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| <strong class="Latn headword" lang="la">theōrēma</strong><p>From <span class="etyl">[https://en.wikipedia.org/wiki/Ancient_Greek Ancient Greek]</span> <em class="Polyt mention" lang="grc">[https://en.wiktionary.org/wiki/%CE%B8%CE%B5%CF%8E%CF%81%CE%B7%CE%BC%CE%B1#Ancient_Greek θεώρημα]</em> <span class="mention-gloss-paren annotation-paren">(</span><span class="mention-tr tr Latn" lang="grc-Latn">theṓrēma</span>, <span class="mention-gloss-double-quote">“</span><span class="mention-gloss">speculation, proposition to be proved</span><span class="mention-gloss-double-quote">”</span><span class="mention-gloss-paren annotation-paren">)</span> (Euclid), from <em class="Polyt mention" lang="grc">[https://en.wiktionary.org/wiki/%CE%B8%CE%B5%CF%89%CF%81%CE%AD%CF%89#Ancient_Greek θεωρέω]</em> <span class="mention-gloss-paren annotation-paren">(</span><span class="mention-tr tr Latn" lang="grc-Latn">theōréō</span>, <span class="mention-gloss-double-quote">“</span><span class="mention-gloss">I look at, view, consider, examine</span><span class="mention-gloss-double-quote">”</span><span class="mention-gloss-paren annotation-paren">)</span>, from <em class="Polyt mention" lang="grc">[https://en.wiktionary.org/wiki/%CE%B8%CE%B5%CF%89%CF%81%CF%8C%CF%82#Ancient_Greek θεωρός]</em> <span class="mention-gloss-paren annotation-paren">(</span><span class="mention-tr tr Latn" lang="grc-Latn">theōrós</span>, <span class="mention-gloss-double-quote">“</span><span class="mention-gloss">spectator</span><span class="mention-gloss-double-quote">”</span><span class="mention-gloss-paren annotation-paren">)</span>, from <em class="Polyt mention" lang="grc">[https://en.wiktionary.org/wiki/%CE%B8%CE%AD%CE%B1#Ancient_Greek θέα]</em> <span class="mention-gloss-paren annotation-paren">(</span><span class="mention-tr tr Latn" lang="grc-Latn">théa</span>, <span class="mention-gloss-double-quote">“</span><span class="mention-gloss">a view</span><span class="mention-gloss-double-quote">”</span><span class="mention-gloss-paren annotation-paren">)</span> + <em class="Polyt mention" lang="grc">[https://en.wiktionary.org/wiki/%E1%BD%81%CF%81%CE%AC%CF%89#Ancient_Greek ὁράω]</em> <span class="mention-gloss-paren annotation-paren">(</span><span class="mention-tr tr Latn" lang="grc-Latn">horáō</span>, <span class="mention-gloss-double-quote">“</span><span class="mention-gloss">I see, look</span><span class="mention-gloss-double-quote">”</span><span class="mention-gloss-paren annotation-paren">)</span>.</p> | | <span class="headword-line">[[theōrēma]]</span> (lat.), {{dt.-lat.-grie.}} ‘‚[[Angeschautes]], [[Untersuchung]], [[Lehrsatz]]‘; "[[Naturgesetz]] oder [[Physikalisches Gesetz]]" |
| === <span id="Pronunciation_2">Pronunciation</span> ===
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| *<span class="ib-brac">(</span><span class="ib-content">[https://en.wikipedia.org/wiki/Classical_Latin Classical]</span><span class="ib-brac">)</span> [https://en.wiktionary.org/wiki/Wiktionary:International_Phonetic_Alphabet IPA]<sup>([https://en.wiktionary.org/wiki/Appendix:Latin_pronunciation key])</sup>: <span class="IPA">/tʰe.oːˈreː.ma/</span>, <span class="IPA">[t̪ʰeoːˈreːmä]</span> | | * Theorem ‘‚Angeschautes, Untersuchung, Lehrsatz‘; |
| *<span class="ib-brac">(</span><span class="ib-content">[https://en.wikipedia.org/wiki/Latin_phonology_and_orthography#Ecclesiastical_pronunciation modern Italianate Ecclesiastical]</span><span class="ib-brac">)</span> [https://en.wiktionary.org/wiki/Wiktionary:International_Phonetic_Alphabet IPA]<sup>([https://en.wiktionary.org/wiki/Appendix:Latin_pronunciation key])</sup>: <span class="IPA">/te.oˈre.ma/</span>, <span class="IPA">[t̪eoˈrɛːmä]</span> | | ** ursprünglich nach Euklid grie. ''[[theṓrēma]] θεώρημᾰ'' „Mutmaßung, zu beweisender [[Satz]]“ (Euklid), |
| | | ** allgemein ein [[Lehrsatz]] einer [[Lehrmeinung]] oder den Bestandteil einer wissenschaftlichen [[Theorie]]; |
| === <span id="Noun_2">Noun</span> ===
| | *** spezieller „die erklärten Sätze (Aussagen, Normen) eines Systems“ bzw. die in einer Theorie bewiesene [[Aussage]] respektive einen bewiesenen Satz. |
| <p><span class="headword-line"><strong class="Latn headword" lang="la">theōrēma</strong> <span class="gender"><abbr title="neuter gender">n</abbr></span> (''genitive'' <strong class="Latn" lang="la">[https://en.wiktionary.org/wiki/theorematis#Latin theōrēmatis]</strong>)</span>; ''[https://en.wiktionary.org/wiki/Appendix:Latin_third_declension third declension]''</p>
| | ** In einer [[axiomatisch]]-[[deduktiv|deduktiven]] Theorie bedeutet ''Theorem'' in einem engeren Sinn „der aus den [[Axiomen]][[logisch]] abgeleitete Satz“. |
| #a [https://en.wiktionary.org/wiki/theorem theorem], a [https://en.wiktionary.org/wiki/proposition proposition] to be proved
| | *** Teilweise werden dann auch die Axiome als Theoreme der Theorie bezeichnet. |
| | | ** In der [[Mathematik]] spricht man statt vom Theorem oder Lehrsatz oft auch einfach vom [[Satz (Mathematik)]]. |
| ==== <span id="Declension">Declension</span> ====
| | *** Damit er als wahr anerkannt wird, muss er aus den Axiomen der Theorie mit den [[Schlussregeln]] der Theorie [[bewiesen]] werden. (s. ([[Beweis (Mathematik)]]) |
| <p>[https://en.wiktionary.org/wiki/Appendix:Latin_third_declension Third-declension] noun (neuter, imparisyllabic non-i-stem).</p>
| | ** In der [[Physik]] nennt man einen Lehrsatz auch ein [[Naturgesetz]] oder [[Physikalisches Gesetz]]. |
| {| class="wikitable inflection-table inflection-table-la"
| | *** Im Unterschied zur Mathematik spielt hier der Bezug zur [[Wirklichkeit]] eine entscheidende Rolle. |
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| | *** Der Lehrsatz muss durch [[Experimente]] als [[adäquat]] nachgewiesen werden. |
| ! class="corner-header" | Case
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| ! class="number-header" | Singular
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| ! class="number-header" | Plural
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| ! class="case-header" | [https://en.wiktionary.org/wiki/nominative_case Nominative]
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| | class="form-cell" | <span class="Latn form-of lang-la nom|s-form-of origin-theōrēma" lang="la"><strong class="selflink">theōrēma</strong></span>
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| | class="form-cell" | <span class="Latn form-of lang-la nom|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theoremata#Latin theōrēmata]</span>
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| |-
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| ! class="case-header" | [https://en.wiktionary.org/wiki/genitive_case Genitive]
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| | class="form-cell" | <span class="Latn form-of lang-la gen|s-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theorematis#Latin theōrēmatis]</span>
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| | class="form-cell" | <span class="Latn form-of lang-la gen|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theorematum#Latin theōrēmatum]</span>
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| |-
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| ! class="case-header" | [https://en.wiktionary.org/wiki/dative_case Dative]
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| | class="form-cell" | <span class="Latn form-of lang-la dat|s-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theoremati#Latin theōrēmatī]</span>
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| | class="form-cell" | <span class="Latn form-of lang-la dat|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theorematis#Latin theōrēmatīs]</span>
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| |-
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| ! class="case-header" | [https://en.wiktionary.org/wiki/accusative_case Accusative]
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| | class="form-cell" | <span class="Latn form-of lang-la acc|s-form-of origin-theōrēma" lang="la"><strong class="selflink">theōrēma</strong></span>
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| | class="form-cell" | <span class="Latn form-of lang-la acc|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theoremata#Latin theōrēmata]</span>
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| |-
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| ! class="case-header" | [https://en.wiktionary.org/wiki/ablative_case Ablative]
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| | class="form-cell" | <span class="Latn form-of lang-la abl|s-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theoremate#Latin theōrēmate]</span>
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| | class="form-cell" | <span class="Latn form-of lang-la abl|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theorematis#Latin theōrēmatīs]</span>
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| |-
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| ! class="case-header" | [https://en.wiktionary.org/wiki/vocative_case Vocative]
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| | class="form-cell" | <span class="Latn form-of lang-la voc|s-form-of origin-theōrēma" lang="la"><strong class="selflink">theōrēma</strong></span>
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| | class="form-cell" | <span class="Latn form-of lang-la voc|p-form-of origin-theōrēma" lang="la">[https://en.wiktionary.org/wiki/theoremata#Latin theōrēmata]</span>
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| |}
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theōrēma (lat.), Vorlage:dt.-lat.-grie. ‘‚Angeschautes, Untersuchung, Lehrsatz‘; "Naturgesetz oder Physikalisches Gesetz"
- Theorem ‘‚Angeschautes, Untersuchung, Lehrsatz‘;
- ursprünglich nach Euklid grie. theṓrēma θεώρημᾰ „Mutmaßung, zu beweisender Satz“ (Euklid),
- allgemein ein Lehrsatz einer Lehrmeinung oder den Bestandteil einer wissenschaftlichen Theorie;
- spezieller „die erklärten Sätze (Aussagen, Normen) eines Systems“ bzw. die in einer Theorie bewiesene Aussage respektive einen bewiesenen Satz.
- In einer axiomatisch-deduktiven Theorie bedeutet Theorem in einem engeren Sinn „der aus den Axiomenlogisch abgeleitete Satz“.
- Teilweise werden dann auch die Axiome als Theoreme der Theorie bezeichnet.
- In der Mathematik spricht man statt vom Theorem oder Lehrsatz oft auch einfach vom Satz (Mathematik).
- In der Physik nennt man einen Lehrsatz auch ein Naturgesetz oder Physikalisches Gesetz.
- Im Unterschied zur Mathematik spielt hier der Bezug zur Wirklichkeit eine entscheidende Rolle.
- Der Lehrsatz muss durch Experimente als adäquat nachgewiesen werden.
