"q.e.d. (quod erat demonstrandum)" (Latin)

What does the Latin term q.e.d. (quod erat demonstrandum) mean?

"Q.E.D." is an abbreviation derived from the Latin phrase "quod erat demonstrandum," which translates to "which was to be demonstrated" in English. It is used at the end of a proof or argument to signify that the desired outcome or conclusion has been successfully demonstrated or proven. It serves as a concise way to indicate the completion of a logical argument or mathematical proof.

Examples in Sentences

Here are three example sentences:

After a series of rigorous mathematical calculations, the equation simplifies to 2x + 5 = 13. Solving for x yields x = 4. Q.E.D.
The scientific experiment yielded consistent results across multiple trials, supporting the hypothesis that A leads to B. Q.E.D.
By analyzing historical data and conducting statistical tests, the researchers conclusively demonstrated a correlation between smoking and lung cancer incidence. Q.E.D.