§9.20.1διὸ πάλιν ἐν τούτοις φανερὸν ὅτι δεήσει τοὺς βουλομένους εὐστοχεῖν ἐν ταῖς ἐπιβολαῖς καὶ πράξεσι γεγεωμετρηκέναι μὴ τελείως, ἀλλʼ ἐπὶ τοσοῦτον ἐφʼ ὅσον ἀναλογίας ἔννοιαν ἔχειν καὶ τῆς περὶ τὰς ὁμοιότητας θεωρίας.
Therefore, in these matters again, it is clear that those who wish to succeed in their undertakings and actions must have studied geometry, not indeed perfectly, but so far as to have a concept of proportion and of the theory of similarities.
§9.20.2οὐ γὰρ περὶ ταῦτα μόνον, ἀλλὰ καὶ περὶ τὰς τῶν σχημάτων μεταλήψεις ἐν ταῖς στρατοπεδείαις ἀναγκαῖός ἐστιν ὁ τρόπος, χάριν τοῦ δύνασθαι ποτὲ μὲν πᾶν σχῆμα μεταλαμβάνοντας τηρεῖν τὴν αὐτὴν συμμετρίαν τῶν ἐν ταῖς παρεμβολαῖς περιλαμβανομένων, §9.20.3ποτὲ δὲ πάλιν ἐπὶ τῶν αὐτῶν σχημάτων μένοντας αὔξειν ἢ μειοῦν τὸ περιλαμβανόμενον τῇ στρατοπεδείᾳ χωρίον, κατὰ λόγον ἀεὶ τῶν προσγινομένων ἢ τῶν χωριζομένων ἐκ τῆς παρεμβολῆς·
For this method is necessary not only in these matters, but also in the alterations of figures in camp-making, for the sake of being able at one time, while changing into any figure, to maintain the same proportion of the things enclosed in the encampments, and at another time again, while remaining with the same figures, to increase or decrease the area enclosed by the camp-making, always in proportion to those added to or separated from the encampment.
§9.20.4ὑπὲρ ὧν ἡμῖν ἐν τοῖς περὶ τὰς τάξεις ὑπομνήμασιν ἀκριβέστερον δεδήλωται.
Concerning these things, we have explained them more precisely in our memoirs on tactics.
§9.20.5οὐ γὰρ οἴομαι τοῦτό γε μετρίως ἡμῖν ἐποίσειν οὐδένα διότι πολλά τινα προσαρτῶμεν τῇ στρατηγίᾳ, κελεύοντες ἀστρολογεῖν καὶ γεωμετρεῖν τοὺς ὀρεγομένους αὐτῆς.
For I do not think that anyone will bring this as a reasonable charge against us, because we attach so many things to generalship, bidding those who aspire to it to study astronomy and geometry.
§9.20.6ἐγὼ δὲ τὰ μὲν ἐκ περιττοῦ παρελκόμενα τοῖς ἐπιτηδεύμασι χάριν τῆς ἐν ἑκάστοις ἐπιφάσεως καὶ στωμυλίας πολύ τι μᾶλλον ἀποδοκιμάζων, παραπλησίως δὲ καὶ τὸ πορρωτέρω τοῦ πρὸς τὴν χρείαν ἀνήκοντος ἐπιτάττειν, περὶ τἀναγκαῖα φιλοτιμότατός εἰμι καὶ σπουδάζων.
For my part, while I reject much more those things which are superfluously dragged into studies for the sake of show and talkativeness in each case, and likewise also the prescribing of things further than what belongs to practical utility, I am most zealous and earnest about necessary things.
§9.20.7καὶ γὰρ ἄτοπον τοὺς μὲν ὀρχηστικῆς ἢ τοὺς αὐλητικῆς ἐφιεμένους ἐπιδέχεσθαι τήν τε περὶ τοὺς ῥυθμοὺς καὶ τὰ μουσικὰ προκατασκευήν, ἔτι δὲ τὰ περὶ τὴν παλαίστραν, διὰ τὸ δοκεῖν προσδεῖσθαι τὸ τέλος ἑκατέρου τῆς τῶν προειρημένων συνεργίας, §9.20.8τοὺς δὲ στρατηγίας ἀντιποιουμένους ἀσχάλλειν, εἰ δεήσει τῶν ἐκτὸς ἐπιτηδευμάτων μέχρι τινὸς ἀναλαβεῖν.
For indeed it is absurd that those who aim at dancing or flute-playing should accept the preliminary training in rhythms and music, and further in the palaestra, because the end of each seems to stand in need of the cooperation of the aforementioned things, but that those who lay claim to generalship should be vexed if they must undertake external studies to some extent.
§9.20.9ὥστε τοὺς περὶ τὰς βαναύσους τέχνας ἀσκοῦντας ἐμμελεστέρους εἶναι καὶ φιλοτιμοτέρους τῶν περὶ τὰ κάλλιστα καὶ σεμνότατα προαιρουμένων διαφέρειν· ὧν οὐδὲν ἂν ὁμολογήσειε νοῦν ἔχων οὐδείς.
The result would be that those who practice the vulgar arts are more systematic and more zealous, and excel those who choose the finest and most noble pursuits; which no one in his right mind would admit.
§9.20.10καὶ περὶ μὲν τούτων ἐπὶ τοσοῦτον ἡμῖν εἰρήσθω.
And concerning these matters, let so much have been said by us.