Pappus Alexandrinus, Mathematical Collection, Book 8, 1876

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 58 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p>
              <s id="id.000057">
                <pb n="1040"/>
              τῆς ΛΜ πρὸς ΛΘ. </s>
              <s id="id.000058">ἀλλ' ὁ μὲν τῆς ΚΛ πρὸς ΛΜ λόγος
                <lb n="1"/>
              ὁ αὐτός ἐστιν τῷ τῆς ΚΕ πρὸς ΕΓ διὰ τὸ παράλληλον
                <lb n="2"/>
              εἶναι πάλιν τὴν ΕΔ τῇ ΓΜ, ὁ δὲ τῆς ΛΜ πρὸς ΛΘ λό-
                <lb n="3"/>
              γος ὁ αὐτός ἐστιν τῷ τῆς ΓΔ πρὸς ΔΘ διὰ τὸ ἰσογώνια
                <lb n="4"/>
              εἶναι τὰ ΔΘΛ ΓΘΜ τρίγωνα· ὁ ἄρα τῆς ΚΛ πρὸς ΛΘ
                <lb n="5"/>
              λόγος ὁ αὐτός ἐστιν τῷ συγκειμένῳ ἔκ τε τοῦ τῆς ΚΕ πρὸς
                <lb n="6"/>
              ΕΓ, τουτέστιν τοῦ τῆς ΔΘ πρὸς ΔΓ, καὶ τοῦ τῆς ΓΔ
                <lb n="7"/>
              πρὸς τὴν ΔΘ λόγου, ὃς τὸν τῆς ἰσότητος λόγον ποιεῖ· καὶ
                <lb n="8"/>
              ὁ τῆς ΚΛ ἄρα πρὸς τὴν ΛΘ λόγος τῆς ἰσότητός ἐστιν·
                <lb n="9"/>
              ἴση ἄρα ἡ ΚΛ τῇ ΛΘ.
                <lb n="10"/>
              </s>
            </p>
            <p>
              <s id="id.000059">ε#. </s>
              <s id="id.000060">Τὸ λοιπὸν τῶν ὑπερτεθέντων. </s>
              <s id="id.000061">ἔστω παράλληλος
                <lb n="11"/>
              ἡ ΑΒ τῇ ΓΔ, καὶ ὡς ἡ ΑΖ πρὸς ΖΒ, ἡ ΓΘ πρὸς ΘΔ,
                <lb n="12"/>
              καὶ ἐπεζεύχθωσαν αἱ ΑΓ ΒΔ τέμνουσαι ἀλλήλας κατὰ τὸ
                <lb n="13"/>
              Ε σημεῖον· ὅτι ἡ διὰ τῶν Ζ Ε Θ εὐθεῖά ἐστιν.
                <lb n="14"/>
              </s>
            </p>
            <p>
              <s id="id.000062">Εἰ γὰρ μή, ἔστω ἡ διὰ τῶν Ζ Ε Η. </s>
              <s id="id.000063">ἐπεὶ οὖν ἐστιν
                <lb n="15"/>
                <figure place="text" number="2"/>
              ὡς ἡ ΑΖ πρὸς ΓΗ, οὕτως
                <lb n="16"/>
              ἡ ΖΕ πρὸς ΕΗ, ὡς δὲ ἡ ΖΕ
                <lb n="17"/>
              πρὸς ΕΗ, οὕτως ἡ ΖΒ πρὸς
                <lb n="18"/>
              ΗΔ, ὡς ἄρα ἡ ΑΖ πρὸς ΓΗ,
                <lb n="19"/>
              οὕτως ἡ ΖΒ πρὸς ΗΔ, καὶ
                <lb n="20"/>
              ἐναλλὰξ ὡς ἡ ΑΖ πρὸς ΖΒ,
                <lb n="21"/>
              τουτέστιν ὡς ἡ ΓΘ πρὸς ΘΔ,
                <lb n="22"/>
              οὕτως ἡ ΓΗ πρὸς ΗΔ, ὅπερ
                <lb n="23"/>
              ἀδύνατον· ἡ ἄρα διὰ τῶν
                <lb n="24"/>
              Ζ Ε Θ σημείων εὐθεῖά ἐστιν.
                <lb n="25"/>
              </s>
            </p>
            <p>
              <s id="id.000064">ς#. </s>
              <s id="id.000065">Παραλληλογράμμου δοθέντος ὀρθογωνίου τοῦ ΑΓ,
                <lb n="26"/>
              διαγαγεῖν τὴν ΓΔ ὥστε τοῦ ΑΒΓΔ τραπεζίου ἀρτηθέντος
                <lb n="27"/>
              ἀπὸ τοῦ Δ τὰς ΑΔ ΒΓ παραλλήλους εἶναι τῷ ὁρίζοντι.
                <lb n="28"/>
              </s>
            </p>
            <p>
              <s id="id.000066">Γεγονέτω· ἡ ἄρα διὰ τοῦ Δ καὶ τοῦ κέντρου τοῦ βά-
                <lb n="29"/>
              ρους τοῦ τραπεζίου ἀγομένη εὐθεῖα κάθετος ἔσται ἐπὶ
                <lb n="30"/>
              τὸν ὁρίζοντα καὶ ἐπὶ τὴν ΒΓ. </s>
              <s id="id.000067">ἔστω ἡ ΔΛ, καὶ τε-
                <lb n="31"/>
              τμήσθω δίχα ἡ ΔΛ κατὰ τὸ Ε, καὶ ἡ ΑΒ κατὰ τὸ Ζ,
                <lb n="32"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum