Françios Viète (1540–1603) was a geometer in search of better techniques for astronomical calculation. Through his theorem on angular sections he found a use for higher-dimensional geometric magnitudes which allowed him to create an algebra for geometry. We show that unlike traditional numerical algebra, the knowns and unknowns in Viète’s logistice speciosa are the relative sizes of non-arithmetized magnitudes in which the “calculations” must respect dimension. Along with this foundational shift Viète adopted a radically new notation based in Greek geometric equalities. His letters stand for values rather than types, and his given values are undetermined. Where previously algebra was founded in polynomials as aggregations, Viète became the first modern algebraist in working with polynomials built from operations, and the notations reflect these conceptions. Viète’s innovations are situated in the context of sixteenth-century practice, and we examine the interpretation of Jacob Klein, the only historian to have conducted a serious inquiry into the ontology of Viète’s “species”.

中文翻译：

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弗朗索瓦·维埃特的代数革命

Françios Viète (1540–1603) 是一位几何学家，他正在寻找更好的天文计算技术。通过他关于角截面的定理，他发现了高维几何量的用途，这使他能够为几何创建代数。我们表明，与传统的数值代数不同，Viète 的后勤假设中的已知和未知是非算术化幅度的相对大小，其中“计算”必须尊重维度。随着这一基本转变，Viète 采用了一种基于希腊几何等式的全新符号。他的字母代表的是值而不是类型，他的给定值是不确定的。以前代数是在多项式聚合中建立的，Viète 成为第一个处理由运算构建的多项式的现代代数学家，并且符号反映了这些概念。Viète 的创新位于 16 世纪实践的语境中，我们考察了雅各布克莱因的解释，Jacob Klein 是唯一对 Viète 的“物种”本体论进行过认真探究的历史学家。