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”.
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Chapter
Alvarez, Carlos, Jr.;
(2008)
François Viète et la mise en équation des problèmes solides
(/isis/citation/CBB000952191/)
Article
Panza, Marco;
(2007)
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
(/isis/citation/CBB000930653/)
Article
Freguglia, Paolo;
(2008)
Viète reader of Diophantus: An Analysis of Zeteticorum libri quinque
(/isis/citation/CBB000933161/)
Chapter
Freguglia, Paolo;
(2008)
Les équations algébriques et la géométrie chez les algébristes du XVIe siècle et chez Viète
(/isis/citation/CBB000952197/)
Article
Pierre Ageron;
Hmida Hedfi;
(2020)
Ibrāhīm Al-Balīshṭār's Book of Arithmetic (ca. 1575): Hybridizing Spanish Mathematical Treatises with the Arabic Scientific Tradition
(/isis/citation/CBB380231472/)
Book
Pascal Duris;
(2016)
Quelle révolution scientifique? Les sciences de la vie dans la querelle des anciens et des modernes (XVIe -XVIIIe siècles)
(/isis/citation/CBB917689026/)
Chapter
Navarro Brotóns, Víctor;
(2010)
Continuity and Change in Cosmological Ideas in Spain between the Sixteenth and Seventeenth Centuries: The Impact of Celestial Novelties
(/isis/citation/CBB001032024/)
Article
Eli I. Lichtenstein;
(2021)
(Mis)Understanding scientific disagreement: Success versus pursuit-worthiness in theory choice
(/isis/citation/CBB459964165/)
Article
Barbara Bienias;
(2020)
Edward Gresham’s Astrostereon, or A Discourse of the Falling of the Planet (1603), the Copernican paradox, and the construction of early modern proto-scientific discourse
(/isis/citation/CBB482285654/)
Book
Boner, Patrick J.;
Tessicini, Dario;
(2013)
Celestial Novelties on the Eve of the Scientific Revolution, 1540--1630
(/isis/citation/CBB001200998/)
Article
Christián C. Carman;
Gonzalo L. Recio;
(2022)
Tycho Brahe’s Appendix ad Observationes anni 1593 and the date of Brahe’s theory of Mars, the prototype for Kepler’s vicarious hypothesis
(/isis/citation/CBB080413113/)
Book
Cohen, H. Floris;
(2010)
Die zweite Erschaffung der Welt: Wie die moderne Naturwissenschaft entstand
(/isis/citation/CBB001035179/)
Thesis
Schotte, Margaret E.;
(2014)
A Calculated Course: Creating Transoceanic Navigators, 1580--1800
(/isis/citation/CBB001567613/)
Article
Eamon, William;
(2006)
The “Secrets of Nature” and the Moral Economy of Early Modern Science
(/isis/citation/CBB001000055/)
Chapter
Adelino Cardoso;
(2021)
Tradição e inovação na obra de médicos portugueses dos séculos XVI e XVII
(/isis/citation/CBB402459450/)
Book
Andretta, Elisa;
(2011)
Roma medica: anatomie d'un système médical au XVIe siècle
(/isis/citation/CBB001213038/)
Thesis
Shotwell, Allen;
(2013)
The Revival of Anatomical Practices and Techniques in the Renaissance
(/isis/citation/CBB001567529/)
Book
Dear, Peter Robert;
(2001)
Revolutionizing the sciences: European knowledge and its ambitions, 1500-1700
(/isis/citation/CBB000100049/)
Book
Alexander, Amir R.;
(2002)
Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice
(/isis/citation/CBB000202097/)
Article
DeWitt, Richard;
(2004)
The Beginnings of a Modern Copernican Revolution
(/isis/citation/CBB000500054/)
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