Newton, Principia, Scholium to the Definitions and Book III, Regula III (third edition, 1726), Latin
Source: Internet Archive, Google scan
philosophinatur00cotegoog(Ghent University copy); local OCR excerpt.txt, lines 23318–23400 (Regula III) and 1900–2045 (Scholium to the Definitions) of the archive’s_djvu.txt, retrieved 2026-09-29. Metadata: Isaac Newton, Philosophiae naturalis principia mathematica, editio tertia (London: G. & J. Innys, 1726), Liber III, Regulae philosophandi, Regula III, pp. 387–389; Scholium to the Definitions, pp. 9–11. The rule and its commentary, including the divisibility passage, first appear in the second edition (Cambridge, 1713); the archive’s 1713-dated scanprincipiamathem00newtgoogcarries the same passage. Extraction: archive.org OCR of the 1726 printing, with long s as f and ligatures misread. Quotations in the notes are normalized by hand and need the scan for the final text. Rights: public domain.
Source digest
Newton’s rule for universal qualities: those that admit neither intensification nor remission and belong to all bodies within reach of experiment are to be held qualities of all bodies, since “quae minui non possunt, non possunt auferri” and the analogy of nature is “simplex … & sibi semper consona”. The commentary carries extension, hardness, impenetrability, mobility and inertia down to the least parts, then separates two kinds of division: that undivided parts can be distinguished into smaller ones “ex mathematica certum est”, while whether nature’s powers can actually divide and separate them “incertum est”, and a single experiment would settle it. For this project it is Newton’s own statement, in Book III, that the physical limit is an empirical question, used in the continuity note.
Passage anchors
- Printed p. 387: “Qualitates corporum quae intendi & remitti nequeunt, quaeque corporibus omnibus competunt in quibus experimenta instituere licet, pro qualitatibus corporum universorum habendae sunt.”
- Printed pp. 387–388 (the last two clauses on p. 388): “ideoque generales statuendae sunt quotquot cum experimentis generaliter quadrant; & quae minui non possunt, non possunt auferri … nec a naturae analogia recedendum est, cum ea simplex esse soleat & sibi semper consona.”
- Printed pp. 9–11 (Scholium to the Definitions): “Causae, quibus motus veri & relativi distinguuntur ab invicem, sunt vires in corpora impressae ad motum generandum. Motus verus nec generatur nec mutatur, nisi per vires in ipsum corpus motum impressas” (p. 9); “Effectus, quibus motus absoluti & relativi distinguuntur ab invicem, sunt vires recedendi ab axe motus circularis … majores vel minores pro quantitate motus” (p. 10); “Motus quidem veros corporum singulorum cognoscere, & ab apparentibus actu discriminare, difficillimum est … Causa tamen non est prorsus desperata” (p. 11).
- Printed p. 388: “Porro corporum partes divisas & sibi mutuo contiguas ab invicem separari posse, ex phaenomenis novimus, & partes indivisas in partes minores ratione distingui posse ex mathematica certum est. Utrum vero partes illae distinctae & nondum divisae per vires naturae dividi & ab invicem separari possint, incertum est. At si vel unico constaret experimento quod particula aliqua indivisa, frangendo corpus durum & solidum, divisionem pateretur: concluderemus vi hujus regulae, quod non solum partes divisae separabiles essent, sed etiam quod indivisae in infinitum dividi possent.”
Coverage and limits
Reading level passage for pp. 9–11 and 387–389 from the
OCR; Motte’s English is in the
Rules companion.