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I read a previous question on Roman engineers and I was surprized that nobody referred to the Pantheon: its dome is an unrivalled wonder of architecture. Roads and aqueducts can be built without theoritical notions.

It is amazing that people with such a crippled numeral system and little or no math could build such a temple, in comparison to which pyramids and parthenon are child's play.

Do you know if there is any record of formulae the architects used to calculate the shape and the load-carryng capacity of materials and structures?

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    $\begingroup$ They did not have formulae, the earliest versions appear in Diophantus's Arithmetica c. 250 AD, but that does not mean that they did not have a developed mathematical and theoretical background. It was based on Euclidean geometry, see Hadrianic Architecture and Geometry. We also have a multi-volume theoretical treatise De architectura (c. 20 BC) written by famous Roman architect Vitruvius, although it was written before cross vaulting and domes were introduced. Modern way is not the only way. $\endgroup$
    – Conifold
    Nov 25, 2019 at 9:28
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    $\begingroup$ Not in modern sense... Have you have seen an "algebraic expression" of Cardano ? See this post with the original text linked. $\endgroup$ Nov 27, 2019 at 16:24

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