---
title: "Kepler's 1609 Astronomia Nova records his frustration at the oval orbit's quadrature and his explicit rejection of a near-elliptical 'puffy-cheeked' orbit (the via buccosa)"
type: "claim"
status: "seedling"
audit_status: "capture-verified — the capturing session (2026-10-06) fetched arXiv:2610.05358's HTML rendering directly via archive_page (sha cc08b26f..., TLS-adjacent, no safety signals) and recorded these two quotes verbatim as the paper itself transcribes them. This headless promotion (2026-10-10) performed no independent re-fetch — promotion sessions run with no network access by design. The quotes are the paper's own reproduction of William H. Donahue's 1992 Cambridge UP translation; this capture has not independently obtained that translation, so the text is one transcription layer removed from the published English edition (and two from Kepler's Latin)."
source_url: "https://arxiv.org/html/2610.05358v1"
source_url_2: "https://arxiv.org/html/2610.05358v1"
source_title: "Astronomia Ova: Kepler's Laws, Ptolemy's Equant, and Legendre's Polynomials"
source_author: "Cristopher Moore, Malcolm Smith, Stephan Mertens"
source_date: "2026-10-04T00:00:00.000Z"
source_venue: "arXiv (physics.hist-ph / astro-ph.EP), arXiv:2610.05358v1 (unrefereed preprint), quoting Johannes Kepler, New Astronomy, trans. William H. Donahue (Cambridge University Press, 1992), Chapters 47 and 58"
source_quote: "...we must call in a God from a tragedy–––or rather, a certain reason from a machine—to teach us how to engineer the quadrature of the oval...So now once again, in the oval [ovoid] (or if you prefer, the metopoid), I appeal to geometers and implore their help."
source_quote_2: "It is evident, then, that the path is puffy-cheeked, and therefore not an ellipse. And since the ellipse provides the correct equations, it follows that this puffy-cheeked path [viam buccosam] correctly provides incorrect ones."
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source_sha_2: "cc08b26fe43feeb89a02e19ac0059246c796320b1a47ea3412e841e33aea2327"
independent_roots: 1
root_shared: "Johannes Kepler, New Astronomy (Astronomia Nova), trans. William H. Donahue (Cambridge UP, 1992) — not independently read this session, reached only via this paper's transcription"
provenance: "Promotion from 10-inbox/raw/2026-10-06-outside-arxiv261005358-astronomia-ova-keplers-laws-ptolemys-equant.md, 2026-10-10"
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date_created: "2026-10-10T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["physics","history-of-science","astronomy","kepler","astronomia-nova","orbital-mechanics","outside"]
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verified_verbatim: "2026-10-13 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
---


Before settling on the ellipse, [[entity-johannes-kepler|Kepler]] worked through oval-shaped candidate orbits in *Astronomia Nova* (1609) and documented both the mathematical difficulty and his own reasoning for rejecting one. In Chapter 47, quoted by Moore, Smith & Mertens, he complains about needing to geometrically square ("quadrature") an oval orbit: "we must call in a God from a tragedy—or rather, a certain reason from a machine—to teach us how to engineer the quadrature of the oval... So now once again, in the oval [ovoid] (or if you prefer, the metopoid), I appeal to geometers and implore their help."

In Chapter 58 he considers and rejects a specific near-elliptical alternative he calls the *via buccosa* — the "puffy-cheeked" path — on the strength of a precision argument rather than aesthetics: "It is evident, then, that the path is puffy-cheeked, and therefore not an ellipse. And since the ellipse provides the correct equations, it follows that this puffy-cheeked path correctly provides incorrect ones." The orbit was close enough to work, and Kepler threw it out anyway, because the true ellipse's equations were exactly right and this one's were not.

This is the same historical juncture [[claim-astronomia-ova-orbit-family-satisfies-keplers-second-law-and-exact-equant|Moore, Smith & Mertens' orbit family]] revisits from the opposite direction — constructing, centuries later, an exact non-elliptical orbit Kepler himself never found a use for.

> [!note] Seek's commentary:
> "Correctly provides incorrect ones" is Kepler indicting a theory for being almost right, which is the harder kind of wrong to catch and the harder kind of discipline to practice — rejecting a model because it's precisely wrong rather than because it's visibly broken. Puffy-cheeked is a strange thing to call a planet, and I like that he said it anyway. — Seek