Polybius, Histories

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Book 9 - Chapter 26a

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<head lang="la">VI. Res Siciliae</head><w lemma="%2Aoi%28">Οἱ</w> <w lemma="de%5C">δὲ</w> <w lemma="plei%3Dstoi">πλεῖστοι</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="a%29nqrw%2Fpwn">ἀνθρώπων</w> <w lemma="e%29c">ἐξ</w> <w lemma="au%29th%3Ds">αὐτῆς</w> <w lemma="th%3Ds">τῆς</w> <w lemma="perime%2Ftrou">περιμέτρου</w> <w lemma="tekmai%2Frontai">τεκμαίρονται</w> <w lemma="ta%5C">τὰ</w> <w lemma="mege%2Fqh">μεγέθη</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="proeirhme%2Fnwn">προειρημένων</w>.
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<w lemma="loipo%5Cn">λοιπὸν</w> <w lemma="o%28%2Ftan">ὅταν</w> <w lemma="ei%29%2Fph%7C">εἴπῃ</w> <w lemma="tis">τις</w> <w lemma="th%5Cn">τὴν</w> <w lemma="me%5Cn">μὲν</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="%2Amegalopolitw%3Dn">Μεγαλοπολιτῶν</w> <w lemma="po%2Flin">πόλιν</w> <w lemma="penth%2Fkonta">πεντήκοντα</w> <w lemma="stadi%2Fwn">σταδίων</w> <w lemma="e%29%2Fxein">ἔχειν</w> <w lemma="to%5Cn">τὸν</w> <w lemma="peri%2Fbolon">περίβολον</w>, <w lemma="th%5Cn">τὴν</w> <w lemma="de%5C">δὲ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="%2Alakedaimoni%2Fwn">Λακεδαιμονίων</w> <w lemma="o%29ktw%5C">ὀκτὼ</w> <w lemma="kai%5C">καὶ</w> <w lemma="tettara%2Fkonta">τετταράκοντα</w>, <w lemma="tw%3D%7C">τῷ</w> <w lemma="de%5C">δὲ</w> <w lemma="mege%2Fqei">μεγέθει</w> <w lemma="diplh%3Dn">διπλῆν</w> <w lemma="ei%29%3Dnai">εἶναι</w> <w lemma="th%5Cn">τὴν</w> <w lemma="%2Alakedai%2Fmona">Λακεδαίμονα</w> <w lemma="th%3Ds">τῆς</w> <w lemma="%2Amega%2Flhs">Μεγάλης</w> <w lemma="po%2Flews">πόλεως</w>, <w lemma="a%29%2Fpiston">ἄπιστον</w> <w lemma="au%29toi%3Ds">αὐτοῖς</w> <w lemma="ei%29%3Dnai">εἶναι</w> <w lemma="dokei%3D">δοκεῖ</w> <w lemma="to%5C">τὸ</w> <w lemma="lego%2Fmenon">λεγόμενον</w>.
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<w lemma="a%29%5Cn">ἂν</w> <w lemma="de%5C">δὲ</w> <w lemma="kai%5C">καὶ</w> <w lemma="sunauch%3Dsai%2F">συναυξῆσαί</w> <w lemma="tis">τις</w> <w lemma="boulo%2Fmenos">βουλόμενος</w> <w lemma="th%5Cn">τὴν</w> <w lemma="a%29pori%2Fan">ἀπορίαν</w> <w lemma="ei%29%2Fph%7C">εἴπῃ</w> <w lemma="dio%2Fti">διότι</w> <w lemma="dunato%2Fn">δυνατόν</w> <w lemma="e%29sti">ἐστι</w> <w lemma="tettara%2Fkonta">τετταράκοντα</w> <w lemma="stadi%2Fwn">σταδίων</w> <w lemma="po%2Flin">πόλιν</w> <w lemma="h%29%5C">ἢ</w> <w lemma="stratopedei%2Fan">στρατοπεδείαν</w> <w lemma="e%29%2Fxousan">ἔχουσαν</w> <w lemma="th%5Cn">τὴν</w> <w lemma="perigrafh%5Cn">περιγραφὴν</w> <w lemma="diplasi%2Fan">διπλασίαν</w> <w lemma="gi%2Fnesqai">γίνεσθαι</w> <w lemma="th%3Ds">τῆς</w> <w lemma="e%28kato%5Cn">ἑκατὸν</w> <w lemma="stadi%2Fwn">σταδίων</w> <w lemma="e%29xou%2Fshs">ἐχούσης</w> <w lemma="th%5Cn">τὴν</w> <w lemma="peri%2Fmetron">περίμετρον</w>, <w lemma="tele%2Fws">τελέως</w> <w lemma="e%29kplhktiko%5Cn">ἐκπληκτικὸν</w> <w lemma="au%29toi%3Ds">αὐτοῖς</w> <w lemma="fai%2Fnetai">φαίνεται</w> <w lemma="to%5C">τὸ</w> <w lemma="lego%2Fmenon">λεγόμενον</w>.
