Monday, March 22, 2021

Geometrical Algebra?

Reviel Netz reviews Apollonius of Perga's Conica: text, context, subtext, by Michael N. Fried and Sabetai Unguru, at Bryn Mawr Classical Review.

"The historiographical question was first forcefully [Unguru, S. 1975. "On the Need to Rewrite the History of Greek Mathematics", (Archive for the History of Exact Sciences 15) 67-114.] The central notion in this debate is Geometrical Algebra, a concept first developed by Zeuthen in 1886. [Zeuthen, H.G. 1886. Die Lehere von den Kegelschnitten im Alterum. Kopenhagen.] Zeuthen suggested that much of Greek geometry makes sense not as geometry as such but as a geometrical way of presenting algebraical relations — 'geometrical algebra'. Unguru claimed this was false. Zeuthen’s main example was, as is obvious from his very title, Apollonius' Conics; thus it was incumbent upon Unguru to offer a study of this ancient work, showing how it could make sense without any algebra assumed as its background. Now this duty is discharged."

See Apollonius of Perga, On Conic Sections, in Great Books of the Western World (first edition, 52 Vol., 1952) volume 11.

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