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The Archimedean ‘sambukē’ of Damis in Biton

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Abstract

Biton’s Construction of Machines of War and Catapults describes six machines by five engineers or inventors; the fourth machine is a rolling elevatable scaling ladder, named sambukē, designed by one Damis of Kolophōn. The first sambukē was invented by Herakleides of Taras, in 214 BCE, for the Roman siege of Syracuse. Biton is often dismissed as incomprehensible or preposterous. I here argue that the account of Damis’ device is largely coherent and shows that Biton understood that Damis had built a machine that embodied Archimedean principles. The machine embodies three such principles: (1) the proportionate balancing of the torques on a lever (from Plane Equilibria, an early work); (2) the concept of specific gravity or density (from Floating Bodies, a late work); and (3) the κοχλίας, i.e., a worm drive (invented ca 240 BCE), with the toothed wheel functioning as the horizontal axis of rotation of the elevated ladder. Moreover, the stone-thrower of Isidoros of Abydos (the second machine in Biton) also embodies the κοχλίας.

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Notes

  1. Drachmann (1963) 11 guessed that “Damis of Kolophōn” was the same person as the anethnic “Damius” of Livy 44.28.4-5, active in 168 BCE. See Keyser (2008b), who does not consider the alternative spellings of this name in the manuscripts of Biton (Wescher 1867, 58.1). I here use the name “Damis” to be consistent with Marsden (1999, 92–98) and Rihll (2007, 166–167).

  2. Tybjerg (2008) and Lewis (1999) argues that Biton was writing in 156/5 BCE, for the emergency defense of Pergamon against Prusias II of Bithynia, when hair for the fibers of torsion catapults could not be obtained. Rihll (2007, 164–172) counters that the old technology of non-torsion catapults remained fully functional, rejects the hypothesis of an emergency, insisting that hair could be obtained rapidly, and dates Biton’s work to the reign of the scholar-king Attalos III, 138–133 BCE. Note indeed that Biton, §2 (Wescher 1867, 47.2–3) and §3 (Wescher 1867, 51.3–4), calls for hair to be used in making the slings of his two stone-throwers.

  3. According to Philōn of Byzantion, book 5, Poliorketika 4.84–85: Garlan (1974, 325).

  4. Kromayer and Veith (1928, 373–375, 442–443); Garlan (1974, 108–122) on Plataea and Syracuse; and Kern (1999, 108–112) on Plataea, and 124–132 on Syracuse. Lawrence (1979, 53–66) lists over a dozen successful circumvallations: Potidaea (430 BCE), Mitylēnē (428 BCE: Thucydides 3.18.4–5, 3.25–28), Skionē (428–427 BCE: Thucydides 4.131–133, 5.32), Nisaia (424 BCE), Melos (416 BCE), Chalcedon (409 BCE: Diodorus of Sicily 13.66.3), Mantinea (385 BCE), Kromnos (365 BCE), Gaza (332 BCE), Agrinion (314 BCE), Krotōn (295 BCE), Lilybaeum (274 and 250 BCE), Phthiotic Thebes (217 BCE), and Abydos (201 BCE). Add these seven: Phleious (381–379 BCE: Xenophon, Hellenica 5.3.10–17, 21–25), Capua (212 BCE: Livy 25.22, 26.4–6, 26.12–14), Orongis in Spain (207 BCE: Livy 28.3), Oaeneum in Illyria (169 BCE: Livy 43.19.7–12), Numantia (134–133 BCE: Appian, Iberian War §90–94), and Vellaunodunum and Alesia (52 BCE: Caesar, Gallic War 7.11 and 7.68–89).

  5. See Akurgal (2015, 133–136), “Kolophon and Notion;” and Ziegler and Engelmann (2003). Marsden (1999, 96–97), considers only an attack using the sambukē of Damis, not a defense against circumvallation.

  6. Leaving aside the allegation (from the third or the fifth century CE) that Antiochos captured Kolophōn in 193 BCE: Jerome, In Danielem 11.18 = Porphyry, Against the Christians book XII, FGrHist 260 F47; see Toye (2011) F47. Livy says nothing of this (35.13, 35.15, and 35.42), and when Antiochus does besiege Kolophōn, in 190 BCE, Livy 37.26.5–8 (below), it is clear that it is a new venture. Perhaps Jerome in the fifth century, or Porphyry in the third, assumed that Antiochus achieved the intent he had held in 196 BCE, as expressed in Livy 33.38.18?

  7. The “early” and “late” dating per Knorr (1978a).

  8. Dijksterhuis (1956, 286–290); Archimedes’ lost Κεντροβαρικά (“Centers of Weight”) would likely be relevant also: compare Knorr (1978b) and Berryman (2009, 121–122).

  9. The pseudo-Aristotelian Mechanics 3 (850a35–b2) refers to motion of a lever when it is out of equilibrium; compare Berryman (2009, 61–65, 106–114).

  10. I am indebted to an anonymous referee for the suggestion to consider Philon and for the citation.

  11. The earlier scaling tube of Ktesibios was such a device; see §V below.

  12. For other counterweights, compare: (1) the counterweights in Archimedes’ own machines, Polybius, book VIII, fragment 5.8–9 and Livy 34.34.10; and (2) the unattributed “grabber” device in Athenaeus Mech., Wescher (1867, 35–37).

  13. Similarly for the helepolis described by Biton §4 (Wescher 1867, 53.7); see also: Diodoros of Sicily 13.54.7 of military rams; and Strabo 15.3.11 of wooden stakes (for wear-resistance).

  14. Polybios, book VIII, fragment 4.8 records four men atop Marcellus’ sambucae.

  15. See Wescher (1867) 59.5–8, ὑπὸ δυοδεκαπλάσιον, or with Marsden’s emendation, ὑπὸ δυοδέκα<τ>ον<μέρος>.

  16. Marsden (1999, 95, nn. 47–48). He suggests that πάντοθεν “may be taken to imply that the box is a 6 ft. cube,” but then uses the ambiguity to suggest that the box “may have been a shallow tray … only 2 ft. deep”.

  17. Drachmann (1963, 11), concluding that the device was an “armchair invention,” and see also Drachmann (1977), concluding that the whole work cannot be taken seriously, and is a Greco-Roman rhetorical exercise. Marsden (1999, 95, n. 48), remarks that so much space for lead: “seems altogether too much for this machine and also quite unnecessary.” White (1984, 179) approves Drachmann’s objection, and adds that some of the illustrations are “palpably absurd.” On the other hand, Whitehead and Blyth (2004, 132–134, 160–161), cite Biton’s counterweight without rejecting it, and describe as “not unrealistic” the counterweight of a thousand talents in the karkhēsion (καρχήσιον) of Athenaeus Mech., Wescher (1867, 35–37).

  18. Biton, §4 (Wescher 1867, 54.4), and §7 (Wescher 1867, 65.10). See also Philon, Belop., Thévenot (1693, 57, 70, 93, 98, 102, 103); and Heron, Automatic Theater §28, Belop. §16, Pneumatics 1.praef., 1.3, 1.24, 1.30, 1.37, 1.39, 2.14, 2.24, and 2.37.

  19. Biton §5 (Wescher 1867, 58.4–5), and §7 (Wescher 1867, 65.8–9). See also Philon, Belop., Thévenot (1693, 52.45); Diodorus of Sicily 16.82.3; and the commentary on Kallimachos’ Iambs, fragment 196, Pfeiffer (1949, 189).

  20. This is the capacity computed by Drachmann (1963, 11).

  21. Polybius, book VIII, fragment 5.8–9, “engines … some carrying stones weighing no less than ten talents, and others counterweights made of lead” (ὄργανα … ὧν τινὰ μὲν ἐβάσταζε λίθους οὐκ ἐλάττους δέκα ταλάντων, τινὰ δὲ σηκώματα μολίβδινα).

  22. Kroll (2008, 44–47) and Kroll (2012). In these ancient units, the density of lead would be about 0.41 * 1728/57 = 12.4 talents per cubic foot.

  23. The 3.6 tons is from § II; Drachmann (1963, 11), rounds off his calculation of the amount actually needed to “4 tons”, making the ratio 11.

  24. Mantias (Hallum 2008, ca 15 CE) uses water as the standard liquid to perform specific gravity calculations (actually ratio of components of alloy), using a steelyard with a movable counterweight. Menelaos (ca 96 CE) also uses water, see Würschmidt (1925, 379, 384–385) (Menelaos also considers salt versus fresh water as the immersion liquid, 389–392).

  25. The same calculation, performed in ancient units, would be: 140 talents of lead, divided by 12.4 talents per cubic foot (the density of lead, as computed above, near the start of § III), times 11.34 (to allow for the use of any “Earthy” stuff, denser than water), would be 128 cubic feet, and taking the cube root (finding the two mean proportionals), would yield a small bit more than 5 feet on a side. The “5” here calculated is of course the inside dimension of the cubical box.

  26. Liddell, Scott, and Jones (1940), s.v. κύλινδρος, §2. For uses of the word, see especially Philon Mech., Belop. Thévenot (1693, 75); Athenaeus Mech. (Wescher 1867, 14.1, 14.10); Heron, Belop. §33, Kheiroball. 3.6–8 (Wescher 1867, 129.5, 8–9), compare Mechanics, book II, fragment 5 (Nix and Schmidt1900, 282); and Plutarch, Table Talk 5.5 (682D).

  27. Liddell, Scott, and Jones (1940), s.v. σκυτάλη, §III. See especially pseudo-Aristotle, Mechanics §11 (852 a29–37); Heron, Mechanics, book III, fragments 1–2 (Nix and Schmidt 1900, 294, 298); and compare Baika (2002, 49–50).

  28. Such as ὀνίσκος (Athenaeus Mech., Wescher 1867, 23.7); and Liddell, Scott, and Jones (1940), s.v. φάλαγξ, §II.2. See Biton’s near-contemporary Kallixeinos, who has φάλαγγας ἐπικαρσίας “(transverse) rollers,” in Athenaeus 5 (204 cd) = FGrHist 627 F1 = Keyser (2014); as does Apollonius of Rhodes 1.375–376, 388 (under the Argo, for launching). Compare Baika (2002, 44–45, 47–49).

  29. Marsden (1999, 82, n. 16), refers to κοχλίας as a “general-purpose word,” which it certainly is not. Perhaps Marsden was trying to avoid the proper sense, “screw,” in an effort to date Biton as early as possible?

  30. Marsden (1999, 94), n. 41; Schramm in Rehm and Schramm (2019) 5, 8; Lendle (1975, 114, Figs. 3–4, pp. 125–126) and Lendle (1983, 107–113, and note Fig. 30 on p. 112); cf. Fiorucci (2013).

  31. Marsden (1999, 94, n. 41), rejects a vertical screw on those grounds.

  32. Casson (1971, 185), who dates this to ca 240 BCE; Irby-Massie (2008a); and Roller (2019). The word helix (ἕλιξ) in Moschion refers to the screw in the device, as a way to refer to the whole device by synecdoche; compare Nix and Schmidt 1900, 264) for the same synecdoche.

  33. Berryman (2020). Note that the name ought to be spelled βαρυουλκόν, as it is in Olympiodorus, Commentary on Plato’s Alcibiades, Westerink 1956, §191; and Tzetzes, Chiliades 2.158, 11.601 (βαρυολκ–), 12.971. See the numerous parallel formations, such as βαρυαής, βαρυάλγητος, βαρυαχθής, βαρυεγκέφαλος, βαρυεργής, βαρυηκοέω, βαρυηκοΐη, βαρυήκοος, βαρυηχής (βαρυαχής), βαρύοδμος (βαρύοσμος), βαρύοψ, βαρύϋπνος, βαρυώδης, βαρυώδυνος, and βαρυωπέω.

  34. Drachmann (1958); and Drachmann (1963, 22–32), with the diagrams. Nix and Schmidt (1900, 256–267), the Greek fragment of Heron on the βαρυουλκός, with diagrams, pp. 259, 263, showing the worm drive; similarly Heron, Mechanics, book II, fragment 5, Nix and Schmidt (1900, 286).

  35. Consistent with two distinct suggestions, but not proof of either. On the one hand, Drachmann (1963, 11) suggested identifying the maker of the catapult with Antiochos’ anethnic admiral in 191 BCE (Livy 36.20.5–6, 36.33.7); disputed by Marsden (1999, 78). On the other hand, Keyser (2008d) suggested that Isidoros constructed the catapult to defend Thessalonica during the siege of 169 BCE (Livy 44.10.5–7).

  36. The ἐργάτης might be any of several devices for turning, not just a capstan. See, e.g., Heron, Mechanics, book III, fragments 1–2 (Nix and Schmidt 1900, 294–298).

  37. See Heron, Automatic Theater 13.5, and Pneumatics 2.17–18. Drachmann (1973, 41–43) argues that it “originally meant the peg around which the string of the lyre was laid to tune it.” Similarly in Biton §3 (Wescher 1867, 49.9–10 and 50.2–3), the large stone-thrower of Isidoros of Abydos. The text in Biton §5 resembles the text of Heron, Mechanics, book II, fragment 5 (Nix and Schmidt 1900, 286.13–17), as well as in Heron’s fragment on the βαρυουλκός (p. 264), each also describing the means to turn the screw of a worm drive.

  38. I am indebted to Tracy Rihll for the suggestion to investigate parallels to large screws built to move heavy weights.

  39. On the texts of Vitruuius and Pliny, see Drachmann (1932, 125–128); White (1975, 230–232) (only Pliny); Jüngst and Thielscher (1957, 104–111) (also Heron); Frankel (1999, 86–88); and Frankel (2016, 563, 565).

  40. Cato, Agriculture §18–19; Drachmann (1932, 99–121); Drachmann (1963, 110–115); White (1975, 230). Foxhall (1993, 192–193) argues that old-style presses likely stayed in use long after new-style presses had been invented (compare Hadjisavvas 1992, 120). Moreover, Cato’s use of an old-style press is not evidence that the new-style press is later than Cato, since he would have strongly preferred the traditional form.

  41. Or two screws pressing a beam down onto the fruit. For both types of direct screw presses, see Drachmann (1932, 56–58, 73–77), Drachmann (1963, 126–135), White (1975, 231); Frankel (1999, 122–137); and Frankel (2016, 563, 565).

  42. Frankel (1999, 123–124) cites wooden remains of only one press, an undated two-screw direct-pressure device from Theadelphia, Egypt. On this unique survival, see Billiard (1913, 454–455, with Fig. 157); Shenouda (1976) “A large wooden press has been transferred [from Theadelphia] to the garden court of the Graeco-Roman Museum in Alexandria.” On viticulture and oleiculture in Ptolemaic Theadelphia, see Thompson (1999), 123 (citing Strabo 17.1.45), and 131–134; on Roman-era viticulture in Theadelphia, see Sharp (1999, 174–185).

  43. White (1975, 229–233); Hadjisavvas (1992, 119–120); Rossiter (1998, 599); Frankel (1999) CD, list B, attributes a “Hellenistic” date to just seven of many dozens of beam-and-weights presses, and to no screw presses; Foxhall (2007, 184–185); Frankel (2016, 562).

  44. Marsden (1999, 92, n. 37), delineates a history in which: (1) an unknown person invented the σαμβύκη, then (2) Damis built his device, then (3) Ktesibios built a machine “very similar” to Damis’ device, and finally (4) Herakleides of Taras built his devices at Syracuse.

  45. Three example vases: (i) Green (2014) of the mid-fourth century BCE; (ii) Neils and Oakley (2003) 264 ≈ Caskey and Beazley (1963) # 149 and plate LXXXV (same as Green #2), of ca 465 BCE; and (iii) Olmos (1986) same as Green #3, of ca 435 BCE; Olmos also discusses vase (ii). For these references, I am indebted to Sinclair Bell, J. Richard Green, Alan Griffiths, Kenneth Kitchell, Toph Marshall, David Sider, David Thomas, and Stephen Trzaskoma.

  46. Machabey (1949) 15–16, 19, 23–40, with images of Egyptian scales (24, 27), Assyrian scales (30), and Greek scales (31); Martin-Pardey (1986); Anonymous, “Scales” (2008); and Skuse (2018), esp. 222 (Greek scales) and 229, 231 (Egyptian scales).

  47. Liddell, Scott, and Jones (1940), s.v. φάλαγξ, §II.3, citing pseudo-Aristotle, Mechanics §1 (849 b36–37) and §20 (853 b25–854 a15); Knorr (1982, 126–135), referring to the likelihood that calibration was empirical; and Sherwood et al. (2019, 63–64), providing a translation of §20.

  48. In the Mechanics §20 (853 b25–854 a15), no calibration method is described; Heath (1949, 244–245), describes a calibration process, for the movable-fulcrum steelyard, that depends on the Archimedean law of the lever and is not in the text; Damerow et al. (2000, 98–104), explain an empirical means of calibrating the same sort of steelyard that makes no use of the law of the lever (I am indebted to an anonymous referee for the reference to Damerow et al.).

  49. As recorded by Athenaeus Mech., ca 25 BCE, who appears to be quoting Ktesibios, at least for the text in Wescher (1867, 29.11–31.2), see Whitehead and Blyth (2004, 56–59 and 143).

  50. Lendle (1983 113–116), who (p. 115) makes explicit the comparison to a seesaw (German “Wippe”), a comparison approved by Whitehead and Blyth (2004, 143).

  51. Fabricius (1912) and Keyser and Irby-Massie (2008, 370), gather texts that describe Herakleides, but most of what is said involves opportunistic politicking, primarily in service to Philip V of Macedon (Polybius, book XIII, fragment 4; Diodoros of Sicily, book XXVIII, fragments 2 and 9; Livy 31.16.3, etc.). Fabricius denies the identity of the politician with the engineer, though Polybius book XIII, fragment 4, does describe the politician as an ἀρχιτέκτων (chief engineer).

  52. See for example these five: κριός/aries (Xenophon, Cyropaedia 7.4.1; Caesar, Gallic War 7.23.5); κόραξ/coruus (Diodorus of Sicily 17.44.4; Vitruuius 10.13.3); δελφίς (Thucydides 7.41.2–3, Aristophanes, Knights 762); γέρανος/grus (Plutarch, Marcellus 15.2, Pollux 4.130; Vitruuius 10.13.3); and χελώνη/testudo (Xenophon, Hellenica 3.1.7; Livy 34.39.6).

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Keyser, P.T. The Archimedean ‘sambukē’ of Damis in Biton. Arch. Hist. Exact Sci. 76, 153–172 (2022). https://doi.org/10.1007/s00407-021-00281-4

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