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

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

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"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.