Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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    <archimedes>
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        <body>
          <chap>
            <p>
              <s id="id.000301">
                <pb n="1118"/>
              </s>
            </p>
            <p>
              <s id="id.000302">Ἡ μὲν οὖν κατασκευὴ δεδήλωται, χρεία δ' ἐστὶν ἡ
                <lb n="1"/>
              μέλλουσα λέγεσθαι. </s>
              <s id="id.000303">ὅταν γὰρ βουλώμεθα μεγάλα βάρη
                <lb n="2"/>
              κινεῖν ἐλάσσονι βίᾳ, τὰ ἐκδεδεμένα ἐκ τοῦ βάρους ὅπλα
                <lb n="3"/>
              περιθέντες περὶ τὰ σεσιμωμένα τοῦ ἄξονος, καὶ ἐμβαλόν-
                <lb n="4"/>
              τες σκυτάλας εἰς τὰ ἐν τῷ περιτροχίῳ τρήματα, ἐπιστρέ-
                <lb n="5"/>
              φομεν τὸ περιτρόχιον κατάγοντες τὰς σκυτάλας, καὶ οὕτως
                <lb n="6"/>
              εὐκόπως κινηθήσεται τὸ βάρος ὑπὸ ἐλάσσονος δυνάμεως
                <lb n="7"/>
              τῶν ὅπλων περὶ τὸν ἄξονα ἐπειλουμένων [ἢ καὶ διαμηρυο-
                <lb n="8"/>
              μένων ὑπό τινος πρὸς τὸ μὴ ἅπαν τὸ ὅπλον περικεῖσθαι
                <lb n="9"/>
              τῷ ἄξονι]. </s>
              <s id="id.000304">τοῦ δὲ εἰρημένου ὀργάνου τὸ μὲν μέγεθος ἁρ-
                <lb n="10"/>
              μόζεσθαι δεῖ πρὸς τὰ μέλλοντα κινεῖσθαι βάρη, τὴν δὲ
                <lb n="11"/>
              συμμετρίαν πρὸς τὸν λόγον ὃν ἔχει τὸ κινούμενον βάρος
                <lb n="12"/>
              πρὸς τὴν κινοῦσαν δύναμιν, ὡς ἑξῆς δειχθήσεται.
                <lb n="13"/>
              </s>
            </p>
            <p>
              <s id="id.000305">Ἦν δὲ δευτέρα δύναμις ἡ διὰ τοῦ μοχλοῦ [καὶ τάχα ἡ
                <lb n="14"/>
              προεπίνοια τῆς περὶ τὰ ὑπεράγαν βάρη κινήσεωσ]· προελό-
                <lb n="15"/>
              μενοι γάρ τινες μεγάλα βάρη κινεῖν, ἐπειδὴ ἀπὸ τῆς γῆς ἔδει
                <lb n="16"/>
              πρῶτον μετεωρίσαι, λαβὰς δὲ οὐκ εἶχον διὰ τὸ πάντα τὰ
                <lb n="17"/>
              μέρη τῆς ἕδρας τοῦ φορτίου ἐπικεῖσθαι τῷ ἐδάφει, ὑπο-
                <lb n="18"/>
              ρύξαντες βραχὺ καὶ ξύλου μακροῦ τὸ ἄκρον ὑποβαλόντες
                <lb n="19"/>
              ὑπὸ τὸ φορτίον κατῆγον ἐκ τοῦ ἑτέρου ἄκρου, ὑποθέντες
                <lb n="20"/>
              τῷ ξύλῳ παρ' αὐτὸ τὸ φορτίον λίθον, ὃ δὴ καλεῖται ὑπο-
                <lb n="21"/>
              μόχλιον. </s>
              <s id="id.000306">φανείσης δ' αὐτοῖς τῆς κινήσεως πάνυ εὐκόπου
                <lb n="22"/>
              ἐνόησαν ὅτι δυνατὸν κινεῖσθαι μεγάλα βάρη διὰ τοῦ τρόπου
                <lb n="23"/>
              τούτου. </s>
              <s id="id.000307">καλεῖται δὲ τὸ ξύλον μοχλός, εἴτε τετράγωνον εἴη
                <lb n="24"/>
              εἴτε στρογγύλον. </s>
              <s id="id.000308">ὅσῳ δ' ἂν ἐγγυτέρω τιθῆται τοῦ φορτίου
                <lb n="25"/>
              τὸ ὑπομόχλιον, τοσούτῳ εὐχερέστερον κινεῖται τὸ βάρος,
                <lb n="26"/>
              ὡς ἑξῆς δειχθήσεται.
                <lb n="27"/>
              </s>
            </p>
            <p>
              <s id="id.000309">Ἔστιν δὲ ἡ τρίτη δύναμις ἡ κατὰ τὸ πολύσπαστον.
                <lb n="28"/>
              </s>
              <s id="id.000310">ὅταν γὰρ βουλώμεθά τι βάρος ἕλκειν, ἐξάψαντες ὅπλον
                <lb n="29"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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