Ceva, Giovanni, Geometria motus, 1692

Page concordance

< >
Scan Original
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
< >
page |< < of 110 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="75" xlink:href="022/01/081.jpg"/>
            <p type="main">
              <s id="s.000750">
                <emph type="center"/>
                <emph type="italics"/>
              Exemplum II.
                <emph.end type="italics"/>
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000751">
                <emph type="center"/>
              PROP. XXXIV. THEOR. XXVII.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000752">TEmpora ſimilium vibrationum ſunt in ſubduplicata
                <lb/>
              ratione arcuum exactorum, ſeu longitudinum pen­
                <lb/>
              dulorum, quorum ſunt vibrationes. </s>
              <s id="s.000753">Sint grauia pendula
                <lb/>
              LA, LF, quæ ab eadem recta LF diſcedentia currant ſuſ­
                <lb/>
                <arrow.to.target n="marg177"/>
                <lb/>
              penſa ex L duos ſimiles arcus circulares FI, AC. </s>
              <s id="s.000754">Dico
                <lb/>
              tempora horum deſcenſuum eſſe in ratione ſubduplicatą
                <lb/>
              arcuum FI, AC, ſeu longitudinum filorum, aut haſtularum
                <lb/>
              FA, LA. </s>
              <s id="s.000755">Ducamus quamcumque rectam LBG, erit AB
                <lb/>
              ad BC, vt FG ad GI, & cum præterea velocitates pendu­
                <lb/>
              lorum a quiete in A, F ſint æquales, pariterque velocita­
                <lb/>
              tes æquales a quiete in B, G; erit velocitas in A ad veloci­
                <lb/>
              tatem in B, vt velocitas in F ad velocitatem in G, quare
                <lb/>
              conſideratis arcubus ABC, FGI, vt altitudines rectę, (quæ
                <lb/>
              item forent in B, G proportionaliter ſectę) geneſum ſimi­
                <lb/>
                <arrow.to.target n="marg178"/>
                <lb/>
              lium ſimpliciumque motuum, quarum amplitudines æqua
                <lb/>
              les ſunt, erunt ſpatia in acceleratis decurſubus per FI, AC
                <lb/>
              in ratione duplicata temporum, ſcilicet ipſi arcus, aut lon­
                <lb/>
              gitudines LF, LA erunt in ratione duplicata temporum̨.
                <lb/>
              </s>
              <s id="s.000756">Quod &c. </s>
            </p>
            <p type="margin">
              <s id="s.000757">
                <margin.target id="marg177"/>
                <emph type="italics"/>
              Tab.
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              fig.
                <emph.end type="italics"/>
              2.</s>
            </p>
            <p type="margin">
              <s id="s.000758">
                <margin.target id="marg178"/>
                <emph type="italics"/>
              Def.
                <emph.end type="italics"/>
              7.
                <emph type="italics"/>
              primi.
                <gap/>
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000759">Idem demonſtratum eſſet beneficio imaginum, quæ vt­
                <lb/>
              pote eorundem illorum motuum ſimplicium, forent etiam
                <lb/>
              ſimilium, & ſunt amplitudines æquales, etenim eædem̨
                <lb/>
              ſunt, ac geneſum ergo rurſus ſpatia, hoc eſt arcus ABC,
                <lb/>
              FGI, nempe longitudines filorum IF, AC erunt in ratione
                <lb/>
              duplicata temporum. </s>
              <s id="s.000760">Quod &c. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum