Ptolemy’s treatise on the meteoroscope recovered

2023-04-19 00:07:12

Web page 190 was amongst these on which Heiberg managed to learn a small quantity of textual content by post-mortem; his transcription of the highest three strains is as follows^{Footnote 16}:

. . . . τινα τροπον επεσκεπται ον . . . . .

. . . . τας τε καταβατικας και αντι . . . .

. . . σκιους

The dots present that he didn’t understand that these strains, being a chapter title, are indented from the margins in order that his readings represent a stretch of unbroken textual content. We at the moment are capable of learn and translate strains 1–4 of their entirety:

1

τίνα τρόπον ἐπισκεπταῖον (l. ἐπισκεπτέον).
2

τάς τε κατ̣αβατικὰς καὶ ἀντι-
3

σκίους γω̣νίας ἐπὶ τοῦ ὑποτι-
4
[θ]εμένου κλ̣ί̣ματος.
1

In what method one ought to look at.
2

the katabatikê and anti–
3

skios angles on the hypo-
4

thesized klima (i.e., terrestrial latitude).

The chapter itself occupies strains 6–26 and is adopted by one other chapter title cited above (strains 28–30).^{Footnote 17} The subject is a computational, not an observational, process. It’s presupposed that the Solar’s longitude has been set for a given date utilizing some sort of marker on the zodiac ring and that the revolver ring has been rotated in order that the Solar is on the acceptable ascensional distance from the meridian for the given time. Then, the all-tilter ring is manipulated in order that it passes by each the zenith and the Solar’s place (within the textual content that is referred to as τὸ κατὰ κορυφὴν ἐπίπεδον, “the aircraft by the zenith,” in fashionable terminology a vertical circle). The textual content continues (strains 14–23; for photographs see Figs. 3, 4, 5, 6 and 7):

ἥ τε ἀπολαμβανομένη α̣ὐτοῦ π̣εριφέ̣ρε̣ι̣α̣ ἡ̣ μεταξὺ τοῦ τε ἡλίου καὶ τοῦ κατὰ κορυφὴν (about 3 incompletely legible phrases) ὑ̣π̣ο̣τ̣[ί]ν̣ο̣υ̣σ̣α̣ (l. ὑποτείνουσα) [τὴν] γωνί̣αν τη̣ν̣ ὑ̣φ᾿ ἡμῶν καλουμένην κ̣αταβατι̣κὴν κα̣ὶ τὴν λείπουσαν εἰς τὴν μίαν ὀρθὴ̣ν̣ ⟨ἣν⟩ οὕτως ὠνόμ̣ασαν οἱ̣ πρὸ̣ ἡμῶν, καὶ ἔτι ἡ ἀπ̣ολαμβανομένη περιφέρεια τοῦ ὁρίζοντος μεταξὺ τοῦ τε μεσημβρινοῦ καὶ τοῦ παγκλινοῦς, ὑποτίνουσα (l. ὑποτείνουσα) καὶ αὐτὴ τὴν γωνίαν <τὴν> ὑπὸ τῶν παλαιῶν ἀντίσκιον καλουμένην …

… the arc of it (scil. the all-tilter) lower off between the Solar and the zenith (about 3 incompletely legible phrases) which subtends the angle named by us katabatikê (“downward-heading”) and the remaining (angle to finish) one proper angle, to which our predecessors gave this identify (scil. katabatikê), and furthermore the arc of the horizon lower off between the meridian and the all-tilter, which itself subtends the angle that was named antiskios (“counter-shadow”) by the previous ones…

In Fig. 8, which reveals the configuration of the rings schematically, C is the middle level of the instrument, S the Solar, Z the zenith, M the southernmost level of the horizon, E the easternmost level of the horizon, and H the intersection of the all-tilter—right here functioning as a vertical circle—with the horizon. The angle that the creator calls katabatikê and the one which the creator says his predecessors referred to as katabatikê are, respectively, ok₁ and ok₂; and a is the angle that, in accordance with the creator, his predecessors referred to as antiskios.

These angles are acquainted from Ptolemy’s Analemma as being a part of the specialised terminology of the mathematical idea of sundials (gnomonics), and crucially, the excellence between names that our textual content’s creator makes between his personal nomenclature and that of earlier writers agrees exactly with how Ptolemy modifies his predecessors’ coordinate system in On the Analemma^{Footnote 18}; see particularly ed. Heiberg p. 191, l. 27–34:

As an alternative of the angle bounded by the gnomon and the ray, they use (the angle) missing (to finish) one proper angle, and name this the descensivum (William’s Latin rendering of katabatikê, cf. ed. Heiberg p. 191, ll. 5–6: circulum quem uocamus katauaticum id est descensiuum). As an alternative of the angle which is bounded by the inclination of the katabatikê (arc) to the zenith circle (i.e., the good circle by the zenith and the easternmost and westernmost factors of the horizon), they use the one comprised by its inclination to the meridian and name it the antiskios, which suggests “reverse the shadow.” (ed. Heiberg p. 191, l. 27–34—the final phrase is William’s gloss)

The content material of this chapter thus offers the strongest proof to this point that the brand new textual content’s creator is Ptolemy.^{Footnote 19} Furthermore, it dietary supplements our info in regards to the chronological sequence of his works.^{Footnote 20} We already might presume that the instrument, and the treatise describing it, postdate the Almagest (which itself was accomplished after AD 146/147, the date of the Canobic Inscription) for the reason that meteoroscope is clearly a improvement on the seven-ringed armillary. To this, we now can add the robust probability that On the Meteoroscope was written after On the Analemma, whose place relative to Ptolemy’s different writings was hitherto totally undetermined. A possible terminus ante quem is the composition of Ptolemy’s Geography, which refers back to the meteoroscope as a longtime factor that the reader might be taught extra about elsewhere.

