Constructing the Unity of the Cosmic Body in the Timaeus and Archytas's Solution to the Doubling the Cube Problem

Abstract

This paper examines the mathematical model of the Cosmos presented in Plato’s Timaeus, focusing on how geometrical proportions construct the unity of the Cosmos's body. It argues that Plato’s proportions are fundamentally based on magnitudes rather than numbers, a significant point of contention in scholarly interpretations. Engaging with influential scholars such as Heath, Cornford, and Taylor, who contend that Plato's ratios involve numbers due to his Pythagorean influences, this paper challenges these views. It emphasizes Plato's deployment of geometrical concepts, particularly βάθος (depth) in a specific way, which strongly indicates a concern with continuous magnitudes rather than discrete numbers. Crucially, in constructing the body of the Cosmos, Plato appears to allude to Archytas’s solution to the Delian problem. Archytas’s famed solution geometrically determines two mean proportionals between two lines through the intersection of three-dimensional solids. This paper contends that Plato, in his account of the proportional unity of the Cosmos's solid body, draws inspiration from this landmark achievement in stereometry.

Keywords

• Archytas
• Timaeus
• Doubling The Cube
• Cosmos
• Geometry

Evrenin Bedeninin Birliğinin İnşası ve ‘Küpü İki Katına Çıkarma Sorunu’na Arkhutas’ın Çözümü

Abstract

Bu makale, Platon’un Timaeus diyalogunda sunulan Kozmos’un matematiksel modelini, geometrik oranların Kozmos’un bedeninin birliğini nasıl inşa ettiğine odaklanarak incelemektedir. Makale, Platon’un oranlarının sayılardan ziyade temelde büyüklüklere dayandığını savunmaktadır ki bu, akademik yorumlarda önemli bir tartışma noktasıdır. Platon’un oranlarının Pythagorasçı etkiler nedeniyle sayıları içerdiğini öne süren Heath, Cornford ve Taylor gibi etkili akademisyenlerle tartışmaya girerek, bu makale söz konusu görüşlere meydan okumaktadır. Platon’un geometrik kavramları, özellikle de ayrık sayılardan ziyade sürekli büyüklüklerle ilgili bir kaygıya güçlü bir şekilde işaret eden βάθος (derinlik) kavramını kullanımını vurgulamaktadır. Daha da önemlisi, Kozmos’un bedenini inşa ederken Platon’un, Archytas’ın Delos problemine getirdiği çözüme atıfta bulunduğu görülmektedir. Archytas’ın meşhur çözümü, üç boyutlu katı cisimlerin kesişimi yoluyla iki doğru arasında iki orta orantılıyı geometrik olarak belirler. Bu makale, Platon’un Kozmos’un katı bedeninin orantısal birliğine dair anlatımında, stereometrideki (katı cisimler geometrisi) bu dönüm noktası niteliğindeki başarıdan ilham aldığını öne sürmektedir.

Keywords

• Arkhutas
• Timaios
• Küpü İki Katına Çıkarma
• Kozmos
• Geometri

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