Benedetti's constructions of ovals

Giovanni Battista Benedetti (1530--1590) derived two constructions of ovals given their minor and major axes. These were published in~1585 and seem to be the first solution to this problem. Therefore, the generally accepted view that ``the geometrical construction for drawing an oval for any given proportion was not known in the sixteenth century'' (Ana López-Mozo, 2011; Nexus Network Journal, p. 571) has to be revised. We provide a transcription of Benedetti's Latin text as well as a translation into English and analyze his mathematical reasoning in detail. This is the first main focus of the present note. The second focus is the impact of Benedetti's contributions to ovals. In particular, it is observed that they were rarely mentioned in the mathematical and architectural literature.乔瓦尼·巴蒂斯塔·贝内代蒂（Giovanni Battista Benedetti，1530–1590）基于给定的长短轴，推导出两种卵形线作图方法。该成果于1585年发表，被公认为该问题的首个解决方案。因此，安娜·洛佩斯-莫佐（Ana López-Mozo）2011年发表于《Nexus Network Journal》第571页的广为接受的论断——"针对任意给定比例绘制卵形线的几何作图法在16世纪尚未为人所知"——亟需修正。本研究的首要核心内容为：转录贝内代蒂的拉丁文原文并将其译为英文，同时对其数学推理过程展开详尽剖析。本短文的第二个研究重点则是贝内代蒂在卵形线领域的研究贡献所产生的学术影响。特别值得指出的是，这些研究成果在数学与建筑类文献中极少被提及。