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<w lemma="tou%3Dto">τοῦτο</w> <w lemma="d%27">δ᾽</w> <w lemma="e%29sti%5Cn">ἐστὶν</w> <w lemma="ai%29%2Ftion">αἴτιον</w> <w lemma="o%28%2Fti">ὅτι</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29n">ἐν</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="paidikoi%3Ds">παιδικοῖς</w> <w lemma="maqh%2Fmasi">μαθήμασι</w> <w lemma="paradidome%2Fnwn">παραδιδομένων</w> <w lemma="h%28mi%3Dn">ἡμῖν</w> <w lemma="dia%5C">διὰ</w> <w lemma="th%3Ds">τῆς</w> <w lemma="gewmetri%2Fas">γεωμετρίας</w> <w lemma="ou%29">οὐ</w> <w lemma="mnhmoneu%2Fomen">μνημονεύομεν</w>.
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<w lemma="peri%5C">περὶ</w> <w lemma="me%5Cn">μὲν</w> <w lemma="ou%29%3Dn">οὖν</w> <w lemma="tou%2Ftwn">τούτων</w> <w lemma="proh%2Fxqhn">προήχθην</w> <w lemma="ei%29pei%3Dn">εἰπεῖν</w> <w lemma="dia%5C">διὰ</w> <w lemma="to%5C">τὸ</w> <w lemma="mh%5C">μὴ</w> <w lemma="mo%2Fnon">μόνον</w> <w lemma="tou%5Cs">τοὺς</w> <w lemma="pollou%5Cs">πολλοὺς</w> <w lemma="a%29lla%5C">ἀλλὰ</w> <w lemma="kai%5C">καὶ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="politeuome%2Fnwn">πολιτευομένων</w> <w lemma="kai%5C">καὶ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29n">ἐν</w> <w lemma="tai%3Ds">ταῖς</w> <w lemma="h%28gemoni%2Fais">ἡγεμονίαις</w> <w lemma="a%29nastrefome%2Fnwn">ἀναστρεφομένων</w> <w lemma="tina%5Cs">τινὰς</w> <w lemma="e%29kplh%2Fttesqai">ἐκπλήττεσθαι</w>, <w lemma="qauma%2Fzontas">θαυμάζοντας</w> <w lemma="pote%5C">ποτὲ</w> <w lemma="me%5Cn">μὲν</w> <w lemma="ei%29">εἰ</w> <w lemma="dunato%2Fn">δυνατόν</w> <w lemma="e%29sti">ἐστι</w> <w lemma="mei%2Fzw">μείζω</w> <w lemma="th%5Cn">τὴν</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="%2Alakedaimoni%2Fwn">Λακεδαιμονίων</w> <w lemma="po%2Flin">πόλιν</w> <w lemma="ei%29%3Dnai">εἶναι</w>, <w lemma="kai%5C">καὶ</w> <w lemma="pollw%3D%7C">πολλῷ</w> <w lemma="mei%2Fzw">μείζω</w>, <w lemma="th%3Ds">τῆς</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="%2Amegalopolitw%3Dn">Μεγαλοπολιτῶν</w>, <w lemma="to%5Cn">τὸν</w> <w lemma="peri%2Fbolon">περίβολον</w> <w lemma="e%29%2Fxousan">ἔχουσαν</w> <w lemma="e%29la%2Fttw">ἐλάττω</w>,
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<w lemma="pote%5C">ποτὲ</w> <w lemma="de%5C">δὲ</w> <w lemma="to%5C">τὸ</w> <w lemma="plh%3Dqos">πλῆθος</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="a%29ndrw%3Dn">ἀνδρῶν</w> <w lemma="tekmai%2Fresqai">τεκμαίρεσθαι</w>, <w lemma="stoxazome%2Fnous">στοχαζομένους</w> <w lemma="e%29c">ἐξ</w> <w lemma="au%29th%3Ds">αὐτῆς</w> <w lemma="th%3Ds">τῆς</w> <w lemma="perime%2Ftrou">περιμέτρου</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="stratopedeiw%3Dn">στρατοπεδειῶν</w>.