There may be additionally appreciable linguistic proof that this textual content was written by Ptolemy. Most placing is the overlap between the phrase ὥστε… καὶ μίαν ἐπιφάνειαν ποιεῖν τῶν τε κυρτῶν ἐμ μέρει καὶ τῶν κοίλων ἐπιφανειῶν (“in order that… it makes a single floor out of each the convex, respectively, and the concave surfaces,” p. 251, ll. 1–4) and the practically equivalent ὥστε… καὶ μίαν ἐπιφάνειαν ποιεῖν κατά τε τὴν κυρτὴν καὶ τὴν κοίλην in Pappus’ description of the meteoroscope (ed. Rome p. 7, ll. 3–4). Of nice import as properly are syntagms that bear no relation to the astronomical subject-matter: thus, ἐφεξῆς δὲ καί (p. 251, l. 11) is unattested earlier than the 2nd c. CE, and uncommon afterwards besides for enormous use by Galen, a recent of Ptolemy; Ptolemy and Alexander of Aphrodisias each use it twice, and no different historical creator makes use of it greater than as soon as. ἕνεκεν δὲ τοῦ + infinitive (p. 249, ll. 6–7) and the aorist type παρεσημειωσάμεθα (p. 249, l. 9) are additionally “verbal fingerprints” of Ptolemy. Whereas not particular to Ptolemy, φέρε εἰπεῖν (p. 195, ll. 28–29) is used typically by him (12 occasions).

Attribute astronomical phrases may also be recognized by corpus-wide TLG searches, like ἡ ὑπόθεσις τῆς κινήσεως αὐτοῦ (scil. τοῦ ἡλίου), “the speculation for its movement (sc. of the solar)” (p. 241, ll. 21–22). Ptolemy in his recognized works makes use of such a phrase at least 5 occasions, whereas no different creator makes use of it greater than as soon as, and all of those that use it are closely influenced by Ptolemy (i.e., Porphyry, Theon of Alexandria, Proclus, Manuel Bryennius and Theodorus Metochites). In different authors, the identical concept is expressed with much less abrupt syntax, e.g., αἱ περὶ τὰς κινήσεις ὑποθέσεις (Aristotle, Simplicius) or αἱ ὑποθέσεις δι᾽ ὧν ποιεῖται τὰς κινήσεις (Theon of Alexandria). The phrases μοιρογραφία (p. 251, l. 23) and ἐμπολίζειν (p. 249, ll. 13, 15, and 27–28; p. 251, l. 25; p. 252, l. 11) and the phrase ἡ τοῦ κόσμου θέσις (p. 190, l. 9), whereas not unique to Ptolemy, are additionally attribute of his type.

Lastly, we may argue by elimination. The three most believable candidates for authorship are Ptolemy and his commentators Pappus and Theon of Alexandria. However Pappus, who offers many particulars about Ptolemy’s armillary spheres, nowhere says or implies that he wrote a separate textual content concerning the meteoroscope. However, two Arabic manuscripts comprise carefully associated variations of a textual content a couple of nine-ring armillary sphere and ascribe it to Theon.^{Footnote 21} Within the ninth c., Ibn Wāḍiḥ al-Ya‘qūbi in his Chronicle (Ta’rīkh, p. 154–157 Houtsma) summarized a carefully associated textual content, and ascribed it to Ptolemy (p. 154–157 Houtsma).^{Footnote 22} The armillary sphere described within the Arabic texts of ‘Theon’ and al-Ya‘qūbi is assembled in exactly the identical manner as within the Milan palimpsest. Nevertheless, the Greek textual content, though it has the identical normal construction (an introduction concerning the instrument, adopted by a sequence of chapters with sensible directions for measurements), displays many variations from the Arabic textual content. Probably the most affordable rationalization, already given by Richard Lorch, is that the Arabic textual content was translated (with some components of paraphrase) from a piece by Theon on Ptolemy’s meteoroscope, and that al-Ya‘qūbi misunderstood the ascription of the textual content he summarized.^{Footnote 23}

Taken collectively, the proof demonstrates that the newly deciphered textual content from Ambrosianus L 99 Sup. is Claudius Ptolemy’s treatise about his meteoroscope, constantly with the textual content’s content material and language, and with its being contained in the identical codex as Ptolemy’s treatise On the Analemma. Work on this new textual content is ongoing: following a second imaging session, additional progress in decipherment and interpretation is to be anticipated.

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