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The pneumatics of Hero of Alexandria

Chapter 83: APPENDIX.
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A systematic practical handbook of machines and demonstrations that uses air, steam, heat, and water to produce mechanical effects. The text gives clear descriptions, construction details, and diagrams for siphons, valves, pumps, fountains, jets, self‑acting mechanisms, and ritual or theatrical contrivances driven by pressure and temperature changes. Explanations focus on the mechanical principles behind pneumatic and hydraulic behaviors and on ways to control flow and timing, with numbered propositions that pair instructional steps with illustrative figures for building and operating each apparatus.

APPENDIX.

There are four MSS. of Hero contained in the British Museum. Two belong to the Harleian Collection: they are numbered 5605 and 5589, and are assigned, the first to the fifteenth, the second to the sixteenth century; they are distinguished in the table below by the letters a and b. The others are among the Burney MSS., (108 and 81), and are both assigned to the sixteenth century: they are cited as c and d. Of these MSS. the first and third, (a and c), are by far the most trustworthy: they generally supply the clauses missing in the printed text, and often furnish emendations of passages otherwise corrupt. The other two agree, for the most part, with each other, and with the printed text, both in the omission of numerous clauses and in the grossest errors in individual words. It is thus rendered probable that the defects of the Paris edition are in great measure due, not to the Editors, but to the MS. followed.

In the following table of emendations made in the text of Hero as it appears in the Veterum Mathematicorum Opera, those only have been noticed which appeared curious or important. Many more have been passed over in which the correction was obvious even without the aid of any MS. The references are to the page and line of the Paris edition.

Page and Line of Paris edition. Reading of Paris Text. Reading adopted.
147 - 29 συκίαν a b d. σικύαν c.
150 - 10 ἐκφανείας ἐπιφανείας a b c d.
- 34 τὴν—διαστολὴν κατὰ τὴν—διαστολὴν a.
151 - 8 μυκτῆρσιν d.
μυκτῆρσιν ἀέρος
a b c.
- 51 ὅσας ὅσαι a b c d.
153 - 6 βαθύτερον d. βαρύτερον a b c.
- 23 στεγνὸν d. στενὸν a c.
155 - 3 ἀντέχον a c d. ἀντέχων b.
156 - 1 πνυκτικὸς a b. πνικτικὸς c. Commandine reads πνευματικὸς.
- 24 ἀλλὰ τὸ μὴ c. ἀλλὰ τῷ μὴ a b d.
- 26 ἀντεπεξίοντος ἀντὶ τοῦ ἐπεξίοντος a b c d.
159 - 17 τὸ ἐν τῷ ὑγρῷ
(τὸ εν τῷ ὑγρον b.)
τὸ ἐν ἀυτῷ ὑγρὸν a c.
161 - 2 ἰσθμὸς

ἠθμὸς. This correction, adopted originally on the conjecture of Professor Malden, is supported by the variations of the MSS.; a reads ἱθμος, b ἡθμος. In like manner elsewhere read ἠθμοειδή, &c. for ἰσθμοειδή.

- 20 ἐκκεκρυήσεται
(so all the MSS.)
οὐκ ἐκρυήσεται
170 - 30 ἐκείνοις ἔκεινον a b c.
172 - 17 κατέχοντος c. κατέχοντες a b.
- 18 ἐὰν δὲ ἄνω ὄντος ἐὰν δὲ ἀνῶμεν ἔτι ἄνω ὄντος a b c.
- 30 ἴσον, ἐὰν ὅσον ἐὰν a b c.
173 - 20–24

This passage is unintelligible as it stands. It should be read (with a b c) as follows:—

Ἐγχέωμεν οὖν καὶ εἰς τὴν ΜΝΞΟ βάσιν καὶ εἰς τὸν ΠΡ κρατῆρα τὸν οἶνον ὥστε πλήρη εἶναι τὸν ΠΡ κρατῆρα, καὶ τὴν ΜΝΞΟ βάσιν πεπληρῶσθαι ἄχρι τοῦ Η στομίου τοῦ σωλῆνος· τούτου δὲ γενομένου, καὶ φραγέντος τοῦ Ε, οὐ διὰ τοῦ ΚΛ σωλῆνος, &c. In the printed text all the words from τὸν οἶνον to τὸν κρατῆρα inclusive are omitted; so is the οὐ after φραγέντος. In the translation the MSS. have been departed from in reading “as high as the mouth of the tube G H,” instead of “as high as the mouth G of the tube G H.” The latter reading is clearly inconsistent with the argument.

174 - 3

εἰσχωρεῖ καὶ διὰ τοῦ τρήματος

εἰσχωρεῖν καὶ διὰ τοῦ Υ τρήματος a b c.

- 13 ὁ Κ, ὁ κενὼν ὁ Κ ἔνων a b c.
177 - 1 ἀνακεκαμφθέντα ἀγγεῖα

ἀνακεκάμφθω εἰς τὰ ἀγγεῖα c. a b have ἀνακεκάμφω.

- 24

The printed text is here quite unintelligible. We find (beginning of § 24 in translation) these words:— ἔστω σμηρισμάτιον ᾧ ἐὰν βουλώμεθα λόγῳ· ἔστω δὲ τὸ ὕδωρ τοῦ οἴνου διπλάσιον. The opening sentence should be as follows: Ἀγγείου ὄντος κενοῦ καὶ ἑτέρου οἶνον ἔχοντος, ὅσον ἐὰν ὕδωρ εἰς τὸ κενὸν ἀγγεῖον ἐμβάλωμεν, τοσοῦτον διὰ κρουνοῦ ληψόμεθα κεκραμένον ᾧ ἐὰν βουλώμεθα εἶναι λόγῳ· ἔστω δὲ τὸ ὕδωρ τοῦ οἴνου διπλάσιον. So a c: b d agree with the text.

180 - 11

Omit τρίτου with a c: b d agree with the text in retaining the word, which is unintelligible.

192 - 3 ἐπιληφθέντα b d. ἐπειληθέντα c. a has ἐπειληφθέντα.
193 - 26 ἀποδεδεμένοι ἀποδεδομένοι a b c d.
195 - 7 ἀποδεδόσθω ἀποδεδέσθω a b c d.
197 - 6 ἄνω a b c d.

κάτω, which is given in the margin of d, is necessary to the sense.

200 - 8

Read ἐναρμοσθεὶς εἰς τὸ σφαίριον φερέτω εἰς τὴν χώνην, καὶ ἐμβεβλήσθω εἰς τὸ σφαίριον ὕδωρ. So all the MSS. In the text all from φερέτω to σφαίριον inclusive is omitted.

- 14

After ὑγρὸν add καὶ ἀναπληρώσει τὸν κενωθέντα τόπον. So a b c.

202 - 20

The last clause of § 50 (of the translation) is unintelligible as it stands in the printed text. For στρέφειν εἰς τὴν χώραν a and c give εἰς τὴν σφαῖραν. In the translation σφαῖραν is preferred to χώραν, and εἰς omitted.

205
206
185
-
-
-
10 }
10 }
11 }

Clauses of considerable length are missing in the text from the usual cause. They are supplied in the translation.

212

The arrangement of the three plans for self-acting lamps has been altered in conformity with a and c; b and d, agreeing with the printed text.

216 - 26 ἐκπίπτοντος εἰσπίπτοντος a.
223 - 7 ΓΔ (CD)

ΕΖ (EF): this change has been made on conjecture.

- 16

Before ὥστε ἢ has been inserted, without support from the MSS. The passage is otherwise self-contradictory.

226 - 23 διηνοιγμένον a b c d. διενηνεγμένον?
227 - 21

This passage is corrupt, but the MSS. give no light.

228 - 8 ἐκτὸς ἐντὸς a b c d.
- 41 ἐν τοῖς αὐλοῖς a b c d. τοῖς ἐν τοῖς αὐλοῖς?
229 - 30–40

The reading of the text is evidently corrupt here, but the MSS. do not supply means for correcting it: μίας οὔσης may be a corruption of μενούσης; Hero speaks elsewhere of a περόνη μένουσα.

232 - 14

The text and all the MSS. read ὑπὸ; nevertheless ὑπὲρ has been substituted in the translation. If the holes X and R were beneath the partition, the action of the tubes would fail.