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Euclid · Fragments §3.1

Nature and Educational Role of the Pseudaria

Passage 3 of 29 · Greek

Summary

Through testimonies by Proclus and other ancient commentators, the educational role and nature of Euclid's lost work "Pseudaria" (Book of Fallacies), which was written to help beginners detect paralogisms in geometry, are described.

3.
Proclus Comm. in Eucl. p. 70,1 sqq. (ed.
Proclus Comm. in Eucl. p. 70,1 sqq. (ed.
Friedlein): Ἐπειδὴ δὲ πολλὰ φαντάζεται μὲν ὡς τῆς ἀληθείας ἀντεχόμενα καὶ ταῖς ἐπιστημονικαῖς ἀρχαῖς ἀκολουθοῦντα, φέρεται δὲ εἰς τὴν ἀπὸ τῶν ἀρχῶν πλάνην καὶ τοὺς ἐπιπολαιοτέρους ἐξαπατᾷ, μεθόδους παραδέδωκεν καὶ τῆς τούτων διορατικῆς φρονήσεως, ἃς ἔχοντες γυμνάζειν μὲν δυνησόμεθα τοὺς ἀρχομένους τῆς θεωρίας ταύτης πρὸς τὴν εὕρεσιν τῶν παραλογισμῶν, ἀνεξαπάτητοι δὲ διαμένειν.
Friedlein): Since many things appear as if they hold to the truth and follow scientific principles, but are carried away into error from the principles and deceive the more superficial, he has handed down methods also for the discerning understanding of these, possessing which we shall be able to train beginners in this theory towards the discovery of paralogisms, and to remain undeceived.
καὶ τοῦτο δὴ τὸ σύγγραμμα, διʼ οὗ τὴν παρασκευὴν ἡμῖν ταύτην ἐντίθησι, Ψευδαρίων ἐπέγραψεν τρόπους τε αὐτῶν ποικίλους ἐν τάξει διαριθμησάμενος καὶ καθʼ ἕκαστον γυμνάσας ἡμῶν τὴν διάνοιαν παντοίοις θεωρήμασι καὶ τῷ ψεύδει τὸ ἀληθὲς παραθεὶς καὶ τῇ πείρᾳ τὸν ἔλεγχον τῆς ἀπάτης συναρμόσας.
And this very treatise, through which he instills in us this preparation, he entitled "Pseudaria", having enumerated in order their various modes, and in each case trained our intellect with all kinds of theorems, and having placed the truth alongside the falsehood, and fitted the refutation of the deceit to experience.
τοῦτο μὲν οὖν τὸ βιβλίον καθαρτικόν ἐστι καὶ γυμναστικόν.
This book, then, is purgative and gymnastic.
Cfr.
Cf.
Paeudo - Alexander siue Michael Ephesius in Aristot.
Pseudo-Alexander or Michael of Ephesus, In Aristot.
Soph.
Soph.
Elenchos p. 76, 20 (ed.
Elenchos p. 76, 20 (ed.
Wellies): Οὐ μόνον δὲ τοὺς μὴ ἀπὸ τῶν ἀρχῶν ὡρμημένους τῆς ἐπιστήμης, ὑφʼ ἥν ἐστι τὸ πρόβλημα, δοκοῦντας δὲ εἶναι, ψευδεῖς ἐλέγχους φησίν, ἀλλὰ καὶ τοὺς ἐκ τῶν οἰκείων μὲν τῆς ἐπιστήμης ἀρχῶν, κατά τι δὲ παραλογιζομένους, οἷά εἰσι τὰ τοῦ Εὐκλείδου ψευδογραφήματα.
Wallies): He says that false refutations are not only those that do not start from the principles of the science under which the problem falls, but appear to do so, but also those that start from the proper principles of the science, but reason falsely in some respect, such as the "Pseudographemata" of Euclid.
Scholia in Platonis Theaet. 191 b (p. 248 ed.
Scholia on Plato's Theaetetus 191 b (p. 248 ed.
Hermann): ἐπειδὰν ἡμᾶς ἐρωτᾷ περὶ τῶν ἔξω τῆς αἰσθήσεως, εἰ δυνατὸν συστῆναι ψευδοδοξίαν, οἷον ἐπὶ τῶν παρὰ τοῖς γεωμέτραις καλουμένων ψευδαρίων. 1) οὐ γὰρ διὰ μῖξιν αἰσθήσεως ψευδογραφοῦσιν. 2)
Hermann): Whenever he asks us about things outside sensation, whether it is possible for a false opinion to be established, as in the case of what are called "pseudaria" among geometers. 1) For they do not write false proofs because of a mixture of sensation. 2)

Notes

  1. ¦5¦πολλὰ φαντάζεται ... φέρεται δὲ ... ἐξαπατᾷ — Although the subject is the neuter plural noun πολλά (many things), all corresponding verbs are in the third person singular (φαντάζεται, φέρεται, ἐξαπατᾷ). This reflects the typical Classical Greek syntactic rule (the Attic schema) where a neuter plural subject takes a singular verb.
  2. ¦10¦Ψευδαρίων — The genitive plural form Ψευδαρίων ("Of Pseudaria / Of Fallacies") of the neuter noun ψευδάριον (fallacy, false proof) is placed as the direct object of the verb ἐπέγραψεν (entitled). This represents a standard ancient practice where a book's title is cited in the genitive case.
  3. ¦20¦δοκοῦντας δὲ εἶναι — Following the infinitive εἶναι, which functions as the complement to the participle δοκοῦντας (seeming), the phrase ἀπὸ τῶν ἀρχῶν ὡρμημένους (starting from the principles) is omitted from the preceding clause and must be understood to complete the meaning as 'those that seem [to start from the principles].'

Cite this passage

Euclid, Fragments §3.1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg1799.tlg016.humanitext-grc1:3.1

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