Abstract In this article, we aim at presenting a thorough and comprehensive explanation of the mathematical and theoretical relation between all the aspects of Ptolemaic planetary models and their counterparts which are built according to Kepler’s first two laws (with optimized parameters). Our article also analyzes the predictive differences which arise from comparing Ptolemaic and these ideal Keplerian models, making clear distinctions between those differences which must be attributed to the structural variations between the models, and those which are due to the specific parameters Ptolemy determined in the Almagest. We expect that our work will be a contribution for a better understanding not only of the Ptolemaic theories for planetary longitudes through a clearer perception of the way in which Keplerian features are present—or absent—in Ptolemy’s models, but also for a more balanced judgement of different aspects of the contribution of the first two laws of Kepler to the modern astronomical revolution.

中文翻译：

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托勒密行星模型和开普勒定律

摘要 在本文中，我们旨在对托勒密行星模型的所有方面与其根据开普勒前两条定律（优化参数）建立的对应物之间的数学和理论关系进行彻底而全面的解释。我们的文章还分析了通过比较托勒密模型和这些理想的开普勒模型而产生的预测差异，明确区分了必须归因于模型之间结构变化的差异，以及由托勒密在 Almagest 中确定的特定参数引起的差异。 .