# What is new and what is old in Viète's analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Viète

@article{Panza2007WhatIN, title={What is new and what is old in Vi{\`e}te's analysis restituta and algebra nova, and where do they come from ? Some reflections on the relations between algebra and analysis before Vi{\`e}te}, author={Marco Panza}, journal={Revue d Histoire des Mathematiques}, year={2007}, volume={13}, pages={85-153} }

Francois Viete considered most of his mathematical treatises to be part of a body of texts he entitled "Opus restitutae Mathematicae Analyseos Seu Algebrâ novâ". Despite this title and the fact that the term "algebra'' has often been used to designate what is customarily regarded as Viete's main contribution to mathematics, such a term is not part of his vocabulary. How should we understand this term, in the context of the title of his Opus, where "new algebra'' is identified with "restored… Expand

#### 17 Citations

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#### References

SHOWING 1-10 OF 11 REFERENCES

in [Otte & Panza 1997

- pp. 365–414],
- 1997

in [Otte & Panza 1997

- pp. 261–326],
- 1997

Algèbre et Géométrie au xii siècle, texte établi et traduit par R. Rashed. 2 vols., Paris

- Les Belles Lettres,
- 1986

Viette mis en françois, commentez et augmentez des exemples

- Par I.-L. Sieur de Vav-Lezard
- 1986

Parisiis: Ex typographia Ioannis Laqvehay

- [Viète
- 1983

Stamatis. 5 volumes in 6 tomes

- 1977

Qurra über den geometrischen Richtigkeitsnachweis der Auflösung der quadratischen Gleichungen, Berichte über die Verhandlungen der Sächsischen

- Akademie der Wissenschaften zu Leipzig. Mathematischphysikalische Klasse,
- 1941

Essai sur sa vie et son œuvre, La Revue occidentale philosophique, sociale et politique

- 2e série,
- 1895