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<w lemma="paraplh%2Fsion">παραπλήσιον</w> <w lemma="de%2F">δέ</w> <w lemma="ti">τι</w> <w lemma="kai%5C">καὶ</w> <w lemma="e%28%2Fteron">ἕτερον</w> <w lemma="a%29di%2Fkhma">ἀδίκημα</w> <w lemma="sumbai%2Fnei">συμβαίνει</w> <w lemma="peri%5C">περὶ</w> <w lemma="ta%5Cs">τὰς</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="po%2Flewn">πόλεων</w> <w lemma="e%29pifa%2Fseis">ἐπιφάσεις</w>. <w lemma="oi%28">οἱ</w> <w lemma="ga%5Cr">γὰρ</w> <w lemma="polloi%5C">πολλοὶ</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="a%29nqrw%2Fpwn">ἀνθρώπων</w> <w lemma="ta%5Cs">τὰς</w> <w lemma="perikeklasme%2Fnas">περικεκλασμένας</w> <w lemma="kai%5C">καὶ</w> <w lemma="bounw%2Fdeis">βουνώδεις</w> <w lemma="plei%2Fous">πλείους</w> <w lemma="oi%29ki%2Fas">οἰκίας</w> <w lemma="u%28polamba%2Fnousi">ὑπολαμβάνουσι</w> <w lemma="kate%2Fxesqai">κατέχεσθαι</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29pipe%2Fdwn">ἐπιπέδων</w>.
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<w lemma="to%5C">τὸ</w> <w lemma="d%27">δ᾽</w> <w lemma="ou%29k">οὐκ</w> <w lemma="e%29%2Fsti">ἔστι</w> <w lemma="toiou%3Dton">τοιοῦτον</w> <w lemma="dia%5C">διὰ</w> <w lemma="to%5C">τὸ</w> <w lemma="ta%5C">τὰ</w> <w lemma="teixi%2Fa">τειχία</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="oi%29kodomiw%3Dn">οἰκοδομιῶν</w> <w lemma="mh%5C">μὴ</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="e%29gkli%2Fmasi">ἐγκλίμασι</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="e%29da%2Ffwn">ἐδάφων</w> <w lemma="a%29lla%5C">ἀλλὰ</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="u%28pokeime%2Fnois">ὑποκειμένοις</w> <w lemma="e%29pipe%2Fdois">ἐπιπέδοις</w> <w lemma="oi%29kodomei%3Dsqai">οἰκοδομεῖσθαι</w> <w lemma="pro%5Cs">πρὸς</w> <w lemma="o%29rqa%2Fs">ὀρθάς</w>, <w lemma="e%29f%27">ἐφ᾽</w> <w lemma="w%28%3Dn">ὧν</w> <w lemma="kai%5C">καὶ</w> <w lemma="tou%5Cs">τοὺς</w> <w lemma="lo%2Ffous">λόφους</w> <w lemma="au%29tou%5Cs">αὐτοὺς</w> <w lemma="bebhke%2Fnai">βεβηκέναι</w> <w lemma="sumbai%2Fnei">συμβαίνει</w>.
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<w lemma="gnoi%2Fh">γνοίη</w> <w lemma="d%27">δ᾽</w> <w lemma="a%29%2Fn">ἄν</w> <w lemma="tis">τις</w> <w lemma="e%29k">ἐκ</w> <w lemma="tou%3D">τοῦ</w> <w lemma="fainome%2Fnou">φαινομένου</w> <w lemma="paidikw%3Ds">παιδικῶς</w> <w lemma="o%28%2Fmws">ὅμως</w> <w lemma="to%5C">τὸ</w> <w lemma="lego%2Fmenon">λεγόμενον</w>.
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<w lemma="ei%29">εἰ</w> <w lemma="ga%5Cr">γὰρ</w> <w lemma="noh%2Fsai">νοήσαι</w> <w lemma="tis">τις</w> <w lemma="ei%29s">εἰς</w> <w lemma="u%28%2Fyos">ὕψος</w> <w lemma="a%29natetame%2Fnas">ἀνατεταμένας</w> <w lemma="ta%5Cs">τὰς</w> <w lemma="e%29n">ἐν</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="kli%2Fmasin">κλίμασιν</w> <w lemma="oi%29ki%2Fas">οἰκίας</w> <w lemma="ou%28%2Ftws">οὕτως</w> <w lemma="w%28%2Fste">ὥστε</w> <w lemma="pa%2Fsas">πάσας</w> <w lemma="i%29sou+yei%3Ds">ἰσοϋψεῖς</w> <w lemma="u%28pa%2Frxein">ὑπάρχειν</w>, <w lemma="fanero%5Cn">φανερὸν</w> <w lemma="w%28s">ὡς</w> <w lemma="e%28no%5Cs">ἑνὸς</w> <w lemma="e%29pipe%2Fdou">ἐπιπέδου</w> <w lemma="genome%2Fnou">γενομένου</w> <w lemma="tou%3D">τοῦ</w> <w lemma="kata%5C">κατὰ</w> <w lemma="ta%5C">τὰ</w> <w lemma="te%2Fgh">τέγη</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="oi%29kiw%3Dn">οἰκιῶν</w>, <w lemma="i%29%2Fson">ἴσον</w> <w lemma="kai%5C">καὶ</w> <w lemma="para%2Fllhlon">παράλληλον</w> <w lemma="e%29%2Fstai">ἔσται</w> <w lemma="tou%3Dto">τοῦτο</w> <w lemma="tw%3D%7C">τῷ</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="lo%2Ffois">λόφοις</w> <w lemma="u%28pokeime%2Fnw%7C">ὑποκειμένῳ</w> <w lemma="kai%5C">καὶ</w> <w lemma="toi%3Ds">τοῖς</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="teixw%3Dn">τειχῶν</w> <w lemma="qemeli%2Fois">θεμελίοις</w> <w lemma="e%29pipe%2Fdw%7C">ἐπιπέδῳ</w>.
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<w lemma="peri%5C">περὶ</w> <w lemma="me%5Cn">μὲν</w> <w lemma="ou%29%3Dn">οὖν</w> <w lemma="tw%3Dn">τῶν</w> <w lemma="h%28gei%3Dsqai">ἡγεῖσθαι</w> <w lemma="kai%5C">καὶ</w> <w lemma="politeu%2Fesqai">πολιτεύεσθαι</w> <w lemma="boulome%2Fnwn">βουλομένων</w>, <w lemma="a%29gnoou%2Fntwn">ἀγνοούντων</w> <w lemma="de%5C">δὲ</w> <w lemma="ta%5C">τὰ</w> <w lemma="toiau%3Dta">τοιαῦτα</w>
<head>VI. Sicilian Affairs</head>Most people judge of the size of cities simply from their circumference.
So that when one says that <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a> is fifty stades in circumference and <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> forty-eight, but that <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> is twice as large as <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a>, the statement seems incredible to me.
And when in order to puzzle them still most, one tells them that a city or camp with a circumference of forty stades may be twice as large as one the circumference of which is one hundred stades, this statement seems to them absolutely astounding.
The reason of this is that we have forgotten the lessons in geometry we learnt as children.
I was led to make these remarks by the fact that not only ordinary men but even some statesmen and commanders of armies are thus astounded, and wonder how it is possible for <a class="linkToPlace" target="_blank" href="/place?placename=Sparta&groupId=660&placeId=1208">Sparta</a> to be larger and even much larger than <a class="linkToPlace" target="_blank" href="/place?placename=Megalopolis&groupId=745&placeId=1360">Megalopolis</a>, although its circumference is smaller;
or at other times attempt to estimate the number of men in a camp by taking into consideration its circumference alone.
Another very similar error is due to the appearance of cities. Most people suppose that cities set upon broken and hilly ground can contain more houses than those set upon flat ground.
This is not so, as the walls of the houses are not built at right angles to the slope, but to the flat ground at the foot on which the hill itself rests.
The truth of this can be made manifest to the intelligence of a child.
For if one supposes the houses on a slope to be raised to such a height that their roofs are all level with each other, it is evident that the flat space thus formed by the roofs will be equal in area and parallel to the flat space in which the hill and the foundations of the houses rest.
So much for those who aspire to political power and the command of armies but are ignorant of such things and surprised by them.