Aristotle, Problemata Mechanika, 1831

List of thumbnails

< >
1
1 		2
2
3
3 		4
4
5
5 		6
6
7
7 		8
8
9
9 		10
10
< >
page |< < of 24 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p n="9">
              <s id="g0120602">
                <pb xlink:href="080/01/004.jpg" ed="Bekker" n="848b"/>
                <lb/>
              </s>
            </p>
            <p n="10">
              <s id="g0120701prop01">Πρῶτον μὲν οὖν τὰ συμβαίνοντα περὶ τὸν ζυγὸν ἀπορεῖται,
                <lb/>
              διὰ τίνα αἰτίαν ἀκριβέστερά ἐστι τὰ ζυγὰ τὰ μείζω
                <lb/>
              τῶν ἐλαττόνων.</s>
              <s id="g0120702">τούτου δὲ ἀρχή, διὰ τί ποτε ἐν τῷ κύκλῳ
                <lb/>
              ἡ πλεῖον ἀφεστηκυῖα γραμμὴ τοῦ κέντρου τῆς ἐγγὺς τῇ
                <lb/>
              αὐτῇ ἰσχύι κινουμένης θᾶττον φέρεται τῆς ἐλάττονοσ</s>
              <s id="g0120703">τὸ
                <lb/>
              γὰρ θᾶττον λέγεται διχῶς·</s>
              <s id="g0120704">ἄν τε γὰρ ἐν ἐλάττονι χρόνῳ
                <lb/>
              ἴσον τόπον διεξέλθῃ, θᾶττον εἶναι λέγομεν, καὶ ἐὰν ἐν ἴσῳ
                <lb/>
              πλείω.</s>
              <s id="g0120705">ἡ δὲ μείζων ἐν ἴσῳ χρόνῳ γράφει μείζονα κύκλον·
                <lb/>
              ὁ γὰρ ἐκτὸς μείζων τοῦ ἐντός.</s>
              <s id="g0120706">αἴτιον δὲ τούτων ὅτι φέρεται
                <lb/>
              δύο φορὰς ἡ γράφουσα τὸν κύκλον.</s>
              <s id="g0120707">ὅταν μὲν οὖν ἐν λόγῳ
                <lb/>
              τινὶ φέρηται, ἐπ' εὐθείας ἀνάγκη φέρεσθαι τὸ φερόμενον,
                <lb/>
              καὶ γίνεται διάμετρος αὐτὴ τοῦ σχήματος ὃ ποιοῦσιν αἱ
                <lb/>
              ἐν τούτῳ τῷ λόγῳ συντεθεῖσαι γραμμαί.</s>
              <s id="g0120708">ἔστω γὰρ ὁ λόγος
                <lb/>
              ὃν φέρεται τὸ φερόμενον, ὃν ἔχει ἡ ΑΒ πρὸς τὴν ΑΓ·
                <lb/>
              καὶ τὸ μὲν ΑΓ φερέσθω πρὸς τὸ Β, ἡ δὲ ΑΒ ὑποφερέσθω
                <lb/>
              πρὸς τὴν ΗΓ· ἐνηνέχθω δὲ τὸ μὲν Α πρὸς τὸ Δ, ἡ δὲ ἐφ'
                <lb/>
              ᾗ ΑΒ πρὸς τὸ Ε. εἰ οὖν ἐπὶ τῆς φορᾶς ὁ λόγος ἦν ὃν ἡ
                <lb/>
              ΑΒ ἔχει πρὸς τὴν ΑΓ, ἀνάγκη καὶ τὴν ΑΔ πρὸς τὴν
                <lb/>
              ΑΕ τοῦτον ἔχειν τὸν λόγον.</s>
              <s id="g0120709">ὅμοιον ἄρα ἐστὶ τῷ λόγῳ τὸ
                <lb/>
              μικρὸν τετράπλευρον τῷ μείζονι, ὥστε καὶ ἡ αὐτὴ διάμετρος
                <lb/>
              αὐτῶν, καὶ τὸ Α ἔσται πρὸς Ζ.</s>
              <figure id="id.080.01.004.1.jpg" xlink:href="080/01/004/1.jpg" number="2"/>
            </p>
            <p n="11">
              <s id="g0120801">τὸν αὐτὸν δὴ τρόπον
                <lb/>
              δειχθήσεται κἂν ὁπουοῦν διαληφθῇ ἡ φορά· αἰεὶ γὰρ
                <lb/>
              ἔσται ἐπὶ τῆς διαμέτρου.</s>
              <s id="g0120802">φανερὸν οὖν ὅτι τὸ κατὰ τὴν διάμετρον
                <lb/>
              φερόμενον ἐν δύο φοραῖς ἀνάγκη τὸν τῶν πλευρῶν
                <lb/>
              φέρεσθαι λόγον.</s>
              <s id="g0120803">εἰ γὰρ ἄλλον τινά, οὐκ οἰσθήσεται κατὰ
                <lb/>
              τὴν διάμετρον.</s>
              <s id="g0120804">ἐὰν δὲ ἐν μηδενὶ λόγῳ φέρηται δύο φορὰς
                <lb/>
              κατὰ μηδένα χρόνον, ἀδύνατον εὐθεῖαν εἶναι τὴν φοράν.</s>
              <s id="g0120805">
                <lb/>
              ἔστω γὰρ εὐθεῖα.</s>
              <s id="g0120806">τεθείσης οὖν ταύτης διαμέτρου, καὶ παραπληρωθεισῶν
                <lb/>
              τῶν πλευρῶν, ἀνάγκη τὸν τῶν πλευρῶν λόγον
                <lb/>
              φέρεσθαι τὸ φερόμενον· τοῦτο γὰρ δέδεικται πρότερον.</s>
              <s id="g0120807">οὐκ
                <lb/>
              ἄρα ποιήσει εὐθεῖαν τὸ ἐν μηδενὶ λόγῳ φερόμενον μηδένα
                <lb/>
              χρόνον.</s>
              <s id="g0120808">ἐὰν γάρ τινα λόγον ἐνεχθῇ ἐν χρόνῳ τινί, τοῦτον
                <lb/>
              ἀνάγκη τὸν χρόνον εὐθεῖαν εἶναι φορὰν διὰ τὰ προειρημένα.</s>
              <s id="g0120809">
                <lb/>
              ὥστε περιφερὲς γίνεται, δύο φερόμενον φορὰς ἐν μηθενὶ
                <lb/>
              λόγῳ μηθένα χρόνον.</s>
            </p>
            <p n="12">
              <s id="g0120901">ὅτι μὲν τοίνυν ἡ τὸν κύκλον γράφουσα
                <lb/>
              φέρεται δύο φορὰς ἅμα, φανερὸν ἔκ τε τούτων,
                <lb/>
              καὶ ὅτι τὸ φερόμενον κατ' εὐθεῖαν ἐπὶ τὴν κάθετον ἀφι-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum