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The second and major section of the volume is devoted to what the editor describes as the autograph record of Newton's attempts, here published for the first time, to restore the methods of discovery of the ancient geometers. That the classical synthetic proofs were founded on a prior analysis seemed clear from the accounts given by Pappus of the works collectively described by him as 'The treasury of analysis'. Despite the attempt of Fermat, Euclid's Porisms, a key work of this collection (known only through the account of Pappus), remained essentially unexplained. Whiteside points to the conjecture, that the primary function of' The treasury of analysis' was to provide a collection of basic locus-constructions and curve properties of practical use to geometers in the solution of problems, as Newton's most significant achievement; the intersecting loci of the ancients were the equations of later mathematics. In his restoration of Euclid's Porisms, Newton employed the one-to-one correspondence defined by the general bilinear transformation--in effect, a theory of involution--and then, abandoning his role as classical interpreter, developed an innovatory treatise on curves, which includes, as its principal result, a projective classification of curves of the third degree. From David Gregory, who was allowed to read Newton's papers on the occasion of a visit in 1694, we learn that Newton intended to append his restoration of the geometry of the ancients and his method of quadratures to his projected new edition of the Principia. [ABSTRACT FROM AUTHOR]

On the whole Eisele has organised the manuscripts well into the various volumes, and appears to have edited them carefully. She has also given each volume its own name and subject indexes, an essential facility which editors often fail to provide. But I would have welcomed more editorial intrusions, where Peirce commits the occasional oversight ('Fresnel' for 'Young' in vol. 4.69. for example) or vaguely cites his own publications (as in vol. 4, 19.97). He also alludes to 'other' writings in a vague fashion which requires editorial amplification (for example, to M. Marie's Histoire des sciences mathematiques et physiques (12 vols., 1883-88, Paris), in vol. 2, xvii). Sometimes the references in the editor's own commentaries are not clear: to Lenzen (vol. 1, xxiii) and once to myself (vol. 3, vi) where the allusion is to our correspondence rather than the appropriate paper of mine. [ABSTRACT FROM AUTHOR]