I read R. Netz & W. Noel's The Archimedes Codex: How a Medieval Prayer Book Is Revealing the True Genius of Antiquity's Greatest Scientist to learn about The Method, but I felt that it was not a completely objective book. For example, that book explained that Archimedes clearly recognized actual infinity 2,000 years earlier than Cantor's theory of infinity appeared. So I thought a should read more books about The Method. Therefore, I would appreciate it if you could recommend an article or book that explains The Method in detail and objectively.
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$\begingroup$ Please ignore my previous comment, I had the wrong browser tab in mind. $\endgroup$– Jiminy Cricket.Commented Nov 9 at 18:46
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$\begingroup$ The idea of infinity appeared in mathematics way before Cantor. The symbol $\infty$ is from the 17th century. Also the Ancient Greeks had some idea of infinity. See for example Zeno's paradoxes. $\endgroup$– MauricioCommented Nov 9 at 21:46
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1$\begingroup$ The idea of "actual infinity" as you have used it comes from Aristotle's potentiality vs actuality $\endgroup$– MauricioCommented Nov 9 at 21:48
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2$\begingroup$ As a counter to Netz, look at the brief review of the Palimpsest by Acerbi, who remarks that not much new came up compared to Heiberg's 1915 transcription and that "one should not attach too much importance" to Prop 14 of the Method "as if it was an anticipation of modern set-theoretic treatment of infinities... analogous features can be found outside Archimedes, for instance in Pappus." Acerbi is generally critical of Netz's methodology as ahistorical, see his Archimedes and the Angel. $\endgroup$– ConifoldCommented Nov 10 at 6:52
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The book by Netz and Noel was not meant as a scholarly work, but rather as a popularisation. A scholarly study of the matter appears in
A new reading of method proposition 14: Preliminary evidence from the Archimedes Palimpsest (Part 2) R Netz, K Saito, N Tchernetska - SCIAMVS, 2002.
