The original Cheiroballistra text is copied from Wescher (1867), primarily because it's available in public domain and clean of any copyright issues modern texts might have (e.g. Marsden 1971; Wilkins 1995). The translation is split into chapters, and each chapter into smaller segments. Each segment starts with the Greek original text followed by the translation. At the end of each segment are the comments and notes (if any). The Greek text follows Wescher's line and page numbering.
The text makes heavy use of imperatives, which in Greek can carry tons of nuances, and are tricky to translate. For example 3rd person perfect imperatives are used often, and precisely translating the passive voice of those forms is particularly difficult. The other English translations seem to have dropped the ball on this; take for example the very first three words of the manuscript, that is "Γεγονέτωσαν κανόνες δύο", which is a plural 3rd person passive perfect imperative; while the verb form is active, the sentence lacks a direct object (an accusative), so the verb form (or its meaning) must have originally been passive. This kind of errors prop up often in the text. In any case, Wilkins (1995) translates this as "Let two ... boards be made", thus losing the "perfect tense" nuance. Marsden's (1971) translation, "Fashion two ... boards", is even more pragmatic in converting this into a 2nd person present active imperative. The "correct" translation might be "Let two ... boards have been made", but I'm not sure if that's even correct English.
The text makes little sense without the associated diagrams. Fortunately images from codices M and P were published by Wescher (1867) in black and white outline drawings, and by Schneider (1906) as copies of the actual painted images. Both publications are fortunately in public domain, so using images from them was not an issue. Wilkins (1995) also two images from codex V (pages 11 and 32), but according to him the images are almost identical to those in codex P. I decided not include Wilkins (1995) outline drawings from codex V here, because it is unclear whether the results of one-to-one outlining of public domain works (i.e. the codices) is protected by copyright. Links to the original publications from which the images are taken are available on the bibliography page. All images have been extracted from the PDF files with full available quality.
As this translation is licensed under a Creative Commons license and you are free to improve it. Please discuss any changes on the talk page first, though. Also note I do not translate classical or Koine Greek on a daily basis, so there are probably some minor issues with the translation, especially in the more obscure parts.
Case, slider and crescent-shaped piece Edit
W123 ΗΡΩΝΟΣ ΧΕΙΡΟΒΑΛΛΙΣΤΡΑΣ ΚΑΤΑΣΚΕΥΗ ΚΑΙ ΣΥΜΜΕΤΡΙΑ. Γεγονέτωσαν(1) κανόνες δύο πελεχινωτοὶ οἱ ΑΒ ΓΔ, ἐν τετρα- γώνοις πελεχίνοις, ὧν θῆλυς μὲν ἔστω ὁ ΑΒ, ἄρρην δὲ ὁ ΓΔ. Καὶ τὸ μὲν μῆκος ἐχέτω ὁ ΑΒ πόδας Γ καὶ δαχτύλους Δ, τὸ δὲ πλάτος δακτύλους ΓC, τὸ δὲ πάχος δακτύλους ΔC. Ὁ δὲ ΓΔ 5 τὸ μῆκος ἐχέτω πόδας Γ, τὸ δὲ πλάτος ὡς ΒC, τὸ δὲ πάχος δάκτυλον Α δ.
HERON'S CHEIROBALLISTRA. CONSTRUCTION AND PROPORTIONS.
Let two dovetailed beams, ΑΒ and ΓΔ, be made(1), with four-sided dovetails, of which ΑΒ shall be female and ΓΔ male. And ΑΒ shall be 3 feet and 4 dactyls long, 3½ dactyls wide and 4½ dactyls thick. And ΓΔ shall be 3 feet long, about 2½ dactyls wide and 1¼ dactyls thick.
- This verb is active, but it should be passive, because the sentence lacks an object in accusative. Translating it with passive is thus more correct. The tense is perfect, which emphasizes the fact that the action has been completed already and the results are visible in present. Getting this exact message across using English passive imperatives is very difficult.
