Abstract
Hero of Alexandria, who probably dates to the first or second century CE, produced treatises on a wide range of scientific and technical topics: geometry, surveying, catapult design, elaborate pneumatic devices, and more. The term theōria and its cognates appear throughout Hero’s works to reflect a set of disciplined observational activities that interrogate the links between text and artifact, the boundaries between nature and the artificial structures (including texts) that mediate our experience of it, and the limits of our ability to observe and describe the world around us. The objects observed include natural phenomena and artificial devices, as well as the diagrams in Hero’s own texts and the logical structures that underlie the systematic frameworks of his books. This paper will examine the interplay in Hero’s Dioptra, Belopoeica, and Pneumatica between “diagrammatic” and “theoretical” ways of subjecting technological artifacts to forms of visual discipline. Though Hero’s theōria certainly embraces a wide range of ways of seeing, they cluster semantically around their ability to link domains—the abstract and the concrete, the mathematical and the material, objects in the world and diagrams in the text—while preserving the truth value of observations as they move between domains.
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Notes
- 1.
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τοὺς δὲ ἑξῆς τρόπους τῶν ἐμβολέων δι’ ὑπομνημάτων, ζωγραφικῆς δὲ σκιαγραφίας τῶν κατὰ μέρος ἐξαρθρήσεων παραγωγῆς τε τῶν ἄρθρων ὀφθαλμοφανῶς τὴν θέαν αὐτῶν παρασχησόμεθά σοι (On joints 2.30–33).
- 3.
Carder analyzes the images in the Wolfenbüttel “Arcerianus A,” one of the oldest manuscripts of the Corpus Agrimensorum, and Dilke discusses the images in the corpus more broadly (Carder 1978; Dilke 1967). André Piganiol provides the most comprehensive guide to the Orange cadastral map (Piganiol 1962). Sachiko Kusukawa discusses the reception of Dioscorides in early modern botanical and pharmacological works (Kusukawa 2011, 125–136).
- 4.
(Belopoeica 20.1–13): Ἡ δὲ χοινικὶς γίνεται τόνδε τὸν τρόπον· ἐμβολέα δεῖ κατασκευάσαι ὅμοιον τῷ ΑΒΓΔΕΖ ὑπογεγραμμένῳ, ἔχοντι τὰς μὲν ΑΕ, ΒΖ περιφερείας, τὰς δὲ ΕΓ, ΖΔ εὐθείας, τὴν δὲ ΑΒ ἴσην τῇ τοῦ τρήματος διαμέτρῳ, καὶ πρὸς τοῦτον ἐκτορνεύσασθαι τὴν χοινικίδα· ἐὰν μὲν χαλκῆ μέλλῃ ὑπάρχειν, διαπλάσαντα κύκλῳ χυτὴν ποιῆσαι ἀπὸ ἐλατοῦ χαλκοῦ, πάχος ποιοῦντα τὸ αὔταρκες πρὸς τὴν τοῦ ὀργάνου βίαν.
- 5.
(Belopoeica 18.1–29): Οἱ δὲ πλάγιοι τοῖχοι καλοῦνται μὲν περίτρητα, γίνονται δὲ τὸν τρόπον τοῦτον· ἐγκεῖσθαι δεῖ παραλληλόγραμμον ὀρθογώνιον τὸ ΑΒΓΔ, διπλῆν ἔχον τὴν ΑΒ τῆς ΒΓ, καὶ ἐπιζευχθείσης τῆς ΑΓ, παράλληλον ἀγαγεῖν δεῖ ταύτῃ διὰ τοῦ Δ τὴν ΔΕ, καὶ ἔσται τὸ σχῆμα τοῦ περιτρήτου τὸ ΑΓΕΔ· ἐπιζευχθείσης δὲ καὶ τῆς ΑΕ, περὶ κέντρον τὸ Ζ κύκλον γράψαι ἴσον τῷ τρήματι τῷ τὸν τόνον δεχομένῳ, καὶ διὰ τούτου τοῦ κύκλου ἐκκόψαι τὸ εἰρημένον τρῆμα· ἀγαγόντα δὴ ταῖς ΑΔ ΓΕ παραλλήλους τὰς ΗΘ ΚΛ ἀπολαμβανούσας πρὸς τὰς ΑΔ ΓΕ πλάτη τὰ αὐτὰ τοῖς πάχεσιν τοῦ παραστάτου καὶ ἀντιστάτου, ἐκκόψαι τὰ τρήματα τοῖς τόρμοις ἀραρότα τοῦ τε παραστάτου καὶ τοῦ ἀντιστάτου τὰ Μ, Ν, Ξ, Ο, μὴ δι’ ὅλου δὲ τοῦ πάχους τοῦ περιτρήτου, ἀλλὰ καταλείποντα τοῖς τορμικοῖς ὡς τὸ τρίτον μέρος τοῦ πάχους στερεώματος καὶ εὐπρεπείας ἕνεκα.
- 6.
(Cheiroballistra 4.1): Γεγονέτω δὲ καὶ τὸ καλούμενον Καμάριον, τῷ σχήματι οἷον ὑπογέγραπται τὸ ΑΒΓΔΕΖΗ, ἔχον τὴν μὲν ΓΕ ποδὸς ἑνὸς καὶ δακτύλων ΖΣ, τὸ δὲ διάστημα τοῦ Καμαρίου τὸ ΘΚ δακτύλων Ε.
- 7.
(Cheiroballistra 4.3): Τὸ δὲ καλούμενον Κλιμάκιον ἔστω τὸ ΛΜΝΞ ΟΠΡΣ, ἐκ δύο κανόνων τῷ σχήματι οἷον ὑπογέγραπται, μῆκος ἔχων ὁ μὲν ΟΠΡΣ κανὼν ποδὸς ἑνὸς καὶ δακτύλων Ι, ὁ δὲ ΛΜΝΞ ποδὸς ἑνὸς καὶ δακτύλων Η, πλάτος δὲ πρὸς τοῖς ΥΤ μέρεσι δακτύλους Β, πρὸς δὲ τοῖς [ΛΜ ΝΞ] ΟΠ ΡΣ δάκτυλον ἕνα τέταρτον· πάχος δὲ ἑκάστου τῶν Λ͵Β Ν͵Γ Ο͵Δ Ρ͵Ε τόρμων ἔστω δακτύλων Β.
- 8.
(Cheiroballistra 4.4): Καὶ διῃρήσθωσαν οἱ ΛΜΝΞ ΟΡΠΣ κανόνες εἰς τρία ἴσα, τὰ ΦΤΨΧΥΩ. καὶ τετρήσθω τὰ μὲν ΤΥ κατὰ τὸ μῆκος τρήμασι παραλληλογράμμοις, τὰ δὲ ΦΧΨΩ τρήμασι στρογγύλοις.
- 9.
(Cheiroballistra 3.2–3): Ποιήσαντες γὰρ σιδηροῦς κανόνας τέσσαρας, μῆκος ἔχοντας ἑκάτερον δακτύλους ΙΣ, πλάτος δὲ δακτύλου διμοίρου μικρῷ πλεῖον, πάχος δὲ ὥστε μὴ εὐχερῶς κάμπτεσθαι. Ἔστωσαν δὲ οἱ ΑΒ ΓΔ ΕΖ ΗΘ, οἷοί εἰσι τῷ σχήματι καταγεγραμμένοι, ἔχοντες συμφυεῖς κρίκους τοὺς ΚΛ ΜΝ ΞΟ ΠΡ, τὸ εὖρος ἔχοντας δακτύλους δύο, τὸ δὲ πλάτος δάκτυλον ἕνα, τὸ δὲ πάχος τὸ αὐτὸ τοῖς κανονίοις. Marsden notes that while Wescher preferred M’s reading (ΙΣ, 10½), the alternative Κ (20), easily confused in manuscripts, gives a form factor closer to that of the standard catapult of this type (palintone) (Marsden 1971, 222–223, n. 17).
- 10.
(Cheiroballistra 2.2–3): Γεγονέτω ἐξ ὕλης σιδηρᾶς χειρολάβη ἡ ΑΒΓΔ, τῷ σχήματι οἵα ὑπογέγραπται, δίχηλον δὲ τὸ ΕΖ μέρος ἔχον· τὸ δὲ ΖΘ τόρμος ἔστω τετράγωνος, σχαστηρία δὲ ΚΛΜ, δρακόντιον δὲ τὸ ΝΞ, πιττάριον δὲ τὸ ΟΠΡΣ. Καὶ τετρήσθω ἡ ΑΒΓΔ χειρολάβη κατὰ τὸ Δ· ὁ δὲ ΓΔ κανὼν, ὁ ἐν τῷ πρώτῳ θεωρήματι, τετρήσθω κατὰ ΜΝΞ, καὶ κατὰ μὲν τὰ ΜΝ στρογγύλῳ τρήματι διαμπερὲς, κατὰ δὲ τὸ Ξ παραλληλογράμμῳ· καὶ οὕτως ἐνηρμόσθω ἡ χειρολάβη, ὥστε περόνην διὰ τῆς ΜΝ διωσθῆναι καὶ διὰ τοῦ Δ τρήματος τῆς χειρολάβης κοινωθῆναι.
- 11.
(Cheiroballistra 2.6.1–11): Ἔπειτα τρήσαντες τὸ ΝΞ δρακόντιον κατὰ τὸ Ν, καὶ τὸν ΓΔ κανόνα κατὰ τὸ Π (τὸν ἐν τῷ πρώτῳ θεωρήματι) ἄπεχον τοῦ Μ δακτύλους Δ, καὶ καθέντες διά τε τοῦ τρήματος τοῦ δρακοντίου καὶ τοῦ Π περόνην, κοινοῦμεν ὥστε εὐχερῶς κινεῖσθαι τὸ ΝΞ δρακόντιον περὶ αὐτὴν.
- 12.
(Cheiroballistra 2.7.1–11): Καὶ πάλιν ἀποστήσαντες ἀπὸ τῆς χειρολάβης τῆς [ΑΒ]ΓΔ τὴν ΞΡ, τιτρῶμεν κατὰ τὸ Ρ, καὶ πάλιν ἀπ’ αὐτοῦ μετρήσαντες δακτύλους ΔΣ, ὡς τὴν ΡΣ, τιτρῶμεν κατὰ τὸ Σ, καὶ οὕτω καθίεμεν [τὸ πιττάριον] ἐν τῷ ΓΔ κανόνι, ὅστις ἐστὶν ἐν τῷ πρώτῳ θεωρήματι.
- 13.
(Belopoeica 10.1–12): Τῆς οὖν τῶν ἀγκώνων βίας ἰσχυρᾶς γενομένης, δεῖ καὶ τὴν καταγωγὴν ἰσχυρὰν γενέσθαι διὰ τὸ ἴσης δεῖσθαι βίας πρὸς τὸ τοὺς ἀγκῶνας κατάγεσθαι. διὸ ἀντὶ τῆς καλουμένης ἐπὶ τοῦ ἐπάνω θεωρήματος καταγωγίδος ἄξονα προσέθηκαν τῇ σύριγγι ἐπὶ τοῦ ὀπίσω αὐτῆς ἄκρου πλάγιον στρεφόμενον εὐλύτως.
- 14.
(Metrica 3. pr. 1–5): Οὐ πολὺ ἀπᾴδειν νομίζομεν τὰς τῶν χωρίων διαιρέσεις τῶν γιγνομένων ἐν τοῖς χωρίοις μετρήσεων· καὶ γὰρ τὸ ἀπονεῖμαι χωρίον τοῖς ἴσοις ἴσον καὶ τὸ πλέον τοῖς ἀξίοις κατὰ τὴν ἀναλογίαν πάνυ εὔχρηστον καὶ ἀναγκαῖον θεωρεῖται.
- 15.
(Dioptra 2.1–10): Ὅτι δὲ πολλὰς παρέχεται τῷ βίῳ χρείας ἡ πραγματεία, δι’ ὀλίγων ἐστὶν ἐμφανίσαι. πρός τε γὰρ ὑδάτων ἀγωγὰς καὶ τειχῶν κατασκευὰς καὶ λιμένων καὶ παντὸς οἰκοδομήματος εὔχρηστος τυγχάνει, πολλὰ δὲ ὤνησεν καὶ τὴν περὶ τὰ οὐράνια θεωρίαν, ἀναμετροῦσα τά [τε] μεταξὺ τῶν ἀστέρων διαστήματα, καὶ τὰ περὶ μεγεθῶν καὶ ἀποστημάτων καὶ ἐκλείψεων ἡλίου καὶ σελήνης.
- 16.
(Pneumatica 1. pr. 32–37): κατανοήσειε δ’ ἄν τις τὸ λεγόμενον ἐκ τοῦ τοιούτου· ἐὰν γὰρ εἰς ὕδωρ καταστρέψας ἀγγεῖον τὸ δοκοῦν εἶναι κενὸν πιέζῃς εἰς τὸ κάτω ἀκλινὲς διαφυλάσσων, οὐκ εἰσελεύσεται τὸ ὕδωρ εἰς αὐτό, κἂν ὅλον αὐτὸ κρύψῃς·.
- 17.
(Pneumatica 1. pr. 43–46): πάλιν δὲ πρὸ τοῦ τρυπῆσαι τὸν πυθμένα ἐάν τις ὀρθὸν ἐκ τοῦ ὕδατος τὸ ἀγγεῖον ἐπάρῃ, ἀνατρέψας ὄψεται πᾶσαν τὴν ἐντὸς τοῦ ἀγγείου ἐπιφάνειαν καθαρὰν ἀπὸ τοῦ ὑγροῦ, καθάπερ ἦν καὶ πρὸ τοῦ τεθῆναι.
- 18.
(Pneumatica 1. pr. 49–53): ἐὰν γοῦν τετρυπημένου τοῦ ἀγγείου κατὰ τὸν πυθμένα καὶ εἰσπίπτοντος τοῦ ὕδατος παραθῇ τις τῷ τρυπήματι τὴν χεῖρα, αἰσθήσεται τὸ πνεῦμα ἐκπῖπτον ἐκ τοῦ ἀγγείου· τοῦτο δὲ οὐκ ἄλλο τί ἐστιν ἢ ὁ ἐκκρουόμενος ὑπὸ τοῦ ὕδατος ἀήρ.
- 19.
(Pneumatica 1. pr. 86–91): ἐὰν οὖν ἀγγεῖον λαβών τις κουφότατον καὶ σύστομον, προσθεὶς τῷ στόματι ἐκμυζήσῃ τὸν ἀέρα καὶ ἀφῇ, ἐκκρεμασθήσεται ἐκ τῶν χειλέων τὸ ἀγγεῖον, ἐπισπωμένου τοῦ κενοῦ τὴν σάρκα πρὸς τὸ ἀναπληρωθῆναι τὸν κενωθέντα τόπον· ὥστε ἐκ τούτου φανερὸν γενέσθαι, ὅτι ἄθρους κενὸς ὑπῆρξεν ἐν τῷ ἀγγείῳ τόπος.
- 20.
(Pneumatica pr. 200–213): κατασκευάζεται γὰρ σφαῖρα πάχος ἔχουσα τοῦ ἐλάσματος, ὥστε μὴ εὔθλαστος εἶναι, χωροῦσα ὅσον κοτύλας η. στεγνῆς δὲ οὔσης αὐτῆς πάντοθεν τρυπήσαντα δεῖ σίφωνα καθεῖναι χαλκοῦν, τουτέστι σωλῆνα λεπτόν, μὴ ψαύοντα τοῦ κατὰ διάμετρον τόπου τοῦ τετρυπημένου σημείου, ὅπως ὕδατι διάρρυσις ὑπάρχῃ, τὸ δὲ ἄλλο μέρος αὐτοῦ ἐκτὸς ὑπερέχειν τῆς σφαίρας ὅσον δακτύλους τρεῖς· τὴν δὲ τοῦ τρυπήματος περιοχήν, δι’ οὗ καθίεται ὁ σίφων, στεγνοῦν δεῖ κασσιτέρῳ προσλαμβάνοντα πρός τε τὸν σίφωνα καὶ τὴν ἐκτὸς τῆς σφαίρας ἐπιφάνειαν, ὥστε ὅταν βουλώμεθα τῷ στόματι διὰ τοῦ σίφωνος ἐμφυσᾶν, κατὰ μηδένα τρόπον τὸ πνεῦμα τῆς σφαίρας διεκπίπτειν. σκοπῶμεν δὴ τὰ συμβαίνοντα….
