Experiencing Geometry in Roman Surveyors’ Texts

in Nuncius
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The surveyors who mapped and measured the Roman world engaged broadly with the Greek tradition of mathematical literature, transforming it to fit their profession’s practical needs and to enhance the cultural status of their discipline. This paper will explore the transformative strategies used by Hyginus Gromaticus and Balbus, two agrimensorial authors who wrote in the late first or early second century ce. Both authors work to integrate Greek mathematical knowledge into a literary milieu in which broad appeal is privileged over narrow expertise, and a profession which demanded the application of mathematical knowledge to the experiential needs of surveyors. The hands-on experiences of practicing surveyors selectively re-formed the mathematical and literary structures of Greek mathematics, including both verbal and visual elements. Far from being derivative repetitions or simplifications of the mathematical material, these texts build it into a rich structure of creatively deployed experiential knowledge, giving it a new life in a complex and concrete world.

Experiencing Geometry in Roman Surveyors’ Texts

in Nuncius




HeroMetrica 2.3 (text in Heronis Alexandrini opera quae supersunt omnia edited by Hermann Schöne Stuttgart: Teubner 1976 3:2–184). Tybjerg has collected other appearances of this claim (K. Tybjerg “Hero of Alexandria’s Mechanical Geometry” Apeiron 2004 37:29–56 no. 11). Lewis notes a similar passage crediting the Egyptians with the invention of measurement that appears in various forms at Geometrica 2 and 23.1 as well as Geodesia 72.9–18 107 (M.J.T. Lewis Surveying Instruments of Greece and Rome [Cambridge; New York: Cambridge University Press 2001] p. 14 n. 2). The likely influence of Egyptian and Near Eastern practices on Greek and Roman surveying is indeed one of the more prominent factors complicating this relationship. On this topic see O.A.W. Dilke The Roman Land Surveyors: An Introduction to the Agrimensores (Newton Abbot: David and Charles 1971) pp. 19–30; Lewis Surveying Instruments of Greece and Rome (cit. supra) pp. 13–18 expresses doubts about the contributions made to Greek and Roman surveying by Egyptian astronomy and mathematics arguing for the stronger influence of Mesopotamian methodology.


B. Hillier and J. HansonThe Social Logic of Space (New York: Cambridge University Press1984) p. 1.


See for example F.T. HinrichsHistoire des institutions gromatiques (Paris: P. Geuthner1989) pp. 167–180; M.J. Castillo Pascual Espacio en orden : el modelo gromático-romano de ordenación del territorio (Logroño Logroño: Universidad de La Rioja Servicio de Publicaciones 1996); Campbell Roman Land Surveyors (cit. note 3) xlv–liii; Chouquer and Favory L’Arpentage Romain (cit. note 2) chap. 3–6. For a period earlier than the one under examination here see C. Schubert Land und Raum in der römischen Republik: die Kunst des Teilens (Darmstadt: Wissenschaftliche Buchgesellschaft 1996); Hinrichs Histoire des institutions gromatiques (cit. supra) pp. 79–96; E. Gabba “Storia e Politica nei Gromatici” in O. Behrends and L. Capogrossi Colognesi (eds.) Die Römische Feldmesskunst: Interdisziplinäre Beiträge Zu Ihrer Bedeutung Für Die Zivilisationsgeschichte Roms (Göttingen: Vandenhoeck & Ruprecht 1992) pp. 398–411. For an anthropological approach see Chouquer (cit. note 6).


B. MeißnerDie technologische Fachliteratur der Antike: Struktur Uberlieferung und Wirkung technischen Wissens in der Antike (ca. 400 v. Chr.-ca. 500 n. Chr.) (Berlin: Akademie Verlag1999) pp. 184–194. On Frontinus’s status and possible origins as a homo novus see S. Cuomo “Divide and Rule: Frontinus and Roman Land-Surveying” Studies in the History and Philosophy of Science 2000 31A: 189–202.


P. von CranachDie ‘Opuscula agrimensorum veterum’ und die Entstehung der kaiserzeitlichen Limitationstheorie (Basel: Friedrich Reinhardt Verlag1996).


On this see D. DueckStrabo of Amasia: A Greek Man of Letters in Augustan Rome (London and New York: Routlege2000) particularly pp. 53–62 on scientific geography in Augustan Rome and pp. 85–106 on Strabo’s relationship with contemporary Roman intellectual life.


J. Høyrup“Sub-scientific mathematics: Observations on a pre-modern phenomenon,” History of Science1990 28:63–87.


M. AsperGriechische Wissenschaftstexte: Formen Funktionen Differenzierungsgeschichten (Stuttgart: F. Steiner Verlag2007) pp. 197–210 286–288.


HeroDioptra 34.68–73.


HeroBelopoeica 79.8–12 trans. adapted from E.W. Marsden Greek and Roman Artillery; Technical Treatises (Oxford: Clarendon Press 1971).


HeroBelopoeica 26.23–26.39.


E. PanofskyRenaissance and Renascences in Western Art. (New York: Harper & Row1972) p. 84; Bergemann et al. “Transformation” (cit. note 10) 49 define this as “Transformation bei der ein Inhalt der Referenzkultur in die Form der Aufnahmekultur gekleidet wird oder ein Inhalt der Aufnahmekultur eine in der Referenz kultur verwendete Form erhält.”


R. NetzLudic Proof: Greek Mathematics and the Alexandrian Aesthetic (Cambridge and New York: Cambridge University Press2009) pp. 105–114.




Siculus FlaccusDe condicionibus agrorum 138.15–17 Lachmann.


Agennius UrbicusDe controversiis agrorum70.1–4 Lachmann; trans. Campbell.


  • View in gallery
    Figure 1

    The great marble cadastral plan of Orange. The photograph shows the reassembled fragments of Cadaster B, demonstrating the collocation of the orthogonal boundaries of centuriated land with topographic features such as roads and rivers (here a tributary of the Rhône). The map is oriented with west at the top. Source: Philippe Gromelle.

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    Figure 2

    Detail of Orange Cadaster B, showing the kardo maximus, which bounds the top of the contiguous fragments, as well as an older road that appears to terminate at the boundary of DD XX (i.e. twenty centuriae north of the decumanus maximus).

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    Figure 3

    Straight, circular, and curving lines as depicted in MS J (Thüringer Universitäts- und Landesbibliothek Jena MS Prov. f. 156), f. 64v. Source: Thüringer Universitäts- und Landesbibliothek Jena (ThULB).

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    Figure 4

    Balbus’s diagram of the real-world objects the curving line might enclose: a mountain ridge, a settlement situated on a winding river, a range of hills. MS J, f. 64v. Source: Thüringer Universitäts- und Landesbibliothek Jena (ThULB).

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    Figure 5

    “Enormis” surface, bounded notionally by limites and spatially by straight lines, except for a circular intrusion unidentified in the text. MS J, f. 65r. Source: Thüringer Universitäts- und Landesbibliothek Jena (ThULB).

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    Figure 6

    “Liquis” surface: ager arcifinius or uncenturiated land, bounded on one side by a curving river. MS J, f. 65r. Source: Thüringer Universitäts- und Landesbibliothek Jena (ThULB).

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    Figure 7

    The full pages of figures from Thüringer Universitäts- und Landesbibliothek Jena (ThULB) MS Prov. f. 156, ff. 64v–65r, showing the three genera of lines, the contrast between the straight and circular line, the shapes that might be enclosed by a curving line, the lines that define a surface, the planar surface enclosed by straight lines, the enormis surface, and the liquis surface. Source: Thüringer Universitäts- und Landesbibliothek Jena (ThULB).

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