Miedzy oczywistością a dedukcją. Platon i Euklides o równości
We confront Plato's understanding of equality in geometry with that of Euclid. We comment on Phaedo, 74b-c, Meno, 81e-85d and Elements, Book I. We distinguish between two meanings of equality, congruence and equality of the area, and show that in Plato equality means congruence. In Euclid, star...
| Main Authors: | , |
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| Format: | Article |
| Language: | deu |
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Copernicus Center Press
2011-06-01
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| Series: | Zagadnienia Filozoficzne w Nauce |
| Subjects: | |
| Online Access: | http://zfn.edu.pl/index.php/zfn/article/view/143 |
| _version_ | 1818360125286514688 |
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| author | Piotr Błaszczyk Kazimierz Mrówka |
| author_facet | Piotr Błaszczyk Kazimierz Mrówka |
| author_sort | Piotr Błaszczyk |
| collection | DOAJ |
| description | We confront Plato's understanding of equality in geometry with that of Euclid. We comment on Phaedo, 74b-c, Meno, 81e-85d and Elements, Book I. We distinguish between two meanings of equality, congruence and equality of the area, and show that in Plato equality means congruence. In Euclid, starting with the first definitions until Proposition I.34, equality means congruence. In the proof of Proposition I.35 equality gains a new meaning and two figures that are not congruent, and in this sense unequal, are considered to be equal. While Plato's geometry is based on self-evident facts, Euclid's geometry rests on deduction and the axioms that are by no means self-evident. However, the shift of meaning from congruence to equality of the area can be substantiated by reference to Euclid's axioms of equality. Finally, we present an ontological interpretation of the two attitudes to equality that we find in Plato's and Euclid's writings. |
| first_indexed | 2024-12-13T20:55:49Z |
| format | Article |
| id | doaj.art-b23918e2b18940a2ae04225e497c8e35 |
| institution | Directory Open Access Journal |
| issn | 0867-8286 2451-0602 |
| language | deu |
| last_indexed | 2024-12-13T20:55:49Z |
| publishDate | 2011-06-01 |
| publisher | Copernicus Center Press |
| record_format | Article |
| series | Zagadnienia Filozoficzne w Nauce |
| spelling | doaj.art-b23918e2b18940a2ae04225e497c8e352022-12-21T23:31:46ZdeuCopernicus Center PressZagadnienia Filozoficzne w Nauce0867-82862451-06022011-06-0148127147137Miedzy oczywistością a dedukcją. Platon i Euklides o równościPiotr Błaszczyk0Kazimierz Mrówka1Uniwersytet Pedagogiczny w Krakowie, Instytut MatematykiUniwersytet Pedagogiczny w KrakowieWe confront Plato's understanding of equality in geometry with that of Euclid. We comment on Phaedo, 74b-c, Meno, 81e-85d and Elements, Book I. We distinguish between two meanings of equality, congruence and equality of the area, and show that in Plato equality means congruence. In Euclid, starting with the first definitions until Proposition I.34, equality means congruence. In the proof of Proposition I.35 equality gains a new meaning and two figures that are not congruent, and in this sense unequal, are considered to be equal. While Plato's geometry is based on self-evident facts, Euclid's geometry rests on deduction and the axioms that are by no means self-evident. However, the shift of meaning from congruence to equality of the area can be substantiated by reference to Euclid's axioms of equality. Finally, we present an ontological interpretation of the two attitudes to equality that we find in Plato's and Euclid's writings.http://zfn.edu.pl/index.php/zfn/article/view/143equalityEuclidPlato |
| spellingShingle | Piotr Błaszczyk Kazimierz Mrówka Miedzy oczywistością a dedukcją. Platon i Euklides o równości Zagadnienia Filozoficzne w Nauce equality Euclid Plato |
| title | Miedzy oczywistością a dedukcją. Platon i Euklides o równości |
| title_full | Miedzy oczywistością a dedukcją. Platon i Euklides o równości |
| title_fullStr | Miedzy oczywistością a dedukcją. Platon i Euklides o równości |
| title_full_unstemmed | Miedzy oczywistością a dedukcją. Platon i Euklides o równości |
| title_short | Miedzy oczywistością a dedukcją. Platon i Euklides o równości |
| title_sort | miedzy oczywistoscia a dedukcja platon i euklides o rownosci |
| topic | equality Euclid Plato |
| url | http://zfn.edu.pl/index.php/zfn/article/view/143 |
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