presenting a detailed argument in a legal brief, aiming to convince a judge that a particular legal precedent applies to their client's case. The lawyer meticulously cites previous rulings, analyzes statutory language, and explains how the facts of their case align perfectly with the established law. After laying out all the compelling evidence and legal reasoning, the lawyer might implicitly or explicitly convey a "Q.E.D." moment, asserting that they have definitively proven the applicability of the precedent.

  In this scenario, Q.E.D. signifies that the lawyer believes they have presented an unassailable argument, demonstrating the legal point they intended to establish.

• A scientist conducts an experiment to test a hypothesis about a new drug's effectiveness. After meticulously designing the study, collecting data, and performing statistical analysis, the results consistently show a significant positive effect, far beyond what could be attributed to chance. When presenting their findings, the scientist might conclude by stating that their research has unequivocally demonstrated the drug's efficacy, effectively reaching a "Q.E.D." point for their initial hypothesis.

  Here, Q.E.D. highlights the successful empirical demonstration of a scientific hypothesis, where the evidence gathered directly supports and proves the initial claim.