Aristotle, Problemata Mechanika, 1831

Table of figures

< >
[Figure 1]
Page: 3
[Figure 2]
Page: 4
[Figure 3]
Page: 5
[Figure 4]
Page: 6
[Figure 5]
Page: 7
[Figure 6]
Page: 7
[Figure 7]
Page: 8
[Figure 8]
Page: 9
[Figure 9]
Page: 9
[Figure 10]
Page: 9
[Figure 11]
Page: 10
[Figure 12]
Page: 12
[Figure 13]
Page: 13
[Figure 14]
Page: 13
[Figure 15]
Page: 14
[Figure 16]
Page: 15
[Figure 17]
Page: 16
[Figure 18]
Page: 16
[Figure 19]
Page: 18
[Figure 20]
Page: 19
[Figure 21]
Page: 20
[Figure 22]
Page: 20
[Figure 23]
Page: 21
[Figure 24]
Page: 21
[Figure 25]
Page: 21
[Figure 26]
Page: 21
[Figure 27]
Page: 22
[Figure 28]
Page: 22
[Figure 29]
Page: 24
< >
page |< < of 24 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p n="19">
              <s id="g0130108">
                <pb xlink:href="080/01/007.jpg" ed="Bekker" n="850a"/>
                <lb/>
              τερον γὰρ ἐν ᾧ μέρος ἡ ῥίζα τοῦ ξύλου ἐστίν, ὁ δὲ ὄζος ῥίζα
                <lb/>
              τίς ἐστιν.</s>
            </p>
            <p n="20">
              <s id="g0130201prop02">
                <lb/>
              Διὰ τί, ἐὰν μὲν ἄνωθεν ᾖ τὸ σπαρτίον, ὅταν κάτωθεν
                <lb/>
              ῥέψαντος ἀφέλῃ τὸ βάρος, πάλιν ἀναφέρεται τὸ ζυγόν,
                <lb/>
              ἐὰν δὲ κάτωθεν ὑποστῇ, οὐκ ἀναφέρεται ἀλλὰ μένει; </s>
              <s id="g0130202">ἢ
                <lb/>
              διότι ἄνωθεν μὲν τοῦ σπαρτίου ὄντος πλεῖον τοῦ ζυγοῦ γίνεται
                <lb/>
              τὸ ἐπέκεινα τῆς καθέτου; τὸ γὰρ σπαρτίον ἐστὶ κάθετος.
                <lb/>
              ὥστε ἀνάγκη ἐστὶ κάτω ῥέπειν τὸ πλέον, ἕως ἂν ἔλθῃ ἡ
                <lb/>
              δίχα διαιροῦσα τὸ ζυγὸν ἐπὶ τὴν κάθετον αὐτήν, ἐπικειμένου
                <lb/>
              τοῦ βάρους ἐν τῷ ἀνεσπασμένῳ μορίῳ τοῦ ζυγοῦ.</s>
              <s id="g0130203">
                <lb/>
              ἔστω ζυγὸν ὀρθὸν ἐφ' οὗ ΒΓ, σπαρτίον δὲ τὸ ΑΔ. ἐκβαλλόμενον
                <lb/>
              δὴ τοῦτο κάτω κάθετος ἔσται ἐφ' ἧς ἡ ΑΔΜ.</s>
              <s id="g0130204">
                <lb/>
              ἐὰν οὖν ἐπὶ τὸ Β ἡ ῥοπὴ ἐπιτεθῇ, ἔσται τὸ μὲν Β οὗ τὸ Ε,
                <lb/>
              τὸ δὲ Γ οὗ τὸ Ζ, ὥστε ἡ δίχα διαιροῦσα τὸ ζυγὸν πρῶτον
                <lb/>
              μὲν ἦν ἡ ΔΜ τῆς καθέτου αὐτῆς, ἐπικειμένης δὲ τῆς ῥοπῆς
                <lb/>
              ἔσται ἡ ΔΘ· ὥστε τοῦ ζυγοῦ ἐφ' ᾧ ΕΖ τὸ ἔξω τῆς καθέτου
                <lb/>
              τῆς ἐφ' ἧς ΑΒ, τοῦ ἐν ᾧ ΦΠ, μείζω τοῦ ἡμίσεος.</s>
              <s id="g0130205">
                <lb/>
              ἐὰν οὖν ἀφαιρεθῇ τὸ βάρος ἀπὸ τοῦ Ε, ἀνάγκη κάτω φέρεσθαι
                <lb/>
              τὸ Ζ· ἔλαττον γάρ ἐστι τὸ Ε.</s>
              <s id="g0130206">ἐὰν μὲν οὖν ἄνω τὸ
                <lb/>
              σπαρτίον ἔχῃ, πάλιν διὰ τοῦτο ἀναφέρεται τὸ ζυγόν.</s>
              <figure id="id.080.01.007.1.jpg" xlink:href="080/01/007/1.jpg" number="5"/>
              <s id="g0130207">ἐὰν
                <lb/>
              δὲ κάτωθεν ᾖ τὸ ὑποκείμενον, τοὐναντίον ποιεῖ· πλεῖον γὰρ
                <lb/>
              γίνεται τοῦ ἡμίσεος τοῦ ζυγοῦ τὸ κάτω μέρος ἢ ὡς ἡ κάθετος
                <lb/>
              διαιρεῖ ὥστε οὐκ ἀναφέρεται· κουφότερον γὰρ τὸ ἐπηρτημένον.</s>
              <s id="g0130208">
                <lb/>
              ἔστω ζυγὸν τὸ ἐφ' οὗ ΝΞ, τὸ ὀρθόν, κάθετος δὲ ἡ
                <lb/>
              ΚΛΜ. δίχα δὴ διαιρεῖται τὸ ΝΞ.</s>
              <s id="g0130209">ἐπιτεθέντος δὲ βάρους
                <lb/>
              ἐπὶ τὸ Ν, ἔσται τὸ μὲν Ν οὗ τὸ Ο, τὸ δὲ Ξ οὗ τὸ Ρ, ἡ δὲ
                <lb/>
              ΚΛ οὗ τὸ ΛΘ, ὥστε μεῖζόν ἐστι τὸ ΚΟ τοῦ ΛΡ τῷ ΘΚΛ.</s>
              <s id="g0130210">
                <lb/>
              καὶ ἀφαιρεθέντος οὖν τοῦ βάρους ἀνάγκη μένειν· ἐπίκειται
                <lb/>
              γὰρ ὥσπερ βάρος ἡ ὑπεροχὴ ἡ τοῦ ἡμίσεος τοῦ ἐν ᾧ τὸ Κ.</s>
              <figure id="id.080.01.007.2.jpg" xlink:href="080/01/007/2.jpg" number="6"/>
            </p>
            <p n="21">
              <s id="g0130301prop03">
                <lb/>
              Διὰ τί κινοῦσι μεγάλα βάρη μικραὶ δυνάμεις τῷ μοχλῷ,
                <lb/>
              ὥσπερ ἐλέχθη καὶ κατ' ἀρχήν, προσλαβόντι βάρος
                <lb/>
              ἔτι τὸ τοῦ μοχλοῦ; ῥᾷον δὲ τὸ ἔλαττόν ἐστι κινῆσαι βάρος,
                <lb/>
              ἔλαττον δέ ἐστιν ἄνευ τοῦ μοχλοῦ.</s>
              <s id="g0130302">ἢ ὅτι αἴτιόν ἐστιν ὁ μοχλός,
                <lb/>
              ζυγὸν [ὢν] κάτωθεν ἔχον τὸ σπαρτίον καὶ εἰς ἄνισα διῃρημένον;
                <lb/>
              τὸ γὰρ ὑπομόχλιον ἀντὶ σπαρτίου γίνεται· μένει
                <lb/>
              γὰρ ἄμφω ταῦτα, ὥσπερ τὸ κέντρον.</s>
              <s id="g0130303">ἐπεὶ δὲ θᾶττον ὑπὸ
                <lb/>
              τοῦ ἴσου βάρους κινεῖται ἡ μείζων τῶν ἐκ τοῦ κέντρου, ἔστι δὲ
                <lb/>
              τρία τὰ περὶ τὸν μοχλόν, τὸ μὲν ὑπομόχλιον, σπάρτον
                <lb/>
              καὶ κέντρον, δύο δὲ βάρη, ὅ τε κινῶν καὶ τὸ κινούμενον· ὃ</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum