<w lemma="%2Akai%5C">Καὶ</w> <w lemma="mh%5Cn">μὴν</w> <w lemma="%2Aniki%2Fas">Νικίας</w> <w lemma="o%28">ὁ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="%2A%29aqhnai%2Fwn">Ἀθηναίων</w> <w lemma="strathgo%2Fs">στρατηγός</w>, <w lemma="duna%2Fmenos">δυνάμενος</w> <w lemma="sw%2F%7Czein">σῴζειν</w> <w lemma="to%5C">τὸ</w> <w lemma="peri%5C">περὶ</w> <w lemma="ta%5Cs">τὰς</w> <w lemma="%2Asurakou%2Fsas">Συρακούσας</w> <w lemma="stra%2Fteuma">στράτευμα</w>, <w lemma="kai%5C">καὶ</w> <w lemma="labw%5Cn">λαβὼν</w> <w lemma="th%3Ds">τῆς</w> <w lemma="nukto%5Cs">νυκτὸς</w> <w lemma="to%5Cn">τὸν</w> <w lemma="a%28rmo%2Fzonta">ἁρμόζοντα</w> <w lemma="kairo%5Cn">καιρὸν</w> <w lemma="ei%29s">εἰς</w> <w lemma="to%5C">τὸ</w> <w lemma="laqei%3Dn">λαθεῖν</w> <w lemma="tou%5Cs">τοὺς</w> <w lemma="polemi%2Fous">πολεμίους</w>, <w lemma="a%29poxwrh%2Fsas">ἀποχωρήσας</w> <w lemma="ei%29s">εἰς</w> <w lemma="a%29sfale%2Fs">ἀσφαλές</w>, <w lemma="ka%29%2Fpeita">κἄπειτα</w> <w lemma="th%3Ds">τῆς</w> <w lemma="selh%2Fnhs">σελήνης</w> <w lemma="e%29kleipou%2Fshs">ἐκλειπούσης</w> <w lemma="deisidaimonh%2Fsas">δεισιδαιμονήσας</w>, <w lemma="w%28%2Fs">ὥς</w> <w lemma="ti">τι</w> <w lemma="deino%5Cn">δεινὸν</w> <w lemma="proshmainou%2Fshs">προσημαινούσης</w>, <w lemma="e%29pe%2Fsxe">ἐπέσχε</w> <w lemma="th%5Cn">τὴν</w> <w lemma="a%29nazugh%2Fn">ἀναζυγήν</w>.
<w lemma="kai%5C">καὶ</w> <w lemma="para%5C">παρὰ</w> <w lemma="tou%3Dto">τοῦτο</w> <w lemma="sune%2Fbh">συνέβη</w> <w lemma="kata%5C">κατὰ</w> <w lemma="th%5Cn">τὴν</w> <w lemma="e%29piou%3Dsan">ἐπιοῦσαν</w> <w lemma="au%29tou%3D">αὐτοῦ</w> <w lemma="nu%2Fkta">νύκτα</w> <w lemma="poihsame%2Fnou">ποιησαμένου</w> <w lemma="th%5Cn">τὴν</w> <w lemma="a%29nazugh%2Fn">ἀναζυγήν</w>, <w lemma="proaisqome%2Fnwn">προαισθομένων</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="polemi%2Fwn">πολεμίων</w>, <w lemma="kai%5C">καὶ</w> <w lemma="to%5C">τὸ</w> <w lemma="strato%2Fpedon">στρατόπεδον</w> <w lemma="kai%5C">καὶ</w> <w lemma="tou%5Cs">τοὺς</w> <w lemma="h%28gemo%2Fnas">ἡγεμόνας</w> <w lemma="u%28poxeiri%2Fous">ὑποχειρίους</w> <w lemma="gene%2Fsqai">γενέσθαι</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="%2Asurakosi%2Fois">Συρακοσίοις</w>.
<w lemma="kai%2Ftoi">καίτοι</w> <w lemma="ge">γε</w> <w lemma="para%5C">παρὰ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29mpei%2Frwn">ἐμπείρων</w> <w lemma="i%28storh%2Fsas">ἱστορήσας</w> <w lemma="mo%2Fnon">μόνον</w> <w lemma="peri%5C">περὶ</w> <w lemma="tou%2Ftwn">τούτων</w> <w lemma="dunato%5Cs">δυνατὸς</w> <w lemma="h%29%3Dn">ἦν</w> <w lemma="ou%29x">οὐχ</w> <w lemma="oi%28%3Don">οἷον</w> <w lemma="paralipei%3Dn">παραλιπεῖν</w> <w lemma="dia%5C">διὰ</w> <w lemma="ta%5C">τὰ</w> <w lemma="toiau%3Dta">τοιαῦτα</w> <w lemma="tou%5Cs">τοὺς</w> <w lemma="i%29di%2Fous">ἰδίους</w> <w lemma="kairou%2Fs">καιρούς</w>, <w lemma="a%29lla%5C">ἀλλὰ</w> <w lemma="kai%5C">καὶ</w> <w lemma="sunergoi%3Ds">συνεργοῖς</w> <w lemma="xrh%2Fsasqai">χρήσασθαι</w> <w lemma="dia%5C">διὰ</w> <w lemma="th%5Cn">τὴν</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="u%28penanti%2Fwn">ὑπεναντίων</w> <w lemma="a%29%2Fgnoian:">ἄγνοιαν·</w>
<w lemma="h%28">ἡ</w> <w lemma="ga%5Cr">γὰρ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="pe%2Flas">πέλας</w> <w lemma="a%29peiri%2Fa">ἀπειρία</w> <w lemma="me%2Fgiston">μέγιστον</w> <w lemma="e%29fo%2Fdion">ἐφόδιον</w> <w lemma="gi%2Fnetai">γίνεται</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="e%29mpei%2Frois">ἐμπείροις</w> <w lemma="pro%5Cs">πρὸς</w> <w lemma="kato%2Frqwsin">κατόρθωσιν</w>.
<w lemma=""></w> <w lemma="%2A%29ek">Ἐκ</w> <w lemma="me%5Cn">μὲν</w> <w lemma="ou%29%3Dn">οὖν</w> <w lemma="a%29strologi%2Fas">ἀστρολογίας</w> <w lemma="me%2Fxri">μέχρι</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="proeirhme%2Fnwn">προειρημένων</w> <w lemma="polupragmonhte%2Fon">πολυπραγμονητέον</w>. <w lemma="peri%5C">περὶ</w> <w lemma="de%5C">δὲ</w> <w lemma="th%3Ds">τῆς</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="klima%2Fkwn">κλιμάκων</w> <w lemma="summetri%2Fas">συμμετρίας</w> <w lemma="toiou%3Dto%2Fs">τοιοῦτός</w> <w lemma="ti%2Fs">τίς</w> <w lemma="e%29stin">ἐστιν</w> <w lemma="o%28">ὁ</w> <w lemma="tro%2Fpos">τρόπος</w> <w lemma="th%3Ds">τῆς</w> <w lemma="qewri%2Fas">θεωρίας</w>.
<w lemma="e%29a%5Cn">ἐὰν</w> <w lemma="me%5Cn">μὲν</w> <w lemma="ga%5Cr">γὰρ</w> <w lemma="dia%2F">διά</w> <w lemma="tinos">τινος</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="sumpratto%2Fntwn">συμπραττόντων</w> <w lemma="doqh%3D%7C">δοθῇ</w> <w lemma="to%5C">τὸ</w> <w lemma="tou%3D">τοῦ</w> <w lemma="tei%2Fxous">τείχους</w> <w lemma="u%28%2Fyos">ὕψος</w>, <w lemma="pro%2Fdhlos">πρόδηλος</w> <w lemma="h%28">ἡ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="klima%2Fkwn">κλιμάκων</w> <w lemma="gi%2Fnetai">γίνεται</w> <w lemma="summetri%2Fa:">συμμετρία·</w> <w lemma="oi%28%2Fwn">οἵων</w> <w lemma="ga%5Cr">γὰρ</w> <w lemma="a%29%5Cn">ἂν</w> <w lemma="de%2Fka">δέκα</w> <w lemma="tinw%3Dn">τινῶν</w> <w lemma="ei%29%3Dnai">εἶναι</w> <w lemma="sumbai%2Fnh%7C">συμβαίνῃ</w> <w lemma="to%5C">τὸ</w> <w lemma="tou%3D">τοῦ</w> <w lemma="tei%2Fxous">τείχους</w> <w lemma="u%28%2Fyos">ὕψος</w>, <w lemma="toiou%2Ftwn">τοιούτων</w> <w lemma="dw%2Fdeka">δώδεκα</w> <w lemma="deh%2Fsei">δεήσει</w> <w lemma="ta%5Cs">τὰς</w> <w lemma="kli%2Fmakas">κλίμακας</w> <w lemma="dayilw%3Dn">δαψιλῶν</w> <w lemma="u%28pa%2Frxein">ὑπάρχειν</w>.
<w lemma="th%5Cn">τὴν</w> <w lemma="d%27">δ᾽</w> <w lemma="a%29po%2Fbasin">ἀπόβασιν</w> <w lemma="th%3Ds">τῆς</w> <w lemma="kli%2Fmakos">κλίμακος</w> <w lemma="pro%5Cs">πρὸς</w> <w lemma="th%5Cn">τὴν</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="a%29nabaino%2Fntwn">ἀναβαινόντων</w> <w lemma="summetri%2Fan">συμμετρίαν</w> <w lemma="h%28mi%2Fseian">ἡμίσειαν</w> <w lemma="ei%29%3Dnai">εἶναι</w> <w lemma="deh%2Fsei">δεήσει</w> <w lemma="th%3Ds">τῆς</w> <w lemma="kli%2Fmakos">κλίμακος</w>, <w lemma="i%28%2Fna">ἵνα</w> <w lemma="mh%2Fte">μήτε</w> <w lemma="plei%3Don">πλεῖον</w> <w lemma="a%29fista%2Fmenai">ἀφιστάμεναι</w> <w lemma="dia%5C">διὰ</w> <w lemma="to%5C">τὸ</w> <w lemma="plh%3Dqos">πλῆθος</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29pibaino%2Fntwn">ἐπιβαινόντων</w> <w lemma="eu%29su%2Fntriptoi">εὐσύντριπτοι</w> <w lemma="gi%2Fnwntai">γίνωνται</w> <w lemma="mh%2Fte">μήτε</w> <w lemma="pa%2Flin">πάλιν</w> <w lemma="o%29rqo%2Fterai">ὀρθότεραι</w> <w lemma="prosereido%2Fmenai">προσερειδόμεναι</w> <w lemma="li%2Fan">λίαν</w> <w lemma="a%29krosfalei%3Ds">ἀκροσφαλεῖς</w> <w lemma="w%29%3Dsi">ὦσι</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="prosbai%2Fnousin">προσβαίνουσιν</w>.
<w lemma="e%29a%5Cn">ἐὰν</w> <w lemma="de%5C">δὲ</w> <w lemma="mh%5C">μὴ</w> <w lemma="dunato%5Cn">δυνατὸν</w> <w lemma="h%29%3D%7C">ᾖ</w> <w lemma="metrh%3Dsai">μετρῆσαι</w> <w lemma="mhd%27">μηδ᾽</w> <w lemma="e%29ggi%2Fsai">ἐγγίσαι</w> <w lemma="tw%3D%7C">τῷ</w> <w lemma="tei%2Fxei">τείχει</w>, <w lemma="lhpte%2Fon">ληπτέον</w> <w lemma="e%29c">ἐξ</w> <w lemma="a%29posta%2Fsews">ἀποστάσεως</w> <w lemma="panto%5Cs">παντὸς</w> <w lemma="u%28%2Fyous">ὕψους</w> <w lemma="to%5C">τὸ</w> <w lemma="me%2Fgeqos">μέγεθος</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="pro%5Cs">πρὸς</w> <w lemma="o%29rqa%5Cs">ὀρθὰς</w> <w lemma="e%29festw%2Ftwn">ἐφεστώτων</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="u%28pokeime%2Fnois">ὑποκειμένοις</w> <w lemma="e%29pipe%2Fdois">ἐπιπέδοις</w>.
<w lemma="o%28%2F">ὅ</w> <w lemma="te">τε</w> <w lemma="tro%2Fpos">τρόπος</w> <w lemma="th%3Ds">τῆς</w> <w lemma="lh%2Fyews">λήψεως</w> <w lemma="kai%5C">καὶ</w> <w lemma="dunato%5Cs">δυνατὸς</w> <w lemma="kai%5C">καὶ</w> <w lemma="r%28a%2F%7Cdios">ῥᾴδιος</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="boulome%2Fnois">βουλομένοις</w> <w lemma="polupragmonei%3Dn">πολυπραγμονεῖν</w> <w lemma="ta%5C">τὰ</w> <w lemma="para%5C">παρὰ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="maqhmatikw%3Dn">μαθηματικῶν</w>.
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<head>Example: Why Nicias Failed at Syracuse</head>Again Nicias, the general of the Athenians, had it in<pb n="580" />his power to have saved the army besieging <a class="linkToPlace" target="_blank" href="/place?placename=Syracuse&groupId=994&placeId=1753">Syracuse</a>, and had selected the proper time of the night for escaping the observation of the enemy, and retiring to a place of safety.<note anchored="yes" place="marg" id="note40">Nicias, B.C. 413.<bibl n="Thuc. 7.50" default="NO" valid="yes">Thucyd. 7, 50</bibl>.</note>And then because the moon was eclipsed, regarding it superstitiously as of evil portent, he stopped the army from starting. Thanks to this it came about that, when he started the next day, the enemy had obtained information of his intention, and army and generals alike fell into the hands of the Syracusans. Yet if he had asked about this from men acquainted with such phenomena, he might not only have avoided missing his opportunity for such an absurd reason, but have also used the occurrence for his own benefit owing to the ignorance of the enemy. For the ignorance of their neighbours contributes more than anything else to the success of the instructed.Such then are examples of the necessity of studying celestial<note anchored="yes" place="marg" id="note41">The method of judging of the length necessary for scaling ladders.</note>phenomena. But as for securing the proper length of scaling ladders, the following is the method of making the calculation. Suppose the height of the wall to be given by one of the conspirators within, the measurement required for the ladders is evident; for example, if the height of the wall is ten feet or any other unit, the ladders must be full twelve; and the interval between the wall and the foot of the ladder must be half the length of the ladder, that the ladders may not break under the weight of those mounting if they are set farther away, nor be too steep to be safe if set nearer the perpendicular. But supposing it not to be possible to measure or get near the wall: the height of any object which rises perpendicularly on its base can be taken by those who choose to study mathematics.
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Walbank Commentary