ΜΑΘΗΜΑΤΟΓΟΝΙΑ

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jeidsath
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ΜΑΘΗΜΑΤΟΓΟΝΙΑ

Post by jeidsath »

ΜΑΘΗΜΑΤΟΓΟΝΙΑ.

The mythological Birth of the Nymph Mathesis.

PREFACE.

Where the following curious fragment of antiquity was discovered, the Editor is anxious to conceal; because, about the same spot other curious fragments may still be lurking. For great is the glory of restoring old manuscripts: and the more solitary we are in our fortunate researches, the more exceeding is the lustre of our fame.

The Poem itself was probably written in the reign of Ptolemy Philadelphus, the royal patron of Lycophron and Euclid. To this conjecture we are invited by the general tenor of its language, while the mention of the Parabola and the Ellipse clouds the horizon of that brilliant hypothesis. For although Apollonius of Pamphylia did about that period compose many treatises upon Conic Sections, yet doubtless he invented neither the Ellipse nor the Parabola. The introduction, therefore, of these beautiful but mysterious curves, is an anachronism indeed, but an anachronism of the highest order: for Euripides assigns a premature date to inventions which existed before, our author to discoveries that were made after the age in which he lived. Bold and aspiring, in the extravagance and inebriety of his genius, dashing into the waters of futurity,

"He pass'd the flaming bounds of time and space."

ΜΑΘΗΜΑΤΟΓΟΝΙΑ

ΛΟΓΟΣ τίς ἐστιν, ὥς ποτ’ ἀνθρώπων γένει
ἐλθὼν δι’ ὀργῆς Ζεύς, ὅσ’ ἐξημάρτανον,
ἔχρηζεν αὐτοὺς ἀντιτίσασθαι δίκην.
ἀλλ’ ἠπόρει γὰρ ζημίαν, οἵα ποτὲ
κακοῖσιν ἔργοις προστεθεῖσ’ ἀντιρρέποι.
τέλος δὲ νεύσας τοῖς θεοῖς σιγὴν ἔχειν,
"ἀκούσατ’, ὦ θεοί, φησι, τὸν βραχὺν λόγον·
θνητούς, ἃ δυσσεβοῦσι, τιμωρήσομαι.
Ἥφαιστε, σοὶ δ’ οὖν χρέος ἐπιστέλλω τόδε,
εὐθύς πρὸς Αἴτνην βὰς Ἐρινύων μέτα,
δειναὶ γὰρ εὑρεῖν, ἐκπόνει πόρον μέγαν
κακῶν, ὁποῖον μηδέπω κάτοισθ’ ἰδών."
καὶ ταῦθ’ ἅμ’ ἠγόρευε, χὠ τέκτων πυρὸς
χωλὸν πόδ’ εἷλκε, δρᾷν παρεσκευασμένος.
καὶ δὴ παρῆσαν χθόνιον ἐς κατώρυχα
γραιαὶ παλαιαὶ παῖδες, ὅ τε μουνὼψ στρατός,
οἱ μὲν πονοῦντες, αἱ δὲ μηχανώμεναι.
οἱ γὰρ Κύκλωπες ὠλένας πεδαρσίους
μετὰ ῥυθμοῦ ᾽κούφιζον· ἀντέκλαζε δὲ
μυδροκτυποῦσι βαρύβρομος κοίλη πέτρα·
ἱδρὼς δ’ ἀνῇει χρωτί· θνητῶν γὰρ κακὰ
ἔσπευδον· ἦν δὲ πειστέον Διὸς λόγοις.
ἐν τῷδ’ ἀΰπνοις ῥιπίδων φυσήμασιν
ἤγειρεν ἠρέθιζεν ἄσβεστον φλόγα
Ἥφαιστος· εἶτα, παρθένων σεμνῶν ἅμα
ταυροκτονουσῶν Ζηνὶ μηχανορράφῳ,
ῥαιστῆρ’ ἐπάρας καλλίνικον, ἐν μιᾷ


πληγῇ Τρίγωνον αὐτόχειρ ἐκαίνισε[1],
γοργόν τι μηχάνημ’· ἐθάμβησαν δ’ ὁμοῦ
οἱ δημιουργοὶ πάντες οἱ πελώριοι·
νόμον δ’ ἐπευφήμησαν ὁμόφωνον κόραι
τρισσαὶ τριμόρφῳ τρίποδι τρικαράνῳ δάκει·
μαθὼν δ’ ἑαυτοῦ τριπλάσιον βλαστὸν τέρας
Τυφὼς πρὸς ὁργὴν στόματος Αἰτναίου διὰ
πυρὸς βέλη μετάρσι’ ἐξηκόντισε·
καὶ πᾶσα μὲν χθὼν μυχόθεν ἐσαλεύθη, πυλαὶ δ’
Ἅιδου ᾽κτύπησαν, ἀλαλαγήν θ’ ἧκαν νεκροὶ
τὸν λυμεῶνα τὸν νέον πεφευγότες.
ἐκ γὰρ Τριγώνου, θεομυσοῦς γεννήτορος,
σμερδνόν τι θρέμμ’ ἔβλαστε Τετραγώνου βία,
καὶ Πεντέγωνον προπάτορος μείζων βλάβη,
καὶ πάνθ’ ἃ πλευροῖς γωνίαις θ’ ἁβρύνεται
πολλαῖσιν· οὐ μὴν πάντα γ’ εἶχ’ ὁμόπτερον
φύσιν· τὸ μὲν γὰρ ἦν ἰσοσκελές, τὸ δ’ οὔ·
τὸ δ’ αὖδιαμπὰξ στερεόν[2], ἄλλο δ’ ἐπίπεδον.

τοὐνθένδε μέντοι, πῆμα πήματος πλέον,
χαλκεὺς ὁ δεινὸς αἱμύλῃ πλάσσει χερὶ
κύκλων περιβολὰς διαμέτροις σταθμώμενος·
κανόνας[3] θ’ ὅσοι τρέχουσιν ἀλλήλους πάρα
ἀλγοῦντες, οὐ γὰρ μὴ ξυνάψουσιν γάμους.
καὶ πρός γε τούτοις διπτύχους γραμμὰς λαβὼν
ἴσας τίθησιν, ἄλλοτ’ ἐκτείνει σοφῶς
τὴν ὑστέραν τῆς πρόσθεν εἰς ὑπερβολήν,

[1] Construe, "forged a new and strange thing called a Triangle."

[2] Plato Theaet. c. 14, ed. Bekker.

[3] Euclid's idea of parallel lines. Vide Lib. 1. Def. 35.


μυριάσι μορφῶν ἀδαπάνως τέρπων κέαρ.
ἀφροὺς δὲ φυσῶντ’ Εὐμενίδες οἴστροις πέριξ
ἔχριον, ὠρόθυνον· οὐδ’ εὕδειν παρῆν·
ἐπεὶ μόλις μὲν κεῖνος, ἐξέφυσε δὲ
γραμμήν[4] τιν’ ἀξύμβλητον, ἣν ἐς αἰθέρα
φιλεῖ γράφειν ἰαλτὸς ἐκ χειρῶν λίθος,
εἶτ’, ἐμμανὴς πνοαῖσι δηναιῶν κορῶν,
ἄστρων περιφορὰν πολύπλανον διώρισε,
κύκλον[5] μὲν οὔ, κύκλου δὲ φιλτάτην κάσιν.
κἄτευξεν ἄλλα, κἄτι τῶνδ’ αἰσχίονα,
μαιμῶν θεὸς βροτοῖσι θριγκῶσαι κακά·
παρῆκε δ’ οὐδὲν ἀτελές· ἀλλ’ εὖ μὲν τὸ πᾶν
ἔργον κατερρίνησεν· εὖ δ’ ἐνήρμοσε
πλευροῖς τε πλευρὰ γωνίαις τε γωνίας,
γόμφοις ἐφηλῶν δυσλύτως ἀραρόσιν.

οὕτως, ὅσ’ ἐστὶ πημονῶν βλαστήματα
σπείρας, ἔπειτα δῆτ’ ἀνεψύχθη πόνων
Ἥφαιστος· εἱστήκει δ’ ἐπ’ ἐξειργασμένοις,
κἀπεῖχεν ὄμμα πολύκερων ἐς μηχανὴν
σιγῇ· τέλος δὲ περιχαρὴς θαῦμ’ εἰσορῶν
ὠρχεῖτο, τὸν μὲν χωλὸν εἱλίσσων πόδα
δινῶν τ’ ἀέρδην θατέρου δ’ ὀχούμενος
ἐπ’ ὀρθὸς ὀρθοῦ, τοῖς μονοφθάλμοις γέλων,
πολύστονον δὲ κλῃδόν’ ἁρμόζων ἅμα
Μαθήματ’, ἦν γὰρ ξύμμετρος παθήμασιν,
ἔρρηξεν αὐδήν· "δαίμονες δειναὶ βροτῶν
λώβαις διώκειν ὑστεροφθόροις, ἐπεὶ

[4] The Parabola.

[5] Kepler has observed in his second law that Planets move in Ellipses.


κακῶν ἕκατι κἀγένεσθε, κλῦτέ μου·
ἴδεσθε τήνδε μηχανὴν ἀμήχανον
θνητοῖς πόνων τε πόρον ἄπορον· ἴτ’ ἔγκοτοι,
ἴτ’ ὠκύποινοι, καὶ περιστιχίζετε
ἄπειρον ἀμφίβληστρον ἀνθρώποις τάδε,
ῥίψατε, διάδοτε, σπείρατ’ ἐς πᾶσαν χθόνα,
κακῶν γὰρ ἔσται κλαυμάτων ἀρχηγενῆ."
αἱ δ’ οὖν ταχύποδες ἀπτέροις ποτήμασιν
ᾖσσον, προσελθοῦσαι δὲ Παλλάδος πόλιν[6]
χώρας μετέσχον, γῇ μὲν οὐκ ἀκαρπίαν
φλγμοῖς φέρουσαι, δενδροπήμονα βλάβην,
ἀστοῖς δ’ ἀπεύκτους προσβολὰς μαθημάτων,
κρείσσω νόσον λειχῆνος, αὐονὴν φρεσίν.
κἀνθένδε ῥίμφ’ Αἰγαῖον αἱ κυνώπιδες
ὑπερθοροῦσαι πέλαγος ἐξίκοντο γῆν
τρίγωνον, ἔνθα ποταμὸς Αἰγύπτου[7] βοτὴρ
πηγῶν ἄπαππος εἰς ἅλ’ ἑπτάρους φθίνει,
ᾗ πόλλ’ ἀριθμοῦ θυμοβόρα σοφίσματα
στάζουσιν· εἶτ’ ἔσκηψαν ἄψορροι πάλιν
ἐκεῖσ’ ὅθεν τὸ πρῶτον ὡρμήσαντο δή·
νῦν δ’ εἰς τρίγωνον πατρίδα[8] γῆν κατήγαγον
Ἡφαιστότευκτον μηχανήν, βροτῶν ἄλας.
ἐνθένδε πρὸς βορεάδας ἔσπευδον πνοὰς
μόγις τε πόντου στενὸν ὑπερβᾶσαι πόρον

[6] The residence of Plato.

[7] Alexandria was the scene of many discoveries in Mathematics cf. Aesch. Fragm.

δεινοὶ πλέκειν τοι μηχανὰς Αἰγύπτιοι.

[8] At Syracuse flourished, B.C. 200, the renowned practical mathematician Archimedes.


ἵκοντο καλλιδόνακα πηλώδη ῥοὴν
Κάμον καμοῦσαι ποταμὸν οὐ ψευδώνυμον.
καί τις τάδ’ εἶπε μία κορῶν--"ἅλις γέ τοι,
ἅλις πλανῶν· στήσωμεν ἐς πεδία τάδε
πομπὸν τόδ’ ἄχθος, τοῖς μὲν οἰκητῆρσι γῆς
ἔριδας φύτευσον φρενομανεῖς τε θηγάνας,
ἡμῖν δὲ πλοῦτον αἱματορρόφου χλιδῆς.
ἔσται γάρ, ἔσται τῇδ’ ὑπερφυῶς μέγας
ἀγών· ἐρεβόθεν δ’ ἐμμανὴς τάδ’ ἐννέπω.
στρατὸν δέδορκα διὰ τριῶν τεταγμένον
σπαρτὸν τριγώνων ἔριδος ἐξ ἀγωνίου,
ἐπεὶ βροτοῖς τοῖς ἐνθάδ’ ἀνθήσει χρόνῳ
Ἄρης ἄχαλκος ἀσπίδων ἐμφύλιος
ἄνδρες θ’ ἁμιλλητῆρες ἀσιδήρους χέρας
πτεροῖσι χηνείοισιν ἐξηρτυμένοι
ἴασι σῖγα διὰ μάχης μαθημάτων,
παθήμαθ’ οἷ’ οἴσοντες αὐτὸ σημανεῖ."
Κάμου δὲ λίμναις γειτονοῦσ’ οἰκεῖ πάλαι
ἡ παντομισής, ἡ νόσου πλέα τέχνη.
ὦ Ζεῦ, τί λέξω; πότερά νιν προσεννέπω[9]
ναυαγίοις ἀνθοῦσαν ἀλίμενον χθόνα,

[9] The Author here indulges in extravagant spleen against Mathesis, imaged under various shapes. If as we have ventured to suppose, he resided at the court of Ptolemy Philadelphus, this virulent attack upon so sage a goddess may have sprung from a desire to gratify some secret animosity against Euclid, who was a worshipper of that divinity. That great mathematician, having been tutor to Ptolemy, would probably reign paramount in his favour. Our poet, therefore, kindling with anger, would regard Euclid as an insurmountable barrier between himself and the scope of his ambition: and, while he rioted in the consciousness of his own stupendous powers, would naturally outpour his wrath upon him who narrowed the just area of their display; for he would wisely think with the illustrious Bacon, "Non novit quispiam, quantum in virtute profecerit, nisi honores ei campum praebeant apertum. (Bacon De Augmentis Scientiarum.)

ἢ καὶ δόλον βλέπουσαν ἐξ ὑφασμάτων
Ἄτην ἄπληστον αἵματος; σπόγγον μὲν οὖν
ψυχὰς βροτῶν ῥοφοῦντα μυριόστομον,
ἀνδρῶν ἀπαιόλημα κἂν σοφός τις ᾖ,
πάμφθαρτον Ἅιδην, Σφίγγα δευτέραν τινά,
ἢ δυστόπαστα συμβαλεῖν αἰνίγματα
φύουσα θνητοῖς ξυγγενῆ σπείρει βλάβην.
φεῦ τῆς ἀνοίας, ὅστις ὢν ἐφήμερος[10]
ἔπειτα δεινῇ τῇδε πρόσκειται τέχνῃ·
λόγοισι μὲν γὰρ χρηστὸν ἐκτείνει βίον,
ἔργῳ δ’ ὁ τλήμων τήκεται λύπῃ μακρᾷ
οὔπω μαθὼν κύκλωμα τετράγωνον κτίσαι[11].
πῶς δ’ οὔ τι μεῖζον ἢ κατ’ ἄνθρωπον φρονεῖ
ὅστις κάθηται πύργον εὐαγῆ λαβὼν
καὶ χαλκοτεύκτων οὐρανὸν δι’ ὀργάνων
σκοπεῖ, πεποιθὼς νυκτιφρουρήτῳ θράσει;
ὦ πάννυχοι λαμπτῆρες, οὐκ ἄρ’ ἴστε που
ὄσσοις βροτησίοισιν ὀφθέντες τορῶς,

[10] MS. ἔφη Ὅμηρος. We here insert the opinion of a learned correspondent, as a standard of excellence in note-building to all commentators: "Proponenti ἐφήμερος non assentior; ingeniosius id, quam tutius; legendum cum MS. ἔφη Ὅμηρος: nam textui insistendum semper, repugnante etiam tum sensu, tum metro."

[11] This is a real bane of Mathematics, namely, a restless hankering--an insatiate appetite after squaring the circle. It is, in fact, a canker of the mind--a spreading disease, under the workings of which some are said to have gone mad, others to have died: nor did the renowned Hobbes himself escape its contagion, for a modern Latin stanza-maker has observed,

ad astra tollam laudibus Hobbium,
Thucydidem qui reddidit Anglice, et
rotunda quadravit. quid Hobbi
clarius ingenio? quid Hobbi
uirtute? cedat Roma Britanniae.

ἢ πῶς δι’ ὀργῆς οὔποτ’, ἐσκοτωμένοι
ἀκτῖνας, ἤδη μηχανὰς ἐρρήξατε
βροτῶν; βροτοῖς γὰρ οὐράνια θέμις σκοπεῖν;
τούτων γενοίμην οὐ μεριμνητής ποτ’ ἂν
ἔγωγ’· ἐμοὶ μέν, αἰθέρος μεσόμφαλα
ἔχει βέβαιος εἴτ’ ἀνιδρύτοις ἀεὶ
χειμάζεται δρόμοισιν ἡλίου κύκλος,
ὅμοιον· εἰ γὰρ εὐτρφῆ θερμὴν φλόγα
φίλως ἰάπτει γῆς φερέσβιον γάνος,
ἅλις· τὰ δ’ ἄλλα, θνητὸς ὤν, χαίρειν ἐῶ.

[Composed by T. S. Evans, after he missed out on Classical Honours at Cambridge, due to failing to gain a place in the Mathematical Tripos. --Joel]
“One might get one’s Greek from the very lips of Homer and Plato." "In which case they would certainly plough you for the Little-go. The German scholars have improved Greek so much.”

Joel Eidsath -- jeidsath@gmail.com

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jeidsath
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Re: ΜΑΘΗΜΑΤΟΓΟΝΙΑ

Post by jeidsath »

There is a story, that once to the race of men, came Zeus in anger, so much had they erred, and declared the punishment they were to receive in return. But he was at a loss as to punishment, for what having been imposed could ever balance their evil deeds. Finally having indicated to the gods to be silent, he spoke "Hear, Gods, the heavy judgement. I shall take vengeance on mortals for what they have disrespected. Hephaestus, to you I enjoin this obligation, immediately go to Mount Etna together with the furies, for they are crafty in invention, and labor to create a great means of providing evil, of a sort that you have never seen or known." And as he was saying all this, the smith was dragging his lame foot, preparing to do the work. And indeed there were present in a cavern beneath the earth, old women slaves and the one-eyed army, the men labored, and the women built. For the Cyclopses[1] were tossing up their raised elbows in rhythm, and the hollow stone was loud being struck with forgings of red hot iron. Sweat dripped down their skin, for they worked an evil to mortals, it was something to be obeyed by the words of Zeus.

[1] The Arimaspi
“One might get one’s Greek from the very lips of Homer and Plato." "In which case they would certainly plough you for the Little-go. The German scholars have improved Greek so much.”

Joel Eidsath -- jeidsath@gmail.com

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