rentiel et de Calcul intégral, t. I, Paris, an VI (1798), p. 149.
216. This is how Bossut terms the curves considered in the system of polar co-ordinates.
217. Engels has in mind Fig. 17 and explanation to it on pp. 148-51 of Bossut’s Treatise. This figure has the following form: BMK is the curve. MT is its tangent. P is the pole or origin of the co-ordinates. PZ is the polar axis. PM is the ordinate of the point M (Engels calls it “real abscissa”; nowadays it is called the radius-vector). Pm is the ordinate of point m lying infinitely close to M (Engels calls this radius-vector the “differential imaginary abscissa”). MH, perpendicular to the tangent MT. TPH, perpendicular to the ordinate PM. Mr, the curve described by the radius PM. As MPm – is an infinitesimal angle, PM and Pm are considered parallel. The triangles Mrm and TPM, as also the triangles Mrm and MPH, are. regarded as similar.
218. See Note 95.
219. This note is one of the three larger notes (Noten) which Engels put in the second folder of materials for Dialectics of Nature.
(See Note 204.) It was written originally as the first sketch of a commentary note to pp. 17-18 of the first edition of [Anti]-Dühring.
The heading “On the Prototypes of the Mathematical Infinite in the Real World” was given by Engels in the list of contents of the second folder of Dialectics of Nature. The sub-heading “To pp. 17-18; Concordance of Thought and Being. – The Infinite in Mathematics” stands at the beginning of the note.
220. Nihil est in intellectu, quod non fuerit in sensu (nothing is in the mind which has not been in the senses), the fundamental tenet of sensualism. The content of this formula goes back to Aristotle (see his Posterior Analytics).
221. This figure is given in an article by William Thomson, entitled “The Size of Atoms,” which was first published in the journal Nature No. 22, of March 31, 1870, and afterwards reprinted as an appendix in the second edition of Treatise on Natural Philosophy by Thomson and Tait (Vol. 1, Part II, new ed., Cambridge, 1883, pp. 501-52).
222. One of the dwarf states forming part of the German Empire since 1871.
223. Here Engels possibly has in mind Haeckel’s psychophysical monism and his views on the structure of matter. In Die Perigenesis der Plastidule (The Perigenesis of the Plastidule), which Engels quotes in his Second Note to [Anti]-Dühring (see present edition, p. 252), Haeckel affirms, for example, that the elementary “soul” is inherent not only in “plastidules,” or protoplasm molecules, but also in atoms, and that all atoms are “animate” and possess “sensation” and “volition.” In the same book Haeckel describes atoms as something absolutely discrete, absolutely indivisible and absolutely inalterable, while along with discrete atoms he recognises the existence of ether as something absolutely continuous (op. cit., Berlin, 1876, S. 38-40).
Engels mentions in his note “The Divisibility of Matter” (see present edition, p. 245) how Hegel deals with the contradiction of continuity and discreteness of matter.