In Die antike Buchwesen T. Birt discusses the division of books into chapters. He was to change his views, and I intend to translate his revised statements from 1923 soon. But for now, here is what he says in 1882. I have augmented the footnotes by looking up the reference, and placed my additions in [square] brackets.
The lines in the book.
If we ask antiquity, what measure he uses for the length of his books, his answer is almost unanimous: the line. The occasional use of different methods is easily recognised as insignificant by comparison.
Clement of Alexandria measures, as we saw (p. 148 [=Strom. II fin.], the size of his book by the “number and extent of the chapters”. From this it is already evident that the size of a chapter itself fluctuated. So they could not be used as a yardstick for comparison. Also, the concept of the chapter does not seem to be very old. In Photius this division of the text is of course commonplace, as in the scholiasts of Aristotle and Hippocrates, where it alternates with τμῆμα (1). In the manuscripts, chapter headings appear, perhaps for the first time, in the papyrus chemicus N. 66 of the Leyden Museum; however here they seem to be added afterwards.  Symmachus reads Seneca in chapters  and Cassiodorus reads Josephus in titles . Jerome’s commentaries were present to Rufinus in non-numbered chapters .
1) Dietz, Schol. Hippokr. II 3. Vgl. Bergk Gr. Litterat. vol. I p. 233. [Dietz is Scholia in Hippocratem et Galenum, (1834) vol.II, 3. Page 3, part of the introduction, contains mention of both 6 kephalaia and some tmh/mata (the last word on p.3). Διήρηται δὲ ἡ μὲν πᾶσα πραγματεία εἰς ἑκτὰ κεφάλαια. Ταῦτα δὲ τὰ μέρη ἐν τοῖς Ἱπποκράτους χρόνοις οὐκ ἐζητοῦτο· δυα γὰρ ἧσαν τὰ διδασκόμενα, τοσαῦτα καὶ τὰ τμήματα.]
2) See Leemans, Horapollo, p. XXII. (1835). [This reads: Mercerus in adnot. ad cap. 1. dixit, titulos capitum non ipsius esse Philippi, sed a diligenti postea lectore adjecta; idque patere ex MSto Cod. in quo ad marginem adscribantur. Vellem addidisset quoque, num eadem manu tituli illi scripti essent; nam illud non abhorrere a more posterioris aetatis Graecorum, ut eo modo argumentum capitis vel paragraphi uniuscujusque praemittatur, patet ex papyro Chemico n°. 66. Musei Lugduno Batavi, in quo singulis capitibus tituli, eadem manu atque reliqua, sunt superscripti. Pertinet autem MStum illud, ut ex literarum formis conjicitur, ad tempora Constantinorum. Cf. Cl. Reuvens in Epist. ad Letronnium Ep. III. pag. 65. Art. XI. in Tab. Pap. Gr. et Dem. pag. 4. Art. 40. et in Addend. pag. 162, 163. — Mercer, in a note to Ch.1. said that the titles of the chapters were not by Philip, but added later by a careful reader; and was clear from the manuscript itself, in the margin of which they were written. I would like him to have added also, whether those titles were written in the same hand; for that this does not differ from the manner of the latter age of the Greeks, where in the same way the argument was prefixed to every chapter or paragraph, is clear from the papyrus chemicus n °. 66. of the Leiden Museum, where the titles of individual chapters, in the same hand as the rest, are written over the top. However that manuscript belongs, as may be supposed from the forms of letters, to the time of Constantine. Cl. Reuvens in Epist. ad Letronnium Ep. III. pag. 65. Art. XI. in Tab. Pap. Gr. et Dem. pag. 4. Art. 40. et in Addend. pag. 162, 163.]
3) Symm. ep. X 27. [Possibly Q. Aurelii Symmachi quae supersunt, ed. by Otto Seeck (Berlin, 1883) , but I was unable to locate the passage, and Birt in 1882 must have used an older edition].
4) Cassiodor arithm. 1: Josephus in libro I antiquitatum titulo IX. [i.e. Josephus in book 1 of the “Antiquities”, chapter 9. Cassiodorus appears in Migne, Patrologia Latina, 69-70. Vol.2 containing the Institutiones is here. But I cannot find the reference given. In col.618, tho, in the Expositio in Psalterium, I find: “Josephus quoque … vernaculus Judaeorum in libro octavo Antiquitatum titulo tertio multa de temple constructione locutus est …” and in col. 109 I find “De quo etiam Josephus in libro Antiquitatum tertio, titulo septimo, …”
5) As quoted by Rufinus (Jerome IV. 8. 378 ed. Mart.) in tertio commentariorum (sc. ad Ephesios) libro . . . sub eo capitulo ubi scriptum est “Qui uxorem” eqs. post aliquanta sic ait; if the chapter concerned had been numbered, Rufinus would have found it easier to cite it by number; likewise further on (p. 380): de eo capitulo ubi dicit apostolus „Sicut elegit” eqs. ita ait; see ibid p. 402; finally on p. 405: longum est si velim . . . propositis capitulis ad singula respondere. [not verified; these remarks are Birt’s. From here on I have not looked up the references.]
[p.158] In the year 114 A.D., we find from inscriptions,  the city journal or daily paper  of the country town of Caere was divided into chapters; it had both chapter numbers and page numbers; what determined the size of the chapter here is unclear; but in any case they were not of equal size . Wills were also divided in this way, and a Kaput ex testamento M. Megonii M.F. Cor. Leonis is also reported in an inscription . Cicero’s book of Paradoxes was divided into chapters, and the four logoi paradoxwn of Damascius may be compared with it, of which the first was divided into 352 kefalaia (Phot. cod.130). But since it is a fact to say that Epaphroditus (under Nero) was rather the first to call the books of the Odyssey ‘kefalaia’, a quite adequate explanation for this can be found in another connection.
1) Mommsen, 1 RN. 6828 (Orelli 3787; Gruter S. 214): Q. Ninnio Hasta P. Manilio Vopisco cos.
2) Commentarium cottidianum municipi Caeritum.
3) Ulpius Vesbinus has built the municipality of Caere a phetrium (φράτριον); the inscription gives first the permission of the city magistrates, descriptum et factum recognitum . . . ex commentario quem iussit proferri Cuperius Hostilianus per T. Rustium Lysiponum scribam, etc. then inde pagina XXVII Kapite VI; follows the permission to Vesbinus; followed by a copy of a second document, the request of the magistrates to Curiatius Cosanus that he make no objection to the construction; this was clearly earlier: inde pagina altera capite primo; thirdly, finally follows the undertaking of Cosanus; on pagina VIII kapite primo. So the first chapter covered the first eight pages or more; on page XXVII one was in chapter VI: on the eighteen pages that lay between pp. VIII and XXVII, at least four chapters were covered, each having an average of 4.5 pages.
4) Fleetwood, inscr. ant. sylloge (1691) S. 75.
5) See chapter 9 below.
Another term is related to this, and perhaps identical with it, pars libri and μέρος βιβλίου. When Jerome writes : undecimus liber . . . facilior erit in principiis et usque ad duas sui partes reliqua simili more dictanda sunt, this presupposes that after two partes of his book, more follow and that each pars [p.159] was clearly delineated in appearance [p.159] for the reader, presumably by paragraphing in that contexts. A book of Hippocrates was similarly divided for Galen (1): τούτου τοῦ βιβλίου τὸ μὲν κατὰ τὸ ἕν γράμμα μέρος τὸ πρῶτον εἰς σμ’ στίχους ἐξήκει. And a “part” does not mean any particular length, because its number of stichoi must be counted first. In Hippocrates a μέρη was however a different unconnected treatise. Asconius cited at least one of the speeches of Cicero, the Scauriana, in such “parts”; his first quotation from it is in fact circa ver (a) prim. XXXX, the next ibidem, but the fourth circa tertiam partem α primo, the following is interpolated with statim, then is paulo post, then circa medium, then post dum partes orationis, post tres partes orationis α primo, finally ver.α nov. . . and ver. α novis. CLX. Again, the partes here are not of equal size (2). All the more must they somehow have been distinguished in the text, since the usual citation by lines was not carried out.
6) Hieron. comm. Jesai. XI praef.
1) Galen in Hippokr. de nat. hom. XV S. 9.
2) The second half of the oration after the medium holds the rest of pars II and pars III and IV; so pars I must been have completed with the entire first half of pars II; so circa tertiam partem primo α is incomprehensible to me, as one would expect circa alteram.
Something that is indeed a measurement of space is the sheet, σελίς, pagina. To determine the size of the book from the number of pages appears to be obvious, and in fact in the above-mentioned commentarius of the city of Caere the pages were numbered, so that it almost quotes by them. This happened here, however, probably only because counting the verses in a miscellaneous text like this was not really possible. Otherwise they are quoted, – though rarely – only by verses, and counting the sheets seems never really to have become a common practice. We can quote here especially the fourth Philodemus roll περὶ ῥητορικῆς (3), whose columns of text from sheet VIII onwards (4) are provided with numbers underneath: ΡΛΖ is on p. VIII, ΡΛΘ on XI, again PM, ΡΜΛ etc until PMZ on sheet XIX; so apparently the roll was of 147 sheets. More often we find the number of selides [p.160] given in the subscription at the end of book; this was done mostly on the Eschatocoll beneath the more important number of stichoi, as in the Herculaneum rolls N. 105, 106, 109, 111, 115 in the listing following the stichometry, with which N. 103 is to be compared. Occasionally in these only the selides are recorded: so Vol. Herc. ed. Oxon. index N. 1414: Φιλοδήμου περὶ χάριτος, κολλήματα CEΔΙΟΗ (1). However, they are never found, like the stichoi, written in the old decade numerals and counting them so proves that they were in principle different from the stichoi, as not really belonging to the bibliometric Usus. – A Greek epigram designates at the end an indeterminate mass of poetry books as μυριάδες βυβλιανῶν σελίδων (2), similar to what Juvenal (VII 100) states about historians: Nullo quippe modo millesima pagina surgit omnibus. Martial speaks of a hundred paginae once (VIII 44). That the sheet in ancient times was still not used as a measurement of the size of a book, can only be explained on the theory that using verses was possible, and allowed an even greater accuracy to appear desirable, than pages could provide: because, in fact, the length of a column of text was inconstant and could vary between 20-50 lines (3).
1) Which Spengel and also later Cobet rightly read as 78 Selides (σελι οη’ or rather perhaps σελι. οη’).
2) Julianus Aegyptius to Theodorus, Anthol. Pal. VII 594.
3) Within a single book it can be constant, as in the Bankesianus, ca. 43 lines. But Philodemus περὶ κακιῶν (ed. Oxford) varies between 36, 37, 38; the same p. 83-105 freely between 37 and 46. Vol. Oxon. II p. 1-45 has 25-27, p. 46-116 instead 35. (See Cobet Mnemos. 1878 p. 262).
Aside from Clement, we find in Cornificius and Cicero that the size of a book is counted from the number of letters it contains …
I hope to add tomorrow the couple of pages in which Birt revises his opinion. But these pages, elderly as they are, are fundamental for all subsequent work on the question and so well worth reading even as they stand.