Quod erat demonstrandum definitions
| Word backwards | douq tare mudnartsnomed |
|---|---|
| Part of speech | This phrase is a Latin expression meaning "which was to be demonstrated" and is typically used as an indication that the preceding statement or proof is complete. In this context, "quod erat demonstrandum" is an adverbial phrase. |
| Syllabic division | quod e-rat de-mon-stran-dum |
| Plural | The plural of "quod erat demonstrandum" is "quae erant demonstranda". |
| Total letters | 21 |
| Vogais (4) | u,o,e,a |
| Consonants (7) | q,d,r,t,m,n,s |
Quod erat demonstrandum (abbreviated as Q.E.D.) is a Latin phrase that translates to "which was to be demonstrated" in English. It is commonly used at the end of mathematical proofs to signify that the statement or theorem that was to be proven has indeed been proven.
Quod erat demonstrandum is typically written at the end of a proof following the conclusion, serving as a way to signal the completion of the logical argument. This phrase has been used for centuries in formal mathematical and philosophical contexts as a mark of achievement and completion.
Origin of Quod Erat Demonstrandum
The use of quod erat demonstrandum can be traced back to ancient Greece, where it was originally written as "ὅπερ ἔδει δεῖξαι" in Greek. The phrase was later adopted into Latin and became a staple in mathematical writings.
Symbolic Meaning
When quod erat demonstrandum is written at the end of a proof, it signifies that the mathematical argument has been successfully concluded, and the initial claim has been proven beyond doubt. This phrase indicates that the proof is now complete and the desired result has been achieved.
Common Usage
While quod erat demonstrandum is commonly used in mathematical proofs, it has also found its way into other fields such as philosophy and rhetoric. The phrase serves as a way to denote the completion of an argument or the establishment of a truth.
In conclusion, quod erat demonstrandum is a powerful and timeless phrase that symbolizes the successful completion of a logical argument or proof. Its use in mathematical discourse highlights the rigor and precision required in mathematical reasoning, making it a fundamental part of the language of mathematics.
Quod erat demonstrandum Examples
- I have proven my point beyond doubt, quod erat demonstrandum.
- The conclusion of the experiment was as expected, quod erat demonstrandum.
- After analyzing the data, the hypothesis was confirmed, quod erat demonstrandum.
- The theorem has been successfully demonstrated, quod erat demonstrandum.
- The mathematical proof ended with the phrase quod erat demonstrandum.
- The argument was sound and logical, quod erat demonstrandum.
- The evidence supports the theory, quod erat demonstrandum.
- The results of the study speak for themselves, quod erat demonstrandum.
- The prediction was accurate, quod erat demonstrandum.
- The software performed as expected, quod erat demonstrandum.