Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
81 35
82
83 36
84
85 37
86
87 38
88
89 39
90
91 40
92
93 41
94
95 42
96
97 43
98
99 44
100
< >
page |< < (42) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div175" type="section" level="1" n="55">
          <p style="it">
            <s xml:id="echoid-s2486" xml:space="preserve">
              <pb o="42" file="0095" n="95" rhead="DE IIS QVAE VEH. IN AQVA."/>
            clinata, ut baſis humidum non contingat, ſectur plano per axem,
              <lb/>
            recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
              <lb/>
            ctio: </s>
            <s xml:id="echoid-s2487" xml:space="preserve">ſuperficiei humidi ſectio ſit i o: </s>
            <s xml:id="echoid-s2488" xml:space="preserve">axis portionis, & </s>
            <s xml:id="echoid-s2489" xml:space="preserve">ſectionis
              <lb/>
            diameter b d; </s>
            <s xml:id="echoid-s2490" xml:space="preserve">quæ in eaſdem, quas diximus, partes ſecetur: </s>
            <s xml:id="echoid-s2491" xml:space="preserve">duca-
              <lb/>
            turq; </s>
            <s xml:id="echoid-s2492" xml:space="preserve">m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
              <lb/>
            cótingat: </s>
            <s xml:id="echoid-s2493" xml:space="preserve">mt uero æquidiſtans ipſi b d: </s>
            <s xml:id="echoid-s2494" xml:space="preserve">& </s>
            <s xml:id="echoid-s2495" xml:space="preserve">m s ad eandem perpen
              <lb/>
            dicularis. </s>
            <s xml:id="echoid-s2496" xml:space="preserve">Demonſtrandum eſt non manere portionem, ſed inclinari
              <lb/>
            ita, ut in uno puncto contingat ſuperficiem humidi. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">ducatur enim p c
              <lb/>
            ad ipſam b d perpendicularis: </s>
            <s xml:id="echoid-s2498" xml:space="preserve">& </s>
            <s xml:id="echoid-s2499" xml:space="preserve">iuncta a f uſque ad ſectionem
              <lb/>
            producatur in q: </s>
            <s xml:id="echoid-s2500" xml:space="preserve">& </s>
            <s xml:id="echoid-s2501" xml:space="preserve">per p ducatur p φ ipſi a q æquidiſtans. </s>
            <s xml:id="echoid-s2502" xml:space="preserve">erunt
              <lb/>
            iam ex ijs, quæ demonſtrauimus a f, f q inter ſe ſe æquales. </s>
            <s xml:id="echoid-s2503" xml:space="preserve">& </s>
            <s xml:id="echoid-s2504" xml:space="preserve">cum
              <lb/>
            portio ad humi-
              <lb/>
              <figure xlink:label="fig-0095-01" xlink:href="fig-0095-01a" number="61">
                <image file="0095-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0095-01"/>
              </figure>
            dum eam in gra-
              <lb/>
            uitate proportio
              <lb/>
            nem habeat, quá
              <lb/>
            quadratú p f ad
              <lb/>
            b d quadratum:
              <lb/>
            </s>
            <s xml:id="echoid-s2505" xml:space="preserve">atque eandem ha
              <lb/>
            beat portio ipſi-
              <lb/>
            us demerſa ad to
              <lb/>
            tam portionem; </s>
            <s xml:id="echoid-s2506" xml:space="preserve">
              <lb/>
            hoc eſt quadratú
              <lb/>
            m t ad quadratú
              <lb/>
              <note position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">8. quinti.</note>
            b d: </s>
            <s xml:id="echoid-s2507" xml:space="preserve">erit quadra
              <lb/>
            tum m t quadra-
              <lb/>
            to p f æquale: </s>
            <s xml:id="echoid-s2508" xml:space="preserve">& </s>
            <s xml:id="echoid-s2509" xml:space="preserve">
              <lb/>
            idcirco linea m t
              <lb/>
            æqualis lmeæ p
              <lb/>
            f. </s>
            <s xml:id="echoid-s2510" xml:space="preserve">Itaque quoniam in portionibus æqualibus, & </s>
            <s xml:id="echoid-s2511" xml:space="preserve">ſimilibus a p q l, a
              <lb/>
            m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
              <lb/>
            </s>
            <s xml:id="echoid-s2512" xml:space="preserve">illa quidem ab extremitate baſis; </s>
            <s xml:id="echoid-s2513" xml:space="preserve">hæc uero non ab extremitate: </s>
            <s xml:id="echoid-s2514" xml:space="preserve">ſe-
              <lb/>
            quitur ut a q, quæ ab extremitate ducitur, minorem acutum angulú
              <lb/>
            contineat cum diametro portionis, quàm ipſa i o. </s>
            <s xml:id="echoid-s2515" xml:space="preserve">Sed linea p φ li-
              <lb/>
            neæ a q æquidiſtat, & </s>
            <s xml:id="echoid-s2516" xml:space="preserve">m n ipſi i o. </s>
            <s xml:id="echoid-s2517" xml:space="preserve">angulus igitur ad φ angulo ad </s>
          </p>
        </div>
      </text>
    </echo>