¹ The literature on both Vitruvius and aqueducts is of course vast. Hodge, A.T., Roman Aqueducts and Water Supply (London, 1992)Google Scholar, the standard compendium (hereafter cited as Hodge, Aqueducts), has an admirable bibliography and (pp. 13–16) an excellent critique of Vitruvius. See also Wilson, R.J.A., ‘Tot aquarum tam multis necessariis molibus … Recent studies on aqueducts and water supply’, Journal of Roman Archaeology 9 (1996), 5–29CrossRefGoogle Scholar.

² One might add as a minor exception the short concluding section of Hero, Dioptra 6.

³ This is the time-span for the original work and its revisions envisaged by Fleury, P. (ed.), Vitruve de l'architecture, livre I (Paris, 1990), xvi–xxivGoogle Scholar.

⁴ Hodge, Aqueducts, 280–2.

⁵ Most recent text and commentary Plommer, H., Vitruvius and Later Roman Building Manuals (Cambridge, 1973)Google Scholar.

⁶ Found archaeologically on small systems: Hodge, Aqueducts, 111–13, Wilson, ‘Tot aquarum tam multis necessariis molibus’ (above, n. 1), 21–3. Pliny, Naturalis Historia XVI.224 also mentions them.

⁷ Plommer, Vitruvius and Later Roman Building Manuals (above, n. 5), esp. pp. 1–2.

⁸ He is cited only for Books 16, 35 and 36.

⁹ See Detlefsen, D., ‘Vitruv als Quelle des Plinius’, Philologus 31 (1872), 385–34, esp. pp. 394–406CrossRefGoogle Scholar.

¹⁰ Libro is attested a century and a half before Vitruvius by Cato, de Agricultura 18.7, 22.1, and by CIL I 1687 3 of the second century BC. I intend to explore the history of levelling instruments in greater depth elsewhere.

¹¹ Rome, A. (ed.), Commentaires de Pappus et de Théon sur l'Almageste II (Rome, 1936), 524Google Scholar; Rome, A., ‘Un nouveau renseignement sur Carpus’, Annuaire de l'Institut de Philologie et d'Histoire Orientales 2 (1934), 813–18Google Scholar.

¹² Pappus VIII.3; Proclus, , in primum Euclidis librum commentarius 125.25Google Scholar, 241.19 Friedlein.

¹³ Proclus, , in primum Euclidis librum commentarius 125.25Google Scholar; Iamblichus quoted by Simplicius, , in Aristotelis Physica commentaria 60.15Google Scholar, in Aristotelis Categorias commentarium 192.19.

¹⁴ Pappus VIII.3.

¹⁵ Auzac, G. (ed.), Géminus, Introduction aux phénomènes (Paris, 1975), xiv–xxivGoogle Scholar.

¹⁶ Tannery, P., La géometrie grecque (Paris, 1887), 147Google Scholarn., who allowed that the wording does not demand a later date for Carpus; Neugebauer, O., A History of Ancient Mathematical Astronomy II (Berlin, 1975), 943CrossRefGoogle Scholar.

¹⁷ Fraser, P.M., Ptolemaic Alexandria II (Oxford, 1972), 610Google Scholar (Nicomedes), I, 416 (Apollonius).

¹⁸ Heath, T., A History of Greek Mathematics I (Oxford, 1921), 220–32Google Scholar.

¹⁹ Witness the precise calculation of the height of Mount Olympus recorded by Plutarch (Aemilius Paulus 15.5–7).

²⁰ Lewis, M.J.T., ‘When was Biton?’, Mnemosyne 52 (1999), 159–68CrossRefGoogle Scholar.

²¹ Chorobates as an occupational term, spelt χοροβάτηϛ, is found on a late tombstone at Corycus, (Monumenta Asiae Minoris Antiqua III, 694)Google Scholar. Liddell-Scott-Jones take it as a mis spelling for χωροβάτηϛ meaning a surveyor; but it might equally be correctly spelt, meaning a chorus-dancer.

²² Septuagint, , Joshua 18.8Google Scholar, P. Cair. Zen. 329.11, Hesychius, s.v.

²³ For Italy, apart from Rome and Alatri, Inscriptiones Latinae Liberae Rei Publicae lists only four inscriptions (594, 615, 659, 671) of Republican date that mention aqueducts. See also Wilson, ‘Tot aquarum tam multis necessariis molibus’ (above, n. 1), 14–19, and Coulton, J.J., ‘Roman aqueducts in Asia Minor’, in Macready, S. and Thompson, F.H. (eds), Roman Architecture in the Greek World (Society of Antiquaries Occasional Papers n.s. 10) (London, 1987), 72–84Google Scholar.

²⁴ Callebat, L. (ed.), Vitruve de l'architecture, livre VIII (Paris, 1973), 160Google Scholar; Hodge, Aqueducts, 102, 415 n. 19; Burdy, J., ‘Some directions of future research for the aqueducts of Lugdunum (Lyon)’, in Hodge, A.T. (ed.), Future Currents in Aqueduct Research (Leeds, 1991), 36–40Google Scholar.

²⁵ Ashby, T., The Aqueducts of Ancient Rome (Oxford, 1935), 126Google Scholar.

²⁶ van Deman, E. B., The Building of the Roman Aqueducts (Washington, 1934), 57–9Google Scholar.

²⁷ Ashby, The Aqueducts of Ancient Rome (above, n. 25), 72 and map 4; Blackman, D.R., ‘The length of the four great aqueducts of Rome’, Papers of the British School at Rome 47 (1979), 18CrossRefGoogle Scholar.

²⁸ Ashby, The Aqueducts of Ancient Rome (above, n. 25), 71, 75, 76.

²⁹ Judson, S. and Kahane, A., ‘Underground drainageways in Southern Etruria and Northern Latium’, Papers of the British School at Rome 31 (1963), 80CrossRefGoogle Scholar.

³⁰ Gradients can also be expressed as so much per thousand (in this case 5‰), or as so many metres per kilometre (here 5 m per km), or as the vertical divided by the horizontal (0.005). Confusion abounds: for instance Blackman, , ‘The volume of water delivered by the four great aqueducts of Rome’, Papers of the British School at Rome 46 (1978), 60CrossRefGoogle Scholar, says that Vitruvius gives 0.5‰; Evans, H.R., Water Distribution in Ancient Rome (Ann Arbor, 1994), 66CrossRefGoogle Scholar says that the average gradient of Rome's first aqueduct, the Appia, was the same as Vitruvius's whereas, falling about 8 m in 16 km, it was really 0.05% or 1 in 2,000.

³¹ Blackman, ‘The volume of water delivered by the four great aqueducts of Rome’ (above, n. 30), 62–3; Ashby, The Aqueducts of Ancient Rome (above, n. 25), 318. The only real exception is the Aqua Julia of 33 BC which averaged 1 in 80. Its topmost section had to drop very steeply from a high source in order to meet the existing Tepula and Marcia; thereafter it followed their gentle gradient (Ashby, The Aqueducts of Ancient Rome (above, n. 25), 162–3, 317–18).

³² Burdy, ‘Some directions of future research for the aqueducts of Lugdunum’ (above, n. 24), 32–4; Grenier, A., Manuel d'archéologie gallo-romaine IV (Paris, 1960), 103Google Scholar. For other examples see Hodge, Aqueducts, 161.

³³ Hodge, Aqueducts, 441 n. 13.

³⁴ Greek: Burns, A., ‘Greek water supply and city planning’, Technology and Culture 15 (1974), 342–4CrossRefGoogle Scholar; Crouch, D.P., Water Management in Ancient Greek Cities (New York, 1993), 135–43Google Scholar. Roman: Wilson, R.J.A., Sicily under the Romans (Warminster, 1990), 94–5Google Scholar.

³⁵ CIL X 5807 = Inscriptiones Latinae Selectae 5348; A. Secchi, ‘Intorno ad alcuni avanzi di opere idrauliche antiche rinvenuti nella città di Alatri’, Bullettino degli Annali dell'Instituto di Corrispondenza Archeologica (1865), 65–7. The channel fell some 110 m in about 9 km to the beginning of the siphon.

³⁶ More confusion here. Blackman, ‘The volume of water delivered by the four great aqueducts of Rome’ (above, n. 30), 60 and Smith, N.A.F., ‘The Pont du Gard and the Aqueduct of Nîmes’, Transactions of the Newcomen Society 62 (1990–1991), 59CrossRefGoogle Scholar both assert that all (or some) manuscripts of Vitruvius have sicilici; in fact they all read semipede, and all manuscripts of Pliny read sicilici.

³⁷ —. Duffaud, ‘Notice sur les aqueducs romains de Poitiers’, Mémoires de la Société des Antiquaires de l'Ouest (1854), 83; Fabre, G., Fiches, J.-L. and Paillet, J.-L., L'aqueduc de Nîmes et le Pont du Gard (Nîmes, 1991)Google Scholar, plates VIII–IX. The nearest approach in Vitruvius's day to Pliny's figure is on the Aqua Virgo: see above.

³⁸ W. Kastenbein, ‘Untersuchungen am Stollen des Eupalinos auf Samos’, Archäologischer Anzeiger (1960), 181–2.

³⁹ Garbrecht, G., ‘Die Madradag-Wasserleitung von Pergamon’, Antike Welt 4 (1978), 43Google Scholar. On his figures (854 m fall in 42.3 km), the average gradient was 2.0%, not the 0.7% that is given.

⁴⁰ Weber, G., ‘Die Wasserleitungen von Smyrna’, Jahrbuch des Deutschen Archäologischen Instituts 14 (1899), 21–4Google Scholar and Taf. 2. The known pipeline section fell some 170 m in at least 11 km. On the 7 km above this Weber reported long stretches of built channel; a parallel pipeline he took to be a later replacement, although conceivably it was the original.

⁴¹ Koldewey, R., Die Antike Baureste der Insel Lesbos (Berlin, 1890), 65–8Google Scholar; Weber, G., ‘Die Hochdruck-Wasserleitung von Laodicea ad Lycum’, Jahrbuch des Deutschen Archäologischen Instituts 13 (1898), fig. 1Google Scholar.

⁴² Prager, F.D., Philo of Byzantium, Pneumatica (Wiesbaden, 1974), 47–51Google Scholar.

⁴³ Lewis, M.J.T., Millstone and Hammer: the Origins of Water Power (Hull, 1997), 24–5, 42–8Google Scholar.

⁴⁴ Clément-Mullet, J.-J. (trans.), Le livre de l'agriculture d'ibn-al-Awam I (Paris, 1864), 131Google Scholar.

⁴⁵ Steinschneider, M., ‘Die arabischen Übersetzungen aus dem Griechischen. Erster Abschnitt: Philosophia’, Centralblatt für Bibliothekswesen, Beiheft 12 (Leipzig, 1893), 107Google Scholar; Steinschneider, M., ‘Zweiter Abschnitt: Mathematik’, Zeitschrift der Deutschen Morgenländischen Gesellschaft 50 (1896), 355Google Scholar. The physiognomist Polemo was also called Aflimun by the Arabs, but his subject matter easily distinguishes him from Philo: Rosenthal, F., The Classical Heritage in Mam (London, 1992), 43, 251, 254Google Scholar.

⁴⁶ Contrast the different, probably Muslim, tradition represented by another Spanish writer, Ibn al-Saffar who died in AD 1035. He gives a simpler method of surveying a water course at a minimum gradient of 1 in 100: make it gentler, he says, and the water will not flow (Wiedemann, E., Aufsätze zur Arabischen Wissenschaftsgeschichte I (Hildesheim, 1970), 590Google Scholar).

⁴⁷ Bammer, A., ‘Grabungen in Ephesos von 1960–1969 bzw 1970: Architektur’, Jahreshefte des Österreichischen Archäologischen Institutes 50 Beiblatt (1972–1975), 382 Abb. 1Google Scholar; Bammer, A., Das Heiligtum des Artemis von Ephesos (Graz, 1984), 131Google Scholar and Abb. 28–9.

⁴⁸ Hodge, Aqueducts, 116; Hodge, A.T., ‘Siphons in Roman aqueducts’, Papers of the British School at Rome 51 (1983), 190–1CrossRefGoogle Scholar.

⁴⁹ Notably at Athens, where the original archaic pipeline with its branches totalled about 10 km (Tölle-Kastenbein, R., ‘Das archäische Wasserleitungsnetz für Athen’, in de Haan, N. and Jansen, G.C.M. (eds), Cura Aquarum in Campania (Leiden, 1996), 129–36)Google Scholar; and at Olynthus, whose 8 km clay pipeline of probably the sixth but perhaps as late as the fourth century BC included a small siphon about 10 m deep; for literature and a recent discussion, Crouch, Water Management in Ancient Greek Cities (above, n. 34), 171–5.

⁵⁰ For convenient summaries see Fahlbusch, H., ‘Die pergamenischen Wasserleitungen’, in Wasserversorgung im Antiken Rom 4 Aufl. (Munich, 1989), 176Google Scholar; Garbrecht, G., ‘Die Wasserversorgung des antiken Pergamon’, in Die Wasserversorgung Antiker Städte II (Mainz, 1987), 22–31Google Scholar.

⁵¹ Hodge, Aqueducts, 43–5 rightly has emphasized the reduction in pressure. Anchors: Garbrecht, ‘Die Madradag-Wasserleitung von Pergamon’ (above, n. 39), 48 and Abb. 12.

⁵² Weber, ‘Die Wasserleitungen von Smyrna’ (above, n. 40).

⁵³ Weber's drawings and dimensions are not sufficiently detailed to show whether the stone blocks were wedge-shaped as in Fig. 2. If they were not, tapering joints could be packed with cement, as was standard practice where clay pipes negotiated bends. In good hydraulic practice the flanges always face downstream; but this cannot always apply if, as here, double-socketed pipes are included. The double-flanged pipe in Fig. 2, the only one not recorded by Weber, is the necessary corollary of the double-socketed pipe. The smallest clay pipes (0.13 m in bore with walls 85 mm thick) would easily withstand the pressure involved. A comparable mixture of clay pipes and two kinds of stone ones, all of the same bore (95 mm) and apparently of the same date, is to be found on the aqueduct supplying Methymna (Buchholz, H.-G., Methymna (Mainz, 1975), 57–8)Google Scholar. Because none was in situ, it cannot be told whether the stone pipes were on bends.

⁵⁴ Arches, although not widespread in Hellenistic times, are to be found in contemporary and even earlier Attalid architecture: Boyd, T.L., ‘The arch and vault in Greek architecture’, American Journal of Archaeology 82 (1978), 94, 97CrossRefGoogle Scholar; Hansen, E.V., The Attalids of Pergamon (second edition) (Ithaca, 1971), 254Google Scholar. Pipes in substructio, Weber, ‘Die Wasserleitungen von Smyrna’ (above, n. 40), 12, 14, 24–5.

⁵⁵ Stenton, E.C. and Coulton, J.J., ‘Oinoanda: the water supply and aqueduct’, Anatolian Studies 36 (1986), 43–4, 56–8CrossRefGoogle Scholar. Vitruvius's (and presumably his source's) silence on siphons composed entirely of stone pipes reinforces the suspicion that they were not an early phenomenon.

⁵⁶ This crossed most valleys on substructiones, but two on full-blown arcades: Weber, G., ‘Die Wasserleitungen von Smyrna, II’, Jahrbuch des Deutschen Archäologischen Instituts 14 (1899), 167–74Google Scholar. Date: Cadoux, C.J., Ancient Smyrna (Oxford, 1938), 177, 248Google Scholar.

⁵⁷ Coulton, ‘Roman aqueducts in Asia Minor’ (above, n. 23).

⁵⁸ Alzinger, W., Augusteische Architektur in Ephesos (Sonderschriften des Österreichischen Archäologischen Instituts 16) (Vienna, 1974), 21–4Google Scholar.

⁵⁹ Other aqueducts that are thought to be Hellenistic, though no more precise dating is possible, are at Antioch on the Maeander, Philadelphia and Methymna. All had siphons only about 15–20 m deep and, as far as recorded, no humps; for discussion, see Stenton and Coulton, ‘Oinoanda: the water supply and aqueduct’ (above, n. 55), 52–3. Those at Antioch and Philadelphia had simple clay pipelines, that at Methymna a mixture of clay and stone: see n. 53 and n. 90.

⁶⁰ van uren, A.W., ‘L'iscrizione de Lucio Betilieno Varo ad Alatri’, Rendiconti della Pontiflcia Accademia Romana di Archeologia 9 (1933), 138Google Scholar.

⁶¹ van Buren, A.W., ‘Come fu condotta l'acqua al Monte Capitolino?’, Rendiconti della Pontificia Accademia Romana di Archeologia 18 (1941–1942), 65–70Google Scholar; Evans, Water Distribution in Ancient Rome (above, n. 30), 84–5.

⁶² Notizie degli Scavi di Antichità, ser. 3a, 10 (1882), 584–6Google Scholar. Bassel, R., ‘Antico acquedotto ad alta pressione di Betilieno in Alatri’, Annali dell'Instituto di Corrispondenza Archeologica 53 (1881), 204–13Google Scholar agreed about the high-level route, but visualized it running below the intermediate peaks in order to avoid humps and therefore air pockets. For a recent description, Laurenti, M.C., ‘Brevi note su alcuni rinvenimenti a Monte Daielli di Alatri’, Archeologia Laziale 8 (1987), 302–6Google Scholar.

⁶³ Garbrecht, ‘Die Wasserversorgung des antiken Pergamon’ (above, n. 50), Abb. 10.

⁶⁴ Garbrecht, ‘Die Wasserversorgung des antiken Pergamon’ (above, n. 50), 23.

⁶⁵ Hansen, The Attalids of Pergamon (above, n. 54), 55.

⁶⁶ CIL IX 6079 11–14, XV 2294, 2296, 2312.

⁶⁷ CIL III 7309 44, I² 2232 = III 7212, X 5806. Gasperini, L., Aletrium I. i documenti epigrafici (Alatri, 1965), 87–8Google Scholar lists almost all the known references to the Betilieni and speculates on their relationships.

⁶⁸ For a full exposition see Sambursky, S., Physics of the Stoics (London, 1959), esp. pp. 21–48Google Scholar.

⁶⁹ Colluviaris: Paulus, , Epitoma Festi 57.8Google Scholar. Interchange of -u- and -i-: Lindsay, W.M., The Latin Language (Oxford, 1894), 28–9Google Scholar. Spelling was not yet firmly fixed, and Vitruvius's Latin borders on the vernacular. Both of the most recent commentators prefer to stay with colluviaria / colliviaria rather than adopt an emendation: Hodge, Aqueducts, 154–5; Hodge, ‘Siphons in Roman aqueducts’ (above, n. 48), 214; Callebat, Vitruve de l'architecture, livre VIII (above, n. 24), 172–6; Callebat, L., ‘Le vocabulaire de l'hydraulique dans le livre VIII du de architectura de Vitruve’, Revue de Philologie 48 (1974), 325Google Scholar.

⁷⁰ Hodge, Aqueducts, 154–5, 241–5; Hodge, ‘Siphons in Roman aqueducts’ (above, n. 48), 216–17.

⁷¹ Wasserversorgung im Antiken Rom 4 Aufl. (München, 1989), 184Google Scholar; Fahlbusch, H., ‘Elemente griechischer und römischer Wasserversorgungsanlagen’, Die Wasserversorgung Antiker Städte II (Mainz, 1987), 152Google Scholar, Abb. 18.

⁷² At Les Tourillons on the Yzeron aqueduct at Lyon a 16 m tower came up to the hydraulic gradient, dividing what would be an extremely long siphon into two sections. The two 30 m towers on the Aspendos aqueduct, though puzzling, served a similar role, as did examples at Caesarea on an extremely gentle siphon (Hodge, Aqueducts, 154–60, 241–5). Something similar is postulated for the Barratina siphon of the aqueduct of Termini Imerese in Sicily (Belvedere, O., L'acquedotto Cornelio di Termini Imerese (Studi e Materiali 10) (Rome, 1986), 59–72Google Scholar). But the intermediate tower rises well above the intake, and the system would work only as an inverted siphon followed without a break by a true siphon with a pump to keep it primed. This is both unparalleled and improbable, and the map (tav. 1) suggests that it is unnecessary.

⁷³ Hodge, Aqueducts, 43–5.

⁷⁴ Andrew Wilson has suggested (pers. comm.) that colliviaria is built up of collis and via, a route over hillocks. While admirably descriptive, the derivation does not ring true, since Latin compounds formed from two nouns are exceedingly rare: Palmer, L.R., The Latin Language (London, 1954), 103Google Scholar.

⁷⁵ As Hodge, Aqueducts, 37 rightly has pointed out, though he has not spelt out the details.

⁷⁶ Hodge, Aqueducts, 25.

⁷⁷ First attested in Hippocrates (Prog. 11).

⁷⁸ Cf. the Arabic na'ura (noria, water-lifting wheel) which means snorter or grunter, because of the noise it made: Wiedemann, E. and Hauser, F., ‘Über Vorrichtungen zum Heben von Wasser in der islamischen Welt’, Beitrage zur Geschichte der Technik und Industrie 8 (1918), 129Google Scholar.

⁷⁹ Koilia can mean a belly, as venter normally does, with its implication of a smooth curve; but more commonly, it seems from the lexicon, it and its compounds denote intestines or bowels.

⁸⁰ Both Hodge and Callebat (see n. 69) remark on this equation.

⁸¹ Twort, A.C., Law, F.M., Crowley, F.W. and Ratnayaka, D.D., Water Supply (fourth edition) (London, 1994), 451Google Scholar.

⁸² Wylie, E.B. and Streeter, V.L., Fluid Transients (Ann Arbor, 1983), 154Google Scholar.

⁸³ Twort et al., Water Supply (above, n. 81), 452.

⁸⁴ Discussed briefly by Hodge, Aqueducts, 37–9.

⁸⁵ Weber, ‘Die Wasserleitungen von Smyrna’ (above, n. 40), 12–13 and fig. 11.

⁸⁶ Weber, ‘Die Hochdruck-Wasserleitung von Laodicea ad Lycum’ (above, n. 41), 7–8 and fig. 12.

⁸⁷ On tap design, Hodge, Aqueducts, 322–6.

⁸⁸ For example the Sotiel Coronada pump: Schiøler, T., ‘Bronze Roman piston pumps’, History of Technology 5 (1980), fig. 7Google Scholar.

⁸⁹ Smith, N.A.F., ‘Attitudes to Roman engineering and the question of the inverted siphon’, History of Technology 1 (1976), 66–7Google Scholar.

⁹⁰ So too are some of those at Methymna: see n. 53 and n. 59. Red stone recurs in Vitruvius (VIII. 1.2), equally vaguely for a Roman audience, in a list of rocks and soils and the quality of water they yield. It too may derive from a Pergamene source and possibly from the same one. For outcrops of trachyte and andesite round Pergamon and Smyrna, see the geological maps in Philippson, A., ‘Reisen und Forschungen im westlichen Kleinasien’, Petermanns Mitteilungen Ergänzungsheft 167 and 172 (Gotha, 1911, 1912)Google Scholar, Blatt 1 and 3.

⁹¹ There is always the possibility that Vitruvius used some intermediate Latin source: the architectural book of Varro's Disciplinae would be the most obvious. But even if this were the case, it would merely push the borrowing from the Greek back a few years and would not affect the thrust of the argument. Moreover, the Greek genitive ex librati ventris in VIII.6.8 suggests a direct rather than an indirect influence from a Greek source.

⁹² For the contrast, see Hodge, Aqueducts, 31–3.

⁹³ Hansen, The Attalids of Pergamon (above, n. 54), 50, 58, 77, 92.

⁹⁴ See n. 20.

⁹⁵ Callebat, Vitruve de l'architecture, livre VIII (above, n. 24), xxxviii.

⁹⁶ Smith, ‘Attitudes to Roman engineering and the question of the inverted siphon’ (above, n. 89), 58.