Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
51 20
52
53 21
54
55 22
56
57 23
58
59 24
60
61 25
62
63 26
64
65 27
66
67 22
68
69 29
70
71 30
72
73 37
74
75 32
76
77 25
78
79 34
80
< >
page |< < (16) of 213 > >|
DE IIS QVAE VEH. IN AQVA.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="27">
          <p>
            <s xml:space="preserve">
              <pb o="16" file="0043" n="43" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dratum n o ad quadratum p f. </s>
            <s xml:space="preserve">quadratum igitur n o ad
              <lb/>
            quadratum p f non maiorem proportionem habet, quàm
              <lb/>
            ad quadratum m o. </s>
            <s xml:space="preserve">ex quo eſſicitur, ut p f non ſit minor
              <lb/>
              <anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/>
            ipſa o m; </s>
            <s xml:space="preserve">neque p b ipſa o h. </s>
            <s xml:space="preserve">quæ ergo ab h ducitur ad
              <lb/>
              <anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/>
            rectos angulos ipſi n o, coibit cum b p inter p & </s>
            <s xml:space="preserve">b. </s>
            <s xml:space="preserve">co-
              <lb/>
            eatin t. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam in rectanguli coniſectione p f eſt æqui
              <lb/>
            diſtans diametro n o; </s>
            <s xml:space="preserve">h t autem ad diametrum perpẽ-
              <lb/>
            dicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">r h æqualis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">conſtat r t
              <lb/>
            productam ſacere angulos rectos cum ipſa k p ω. </s>
            <s xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:space="preserve">cum is. </s>
            <s xml:space="preserve">ergo rt perpendicularis eſt ad ſuperſiciem hu
              <lb/>
            midi. </s>
            <s xml:space="preserve">et ſi per b g puncta ducantur æquidiſtantes ipſirt,
              <lb/>
            ad ſuperſiciem humidi perpendicular es erunt. </s>
            <s xml:space="preserve">portio igi
              <lb/>
            tur, qnæ eſt extra humidum, deorſum in humidum feretur
              <lb/>
            ſecundum perpendicularem per b ductam; </s>
            <s xml:space="preserve">quæ uero in-
              <lb/>
            tra humidum ſecundum perpendicularem per g ſurſum
              <lb/>
            feretur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non manebit ſolida portio a p o l, ſedintra hu
              <lb/>
            midum mouebitur, donecutique ipſa n o ſecundum per-
              <lb/>
            pendicularem ſiat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a">
              <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0042-01"/>
            </figure>
            <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">11. quin-
              <lb/>
            ti.</note>
            <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">D</note>
          </div>
        </div>
        <div type="section" level="1" n="28">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_Quare non maiorem proportionem habet tota portio_
              <lb/>
              <anchor type="note" xlink:label="note-0043-03a" xlink:href="note-0043-03"/>
            _ad eam, quæ eſt extra humidum, quam quadratum n o ad_
              <lb/>
            _quadratum m o]_ cum enim magnitudo portionis in bumidum
              <lb/>
            demerſa ad totam portionem non maiorem proportionem babeat,
              <lb/>
            quàm exceſſus, quo quadratum n o excedit quadratum m o, ad ip-
              <lb/>
            ſum no quadratum: </s>
            <s xml:space="preserve">conuertendo per uigeſimáſextam quinti ele-
              <lb/>
            mentorum ex traditione Campani, tota portio ad magnitudinem de
              <lb/>
            merſam non minorem proportionem babebit, quàm quadratum n o
              <lb/>
            ad exceſſum, quo ipſum quadratum no excedit quadratum m o. </s>
            <s xml:space="preserve">In
              <lb/>
            telligatur portio, quæ extra bumidum, magnitudo prima: </s>
            <s xml:space="preserve">quæ in bu
              <lb/>
            mido demerſa est, ſecunda: </s>
            <s xml:space="preserve">tertia autem magnitudo ſit quadratum
              <lb/>
            mo: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">exceſſus