- 21.
Note that para physin should not be taken as meaning “against nature” in the strong sense of being “unnatural,” as Sylvia Berryman has shown (Berryman 2009, 44–46).
- 22.
(Pneumatica pr. 235–242): καὶ μὴν ἐάν τις ἐθέλῃ τὸν σίφωνα βαλὼν εἰς τὸ στόμα ἐμφυσᾶν εἰς τὴν σφαῖραν, πολὺ προσεισκρινεῖ πνεῦμα, μὴ ὑποχωρήσαν τος τοῦ προϋπάρχοντος ἐν αὐτῇ ἀέρος· τούτου δὲ ἀεὶ συμβαίνοντος, σαφῶς δείκνυται συστολὴ γινομένη τῶν ὑπαρχόντων ἐν τῇ σφαίρᾳ σωμάτων εἰς τὰ παρεμπεπλεγμένα κενά. παρὰ φύσιν δὲ ἡ συστολὴ γίνεται διὰ τὴν τῆς εἰσκρίσεως βίαν.
- 23.
(Pneumatica pr. 242–249): ἐάν τις οὖν ἐμφυσήσας καὶ παρ’ αὐτὸ τὸ στόμα προσαγαγὼν τὴν χεῖρα συντόμως ἐπιπωμάσῃ τῷ δακτύλῳ τὸν σίφωνα, μενεῖ πάντα τὸν χρόνον συνεσφιγμένος ὁ ἀὴρ ἐν τῇ σφαίρᾳ· ἐὰν δέ τις ἀναπωμάσῃ, πάλιν ἐκτὸς ὁρμήσει μετά τε ψόφου καὶ βοῆς πολλῆς ὁ προσεισκριθεὶς ἀὴρ διὰ τὸ ἐκκρούεσθαι, καθάπερ προεθέμεθα, κατὰ τὴν τοῦ προϋπάρχοντος ἀέρος διαστολὴν τὴν κατὰ τὴν εὐτονίαν γινομένην.
- 24.
(Pneumatica 1. pr. 127–137): αὕτη δὲ ὑπὸ πυρώδους τινὸς οὐσίας γίνεται, τοῦ ἡλίου ὑπὸ γῆν ὄντος καὶ θερμαίνοντος τὸν κατ’ ἐκεῖνο τόπον, καὶ μᾶλλον ἤτοι θειώδη ἢ ἀσφαλτώδη ὄντα, ὃς θερμαινόμενος ἐπὶ πλεῖον τὴν ἀναθυμίασιν ποιεῖ· καὶ τὰ θερμὰ δὲ τῶν ὑδάτων τὰ ἐν τῇ γῇ εὑρισκόμενα ἐκ τῆς αὐτῆς αἰτίας γίνεται. τῶν οὖν δρόσων τὰ μὲν λεπτότερα εἰς ἀέρα μεταβάλλει, τὰ δὲ παχύτερα ἐπὶ ποσὸν συνανενεχθέντα διὰ τὴν τῆς ἀναθυμιάσεως βίαν, ταύτης ἀποψυχείσης κατὰ τὴν τοῦ ἡλίου μετατροπὴν πάλιν εἰς τὸν κάτω φέρεται τόπον.
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Roby, C.A. (2023). Theorizing Technology: Theōria, Diagram, and Artifact in Hero of Alexandria. In: Valleriani, M., Giannini, G., Giannetto, E. (eds) Scientific Visual Representations in History. Springer, Cham. https://doi.org/10.1007/978-3-031-11317-8_5
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