Berkeley, The Analyst (1734)
Source: Trinity College Dublin, D. R. Wilkins; local typeset PDF (40 pages) and Plain TeX transcription
.tex; retrieved 2026-09-08. Metadata: George Berkeley, The Analyst; or, a Discourse Addressed to an Infidel Mathematician (London: J. Tonson, 1734). Transcribed in Plain TeX by David R. Wilkins, as stated in the TeX header; the editor’s page also lists the ensuing controversy tracts. Extraction: the TeX file is the transcription; the PDF is its typeset form. Section numbers follow the 1734 edition. Rights: public domain text; editor’s transcription as for the Hamilton papers.
Source digest
Berkeley’s objection is that fluxions and evanescent increments are “neither finite Quantities nor Quantities infinitely small, nor yet nothing”, hence “the Ghosts of departed Quantities” (§35). Sections 13–16 argue that correct results in the calculus arise from compensating errors, and the closing Queries ask whether the objects of the method are conceivable at all.
For this project, the tract is the canonical statement of the doubt about vanishing magnitudes that Newton’s closing Scholium to Book I, Section I anticipates, and it frames hypothesis H002 about the delay of the Principia. The project’s finite-speed crossover, which makes a positive coefficient possible only above a window \(\Delta_*\), is a physical answer of a different kind from the logical repair Berkeley demanded.
Passage anchors
- TeX line 1942, §35: “May we not call them the Ghosts of departed Quantities?”, preceded by the sentence quoted above.
- §§13–16: the compensating-errors argument.
- Final Queries: the questions on whether the objects of the calculus are clearly conceived.
Coverage and limits
Reading level passage for §35 and its neighbours;
metadata for the rest. The editor’s index page also links
Jurin’s and Robins’s replies, which are outside this retrieval.