W124 Ἐχέτω δὲ τὸ βάθος ὁ σωλὴν τοῦ ΑΒ κανό- νος δάκτυλον Α· τοῦ δὲ ΑΒ ἡ μὲν ΑΖ σεσωληνίσθω(1) οὖσα ποδῶν ΒC δακτύλων ς· λοιπὴ ἄρα ἑστὶν ἡ ΖΒ δακτύλων ς. Ἀπειλήφθω(2) δὲ πάλιν τοῦ ΑΒ κανόνος ἡ ΑΘ ποδὸς Α ἡμί- σεως καὶ δακτύλων Δ· ἡ δὲ ΑΚ ποδὸς Α καὶ δακτύλου Α· λοιπὴ 5 ἄρα ἡ ΚΘ ἔσται δακτύλων Ζ. Ἀπειλήφθω(2) δὲ πάλιν τοῦ ΑΒ χανόνος τοῦ πάχους τῶν ΔC δακτύλων δάκτυλος ΑC, καὶ τετμή- σθω ἕως τῆς ΑΚ καὶ τῆς ΛΘ, ὥστε εἶναι τὁ ΚΘ μέρος τῶν αὐτῶν 8 δακτύλων ΔC, τουτέστι τὴν ΧΨΥΦ.
The depth of the channel in beam ΑΒ shall be 1 dactyl. And let AZ, being 2½ feet 6 dactyls, be channeled out(1); thus, of course ΖΒ, 6 dactyls, is remaining. Again, let part ΑΘ, 1½ feet and 4 dactyls, be marked off(2) from beam ΑΒ; thus ΑΚ [is] 1 foot 1 dactyl and ΚΘ: thus, of course, 7 dactyls remains. And again, let 1½ dactyls be marked off(2) from the original thickness of 4½ dactyls of beam ΑΒ, and let [parts] up to ΑΚ and ΛΘ be removed, so that the part ΚΘ, that is to say ΧΨΥΦ, is of the mentioned thickness of 4½ dactyls.
- The verb σεσωληνίσθω is a 3rd person passive perfect imperative - a form which repeats many times in the manuscript. I could not find an exact definition for it, but it is clearly based on noun σωλήν, which means "a channel". The verb has been translated as "channel out" by both Marsden (1971) and Wilkins (1995), and I see no reason to interpret it in any other way.
- The Ἀπειλήφθω was translated as "remove" by Marsden (1971) and "mark off" by Wilkins (1995). I could not find the base form from the dictionaries I had at my disposal, but Wilkins' translation seems more plausible, because the actually removing is taken care of later using the imperative τετμήσθω.
8 Γεγονέτω(1) δὲ καὶ σεληνοειδές τι σχῆμα τὸ ΗΒ, καὶ τρηθὲν(2) ἐν μέσῳ τετραγώνῳ τρήματι συμφυὲς 10 γεγενήσθω τῷ ΛΒ ἄκρῳ τοῦ ΑΒ κανονίου, ὡς τὸ σχῆμα ὑπόκει- W125 ται. Τοῦ δὲ ΓΔ ἡ μὲν ΕΔ ἔστω ἄρρην τελεχῖνος, καὶ ἁρμοστὸς γεγονέτω τῷ θήλει πελεχίνῳ τοῦ ΑΒ σωλῆνος τῷ ΑΖ μέρει, τουτέστι τὸ ΔΕ μερος τοῦ ΓΔ κανόνος.
And let a crescent-shaped piece be made(1), which has the form of ΗΒ, and let it have(2) in the middle a rectangular hole, and let it be united with beam ΑΒ's farthest point, ΛΒ, as shown below. Let part ΕΔ of [the beam] ΓΔ be a male dovetail, and let it be made to fit well into the female dovetailed part ΑΖ of [the beam] ΑΒ, that is to say part ΔΕ of beam ΓΔ.
- This verb should probably be in passive, not in active. This is also one of those tricky perfect imperatives.
- The exact form of τρηθὲν has so far eluded me. Given the context and the overall style of the text, it probably attempts to be a passive imperative.
Triggering mechanism Edit
Νῦν δὴ τὰ περὶ τῆς κλείσεως ἐκθησόμεθα. Γεγονέτω(1) ἐξ ὕλης 5 σιδηρᾶς(2) χειρολάβη ἡ ΑΒΓΔ, τῷ σχήματι οἵα ὑπογέγραπται. W126 Δίχηλον δὲ τὸ ΕΖ μέρος ἔχων ὁ ΕΖΗΘ τόρμος ἔστω τετρὰγω- νος· σχαστηρία δὲ ΚΛΜ· δρακόνπον δὲ τὸ ΝΞ· πιττάριον δὲ τὸ 8 ΟΠΡΣ.
And now we shall describe things related to the triggering mechanism. Let handle ΑΒΓΔ be made(1) of wood as strong as iron(2), and of form such as has been drawn below. And the two-pronged component ΕΖ shall have tenon ΕΖΗΘ, which shall be rectangular. And the release mechanism [is] ΚΛΜ. And the little dragon [is] ΝΞ. And the pittarion [is] ΟΠΡΣ.
- This sentence lacks an object: Γεγονέτω ... χειρολάβη ἡ ΑΒΓΔ. The predicate should probably be in passive form, as in most of the text.
- The word ὕλης (genetive of ὕλη) in "ἐξ ὕλης σιδηρᾶς" has been effectively ignored by most scholars. There are several variants of this part; According to Schneider (1906: 150) manuscript V says "ἐχ ξύλης" here, and P says "ἐχ ξυλώσης". Prou (1877: 20) mentions another reading variant, "ἐχ ξύλῳ". In any case, in this context "ὕλη" or the variants can only mean "wood as a material" or "material" in general. Depending on the dictionary one looks at, the latter, more generic usage is said to be rare. Regardless, all scholars seem to have universally accepted the "material in general" interpretation, usually without leaving any trace of "ὕλη" in their translations (e.g. Prou: 1877: 20; Marsden 1971: 213; Wilkins 1995: 14). Schneider's translation, "aus eisenmaterial" ("of iron material") is the best in this regard. Wilkins (1995: 16) kindly notes that the material for a component is only mentioned thrice in the cheiroballistra manuscript, the two other cases being the bronze cylinders ("κύλινδροι χαλκοῖ κοῦφοι") and the iron bars ("σιδηροῦς κανόνας"). As can be seen, in neither of these cases does the word ὕλη show up. A quick look at Heron's Belopoeica also reveals the lack of use of ὕλη: "στήματα ὀρθὰ σιδηρᾶ δύο" ("two vertical iron stanchions", M 76), "σιδηροῦς δάκτυλος" ("iron finger", M 76), "ἐποίουν δὲ αῦτὰς σιδηρᾶς" ("they made these of iron", M 83), "περόνη σιδηρᾶ" ("iron pin", M 89) and "λεπίδας σιδηρᾶς" ("iron plates", M 102). Why not just use this much simpler wording here also, and skip the "iron material" nonsense? In this light my methaphorical translation, "wood as strong as iron", seems quite possible, and it completely changes the nature of the handle, limiting its uses and ruling out, for example, its use as attachment point for the winch. Another translation possibility might be "wood material reinforced with iron" or such.
8 Καὶ τετρήσθω(1) ἡ ΑΒΓΔ χειρολάβη κατὰ τὸ Δ· ὁ δὲ ΕΔ κανὼν ὁ ἐν τῷ πρώτῳ θεωρήματι τετρήσθω(1) κατὰ ΜΝΞ, 5 καἱ κατὰ μὲν τὰ ΜΝ στρογγυλῳ τρήματι διαμπερὲς(2), κατὰ δὲ τὸ Ξ παραλληλογράμμῳ(3)· καὶ οὕτως ἐνηρμόσθω ἡ χειρολάβη, ὥστε περόνην διὰ τῆς ΜΝ διωσθῆναι(4) καὶ διὰ τοῦ Δ τρήματος τῆς χει- 8 ρολάβης κοινωθῆναι(5).
And let a hole be made(1) to the handle ΑΒΓΔ at Δ. And let a hole be made(1) to the beam ΕΔ, described earlier, at ΜΝΞ, at ΜΝ with a round hole right through(2), and at Ξ with a hole that has parallel lines(3); and in this way let the handle be fitted, so that a pin pushed through(4) ΜΝ and through hole Δ of the handle unites them(5).
- The base form of τετρήσθω (3rd person singular imperative passive) seems to be τετραίνω, which can mean boring, perforating or perforating, or in general something that makes a hole.
- The word διαμπερὲς ("right through") seems to emphasize the fact that this hole goes right through the beam, whereas the second hole does not.
- The word παραλληλογράμμῳ (singular dative), which describes the second hole, is not strictly rectangular according to LSJ. Instead, it is given a clunky English meaning of "bounded by parallel lines".
- I could not find a perfect definition for the infinitive διωσθῆναι. The closest match seems to be ὁ διωσμός, which according to LSJ signifies "pushing through of embedded weapons" in surgery.
- The infinite κοινωθῆναι seems to be a derivative of verb κοινόω, which in this context should probably translated can be translated as "unite [one to the other]". The phrase has been previously translated as "dass ... eine verbindung herstellt" (Schneider 1906: 153), "and riveted" (Marsden 1971: 213), "and be fixed" (Wilkins 1995: 14). The latter two translations change the meaning of the word from very generic to more or less specific, which is incorrect.
8 Τρήσαντες δὲ τὸ ΕΘ δίχηλον κατὰ [τὰ] ΤΥ καὶ τὴν ΚΛΜ σχαστηρίαν κατὰ τὸ Φ, καὶ ἐμβαλὸντες περόνην 10 δι´ ἀμφοτέρων τῶν ὀπῶν τῶν ΤΥΦ, κοινοῦμεν, ὥστε περὶ αὐτὴν κινεϊσθαι tὴν σκαστηρίαν ἀνεμποδίστως. Ἐχέτω δὲ ἡ σκαστηρία ἐν- τομὴν τὴν ΛΜ ἔχουσαν κατὰ μῆχος δάκτυλον ἕνα. Λαβόντες(1) οὖν W127 τὴν ΔΟ ἐπὶ τοῦ ΓΔ κανόνος δακτύλων Ε, καὶ τρήσαντες κατὰ τὸ Ο, καθίεμεν τὸ ΕΘ δίχηλον καὶ κοινῦμεν, ὧστε ἀκίνητον διαμένειν(2).
And by perforating the two-pronged [component] ΕΘ at ΤΥ, and [by perforating] the release mechanism ΚΛΜ at Φ, and by pushing a pin through both holes ΤΥΦ, we unite [them], so that the release mechanism can rotate around the pin unhindered. The release mechanism has length-vise slit ΛΜ of one dactyl. Then by measuring(1) ΔΟ, 5 dactyls, on board ΓΔ, and by piercing through Ο, we lower the two-pronged component ΕΘ and we unite [them], so that they are fixed immovably(2).
- In Schneider (1906) and Marsden (1967) "Λαβόντες" is written as "ἀπολαβόντες". Wilkins (1995) gives the ἀπο prefix as optional. In any case, the only suitable generic meaning would seem to be "to take", but in this case "to measure" is a more appropriate translation.
- Apparently this tries to emphasize rigidity of the construction, which is indeed extremely important in practice. If there is any slack in this part of the construction, there will be dangerous dry-fires as the bowstring will slip from the release mechanism at the most inconvenient moment.
ἔπειτα τρήσαντες τὸ ΝΞ δρακόντιον κατὰ τὸ Ν, καὶ τὸν ΓΔ κανόνα κατὰ τὸ Π (τὸν ἐν τῷ πρώτῳ θεωρήματι) ἀπέχον τοῦ Μ 5 δακτύλους Δ, καὶ καθέντες διά τε τοῦ τρήματος τοῦ δρακοντιοῦ καὶ τοῦ Π περονην, κοινοῦμην, ὥστε εὐχερῶς κινεῖσθαι τὸ ΝΞ δρακόν- 7 τιον περἱ αυτήν.
Thereafter, by making a hole to the little dragon ΝΞ at Ν, and to the board ΓΔ (the one shown earlier) at Π, 4 dactyls from Μ, and by lowering the pin through both the hole in the little dragon and [the hole] Π [in the board ΓΔ], we join [them], so that the little dragon ΝΞ moves freely around the pin.
7 Καὶ πάλιν ἀποστήσαντες(1) ἀπὁ τῆς χειρολάβης τῆς [ΑΒ]ΓΔ τὴν ΞΡ, τιτρῶμεν κατὰ τὸ Ρ, καὶ πάλιν ἀπ' αὐτοῦ μετρήσαντες δακτύλους ΔC(2) ὡς τὴν ΠΣ, τιτρῶμεν κατὰ τὸ Σ, W128 καὶ οὗτως καθὶεμεν ἐν τῷ ΓΔ κανόνι, ὅστις ἐστὶν ἐν τῷ πρώτῳ θεωρήματι. Ἑξῆς κεῖται.
And again, by measuring(1) ΞΡ from the handle [ΑΒ]ΓΔ, we make a hole at Ρ, and again by measuring ΠΣ, about 4½ dactyls(2), from it [Ρ], we make a hole at Σ, and in this way we lower [the pittarion] into board ΓΔ, that has been shown before. Here they are [shown] one after another.
- The base form of the participle ἀποστήσαντες does not really mean "measure", but "set" or "place", in this case with emphasis on "away" or "from the handle".
- "About 4½ dactyls" is way too wide for the pittarion to fit inside the slider or the case. Playing the "textual corruption card" is the easy way out here: if we replace Δ with Α and we get a reasonable measurement, "about 1½ dactyls". The word "about" (ὡς) reinforces the interpretation that the pittarion width is related to the width of the slider, which was given as "about 2½ dactyls". The slider's width at top is probably just enough to accommodate the pittarion.
Torsion springs Edit
Field frames Edit
Κατεσκευάσθωσαν δὲ καὶ τὰ καλοίμενα καμβέστρια τρόπῳ τοιῷδε. Ποιήσαντες γὰρ σιδηροῦς κανόνας τέσσαρας, μῆκος ἔχον- 5 τας ἑκάτερον δακτύλουν ΙC, πλάτος δὲ δακτύλου διμοίρου μι- 6 κρῶ πλείω, πάχος δὲ ὥστε μὴ εὐχερῶς κὰμπτεσθαι.
Let the so-called field frames be constructed and let them be made in this way, namely, by making four iron bars having length of 10½ dactyls, and width of ⅔ dactyls or a little more, and thickness such that they do not easily bend.
6 Ἐστωσαν δὲ οἱ ΑΒ ΓΔ ΕΖ ΗΞ, οἷοί εἰσι τῷ σχήματι καταγεγραμμένοι, ἔχοντες συμφυεῖς κρίκους τούς ΚΛ ΜΝ ΞΟ ΠΡ, τὸ εὖρος(1) ἔχοντας δακτύλους δύο, τὸ δὲ πλάτος δάκτυλον ἔνα, τὸ δὲ πάχος W129 τὸ αὐτὸ τοῖς κανονίοις. Ἔστω δὲ τὸ μεταξὺ διάστημα τῶν κανόνων 2 δακτύλων ΓC.
And there shall be [beams] ΑΒ ΓΔ ΕΖ ΗΞ, of such form as have been drawn, having uniting rings ΚΛ ΜΝ ΞΟ ΠΡ, having breadth(1) of 2 dactyls, and width of 1 dactyl, and the same thickness as the beams. There shall be in between the beams an interval of 3½ dactyls.
- This must refer to the inner diameter of the rings
2 Γεγονέτωσαν δὲ καὶ πιττάρια τὰ ΣΤΥΦΧΨΩ,Α συμφυῆ τοῖς ΑΒΓΔΕΖΗΘ κανονίοις, ἔχοντα πλάτος(1) καὶ πά- 4 χος(1) τὸ αὐτὸ τοὶς κανονίοις, τὸ δὲ εὖρος δακτύλου δίμοιρου.
And let pittarions ΣΤΥΦΧΨΩ,Α be made, united to beams ΑΒΓΔΕΖΗΘ. They [the pittarions] have width and thickness of the beams, and breadth(1) of ⅔ dactyls.
- This refers to the height and width of the inside of these parts.
4 Ἔστω- 5 σαν δὲ καὶ κύλινδροι χαλκοῖ κοῦφοι ὁι ,Β,Γ ,Δ,Ε ,Ϝ,Ζ ,Η,Θ, μῆκος ἔχων ἕκαστος δακτύλως δύο, πάχος δὲ ἴσον τῶν κανονίῶν, τὴν δὲ διάμετρον τοῦ ἔυρους δακτύλου Α καὶ γ'. Ἔχετωσαν δὲ καὶ συμφυεῖς κρίκους περιχειμένους τῇ κυρτῇ ἐπιφανείᾳ τῶν κυλίν- δρων, τοὺς ΑΜΒΜ, ΓΜΔΜ, ΕΜϜΜ, ΖΜΗΜ, ἀπέχοντας ἀπὸ τῶν ,Β,Δ,Ϝ,Η 10 δάκτυλον Α καὶ δ': πλάτος δὲ ἐχέτωσαν δακτύλου δίμοιρον, πά- χος δὲ τὸ ἴσον τῶν κανονίων. Ὁι ,Β,Γ ,Δ,Ε ,Ϝ,Ζ ,Η,Θ κύ- λινδροι ἐντομὰς ἐχέτωσαν κατὰ διάμετρον τὰς ϜϜϜϜ, εἰς ἃς W130 κανόνια ἐμβεβλήσθω ἁρμοστὰ κατὰ κρόταφον τὰ ΟΜ, ΟΜ, ΟΜ, ΟΜ, μῆχος ἔχον ἑκάτερον δακτύλους Γ, πλάτος δὲ δακτύλου δί- 3 μοιρον.
And there shall be light bronze cylinders ,Β,Γ ,Δ,Ε ,Ϝ,Ζ ,Η,Θ each having length of two dactyls, and having the same thickness as the beams, and having the diameter of the breadth of 1⅓. And rings shall be united with and go around the surface of the cylinders, and [the rings] are ΑΜΒΜ, ΓΜΔΜ, ΕΜϜΜ, ΖΜΗΜ and [they] are 1¼ dactyls from ,Β,Δ,Ϝ,Η: and the width [of the rings] shall be ⅔ dactyls, and the thickness [shall be] equal to that of the beams. Cylinders ,Β,Γ ,Δ,Ε ,Ϝ,Ζ ,Η,Θ shall have diametrically opposed slits ϜϜϜϜ, and well-fitted bars ΟΜ, ΟΜ, ΟΜ, ΟΜ shall have been placed against the side surfaces [of the cylinders], each [bar] having length of 3 dactyls, and width of ⅔ dactyls.
Little arch Edit
4 Γηγονέτω δὲ τὸ καλούμενον καμάριον, τῷ σχήματι οἷον 5 ὑπογέγραπται τὸ ΑΒΓΔΕΖΗ, ἔχον τὴν μὲν ΓΕ ποδὸς ἑνὸς καὶ δακτύλων ΖC, τὸ δὲ διάστημα τοῦ καμαρίου τὸ ΘΚ δακτύλων Ε. Τὸ δὲ μῆκος ἑκατέρας τῶν ΑΖ δακτύλων Δ, ἑκατέρας δὲ τῶν ΒΗ δακτύλων Β. τὸ δὲ μεταξὺ διάστημα τῶν ΑΒ καὶ ΖΗ ὡς δακτύλον ΓC. πὰχος δὲ ἐχέτω ἴσον τῶν προειρημένων κανο- 10 νίων.
The so-called little arch, ΑΒΓΔΕΖΗ, shall be produced, of a shape such as has been painted below, and ΓΕ being 1 foot and 7½ dactyls, and the interval ΘΚ of the little arch being 5 dactyls. And the length of each of ΑΖ [is] 4 dactyls, and of each of ΒΗ [is] 2 dactyls. And interval between ΑΒ and ΖΗ [is] about 3½ dactyls. And the thickness shall be the same as that of the aforementioned beams.
Little ladder Edit
10 Τὸ δὲ καλούμενον κλιμάκιον ἔστω τὸ ΛΜΝΞΟΠΡΣ, ἐκ W131 δύο κανόνων τῷ σχήματι οἷον ὐπογέγραπται, μῆκος ἔχων ὁ μὲν ΟΠΡΣ κανὼν ποδὸς ἑνὸς καὶ δακτύλων Ι, ὁ δὲ ΛΜΩΞ ποδὸς ἑνὸς καὶ δακτὺλων Η, πλάτος δὲ πρὸς μὲν τοῖς ΥΤ μέρεσι δακτύλους δύο, πρὸς δὲ τοῖς ΟΠΡΣ δάκτυλον ἕνα τέταρτον.
And there shall be the so-called little ladder ΛΜΝΞΟΠΡΣ, [made] from two beams of such shape as has been painted below, beam ΟΠΡΣ having length of 1 foot and 10 dactyls, and [beam] ΛΜΩΞ [having] length of 1 foot and 8 dactyls, and the width at part ΥΤ [being] 2 dactyls, and [the width] at [part] ΟΠΡΣ [being] 1¼ dactyls.
5 πάχος δὲ ἕκαστος τῶν Λ,Β Ν,Γ Ο,Δ Ρ,Ε τόρμων ἔστω δακτύλων Β(1). Καὶ διερήσθωσαν οἱ ΛΜΝΞ ΟΠΡΣ κανόνες εἰς τρία ἴσα τὰ ΦΤΨΧΥΩ: καὶ τετρήσθω, τὰ μὲν ΤΥ κατὰ τὸ μῆκος(2) τρῆμασι παραλληλογράμμοις, τὰ δὲ ΦΧΨΩ τρήμασι 9 στρογγύλοις.
And the thickness of each of Λ,Β Ν,Γ Ο,Δ Ρ,Ε tenons shall be two dactyls(1). And let the beams ΛΜΝΞ ΟΠΡΣ be divided in three equal parts ΦΤΨΧΥΩ: and let holes be made, right-angled holes at ΤΥ along the length(2), and round holes at ΦΧΨΩ.
- The text clearly states that the thickness of the tenons should be 2 dactyls. I disagree with many others (e.g. Wilkins and Marsden) that there has to be an error here. All one has to do is visualize this like you would a mortise and tenon joint, in which case the word πάχος, or "thickness", makes perfect sense. In other words, the thickness figure is added to the length of the beams. If we do this, the length of the little ladder beams and the little arch match very closely.
- The phrase "κατὰ τὸ μῆκος" is a bit challenging. Marsden (1971) did not translate it at all, whereas Wilkins (1995) used a reasonable translation of "running longitudinally".
9 Καὶ γεγενήσθω διαπήγιον(1) τὸ ΤΥ, ἔχον τὸ μὲν μῆκος 10 χωρὶς τῶν τόρμων δακτύλον Γ, τὸ δὲ πλάτος δακτύλους δύο ἥμισυ. Ἔστωσαν δὲ καὶ σιυλάρια(2) τὰ ΦΧΨΩ, ἔχοντα τὸ μῆκος χωρὶς τῶν τόρμων δακτύλους Γ, τὸ δὲ πλάτος δακτύλους ΒC.
And let the cross-piece(1) ΤΥ be made, and having length of 3 dactyls not counting the tenons, and [having] width of 2½ dactyls. And there shall be rungs(2) ΦΧΨΩ, having length of 3 dactyls not counting the tenons, and [having] width of 2½ dactyls.
- Marsden (1971), followed by Wilkins (1995) translate this part (διαπήγιον) as "cross-piece". Prou (1877) translates it to French as "traverse", which could be translated as "rung" in English. The word seems to be a combination of διά and πηγίον, the latter being a diminutive of πηγή. The only meaning of πηγή which even remotely fits this context is the adjective "stout, thick, tough". So διαπήγιον seems to mean "a stout [component] that separates [things]". Translating it as a "cross-piece", "spacer" or a "rung of a ladder" seems just fine.
- Marsden (1971), followed by Wilkins (1995) translate this part (στυλάρια) as a "rung [of a ladder]". Prou (1877) translates it as "colonnette", which means a "small column" in English. The word is a diminutive of στῦλος, which means a pillar. So a "small pillar" is probably the most accurate translation. However, in order not to introduce new confusing terminology, I've chosen to follow Marsden's original translation, "rung".
W132 Καὶ καθείσθωσαν(1) τά τε στυλάρια καὶ τὸ διαπήγιον εἰς τὰς ὀπὰς τῶν κανόνων, καὶ καθηλώσθωσαν ὀι τόρμοι τοῦ διαπηγίου πρὸς τοῖς κανόσιν ἐπὶ οὐρᾶς(2), ὧστε συνέχεσθαι τοὺς κανόνας καὶ εἶναι αὐτῶν τὸ 4 μεταξὺ διάστημα δακτύλων Γ.
And let the rungs and the crosspiece be lowered(1) to the holes of the beams, and let the ends of the tenons(2) of the cross-piece grasp next to the beams(2), so that they hold the beams together and that there is an aperture of 3 dactyls between them.
- The word καθηλώσθωσαν seems to be 3rd person plural aorist passive imperative of the verb αἱρέω, which in this case probably means "to grasp". When coupled with the preposition κατά, the meaning is probably along the lines "to grasp in a downwards motion" or "to grasp down" This sounds a lot like riveting, which is the term Marsden (1971) used in his translation. Wilkins (1995) used the term "to pin", which I think is incorrect.
- This sentence is a bit tricky to interpret. The actors in the sentence are the τόρμοι, which grasp (down) the beams. The πρὸς τοῖς κανόσιν is straightforward enough, meaning "near the beams". So the τόρμοι do their grasping near the beams. The ἐπὶ οὐρᾶς is more challenging. The preposition ἐπί coupled with a genitive can mean "on", "towards" or "at". The noun οὐρά in this context probably means "tail", "rear" or "end". A reasonable translation seems to be "at the end". As "at the end of the beams" makes little sense in this context, the grasping has to be done by the ends of the τόρμοι. This sounds a lot like riveting.
4 Ἔτι δὲ μὲν καθηλὼσθωσαν τῷ 5 ΛΝ κανόνι καὶ τῷ ΟΡ τὰ ϛϛ ἐφ'ἑκάτερα τοῦ ΤΥ διαπήγμα- τος, μῆκος ἔχοντα δακτύλων Γ, πλάτος δὲ δάκτυλον ἕνα, πάχος δὲ σύμμετρον: καὶ τετρήσθωσαν κατὰ τὸ μέσον, ἀπεχέτωσαν δὲ ἀπ'ἀλλήλων δακτύλους ΒC.
And moreover let ϛϛ grasp the beams ΛΝ and ΟΡ on each side of the cross-piece ΤΥ, (the ϛϛ) having length of 3 dactyls, and width of one dactyl, and thickness in suitable proportion: and let them have a hole in the middle, and they shall stay 2½ dactyls from each other.
W133 Πεποιήθωσαν δὲ καὶ κωνοειδῆ δύο τὰ ΑΒΓΔ ΕΖΗΘ, ἔχον μὲν ἑκατερον μῆκος δακτύλων ΙΑ. Τὸ δὲ πάχος τῶν ΑΒ ΕΖ κορυφῶν ἑκάστου κωνοειδοῦς ἐχέτω δακτύλου τὸ ἥμισυ, τὸ δὲ τῆς βάσεως πάχος ἑκάστου τῶν ΓΔ ΗΘ δακτύλου ἑνός. Ἐχέτωσαν 5 δὲ κατὰ μῆκος σωλῆνας τετραγώνους(1) καὶ τόρμους(2) ἐν ταῖς ΑΒ ΕΖ κορυφαῖς, ὥστε κανονίων γενομένων συμφυῶν κρίκοις, ἁρμο- στῶν τοῖς τόρμοις καὶ τοῖς σωλῆσιν, ἐκκομίζεσθαι ἐπι τῶν σω- λήνων καὶ τῶν τόρμων(3) ἐν τοῖς κωνοειδέσι γεγονόσιν. Ἔστωσαν δὲ τὰ μὲν κανόνια συμφυῆ τοῖς κρίκοις τὰ ΚΛΜΝ ΞΟΠΡ, W134 κρίκοι δὲ ὁι ΚΛ ΞΟ· ἀνακαμπὰς δὲ ἐχέτωσαν τὰ κανόνια πρὸς τοῖς πέρασι τὰς ΜΝ ΠΡ, ὕψος δἑ ἐχούσας δακτύλου τὸ ἥμισυ.....
Let two cones, ΑΒΓΔ ΕΖΗΘ, be made, each having length of 11 dactyls. Thickness of the cones at the tips ΑΒ ΕΖ of each cone shall be ½ dactyls, and thickness at each of the bases ΓΔ ΗΘ shall be 1 dactyl. They shall have longitudinal, square(1) channels and sockets(2) at their ends ΑΒ ΕΖ, so that small bars joined with rings and well-fitted to sockets and channel, are carried towards(3) the[se] channels and sockets that have been made into the cones. And the small bars united with the rings are ΚΛΜΝ ΞΟΠΡ and the hoops are ΚΛ ΞΟ: the small bars shall have curves having height of ½ dactyl near the ends ΜΝ ΠΡ.....
- LSJ gives "square" as the most common translation for τετραγώνως. However, it can mean anything with four angles. In one manuscript diagram the channel looks dovetailed. However, as Iriarte (2000: 59) points out, if P.H. had intended to mean that the channel was a dovetail, he could have used a more appropriate word, such as the one he used when describing the case and the slider: πελεκινοειδής.
- The exact meaning of τόρμος is a little unclear. Both LSJ and Middle Liddell give a very generic meaning: "any hole or socket, in which a pin or peg is stuck".
- Translating "ὥστε ... ἐκκομίζεσθαι ἐπι τῶν σωλήνων καὶ τῶν τόρμωνis" is rather tricky. Marsdens (1971) translates this as "so that ... movement is allowed along the grooves and for the tenons". Wilkins (1995) follows this basic idea with "so that ... they can be pulled out along the grooves and tenons". The generic meaning for infinitive ἐκκομίζεσθαι is "carry" or "bring out", and ἐπι + genitive can mean a number of things, but here the only reasonable meaning is "towards" something. Schneider (1906), following Bruno Keil, attempted to correct ἐκκομίζεσθαι to ἐισομίζεσθαι, which changes the meaning to "carry in". While this fits the context better, all primary sources say ἐκ instead of ἐισ here.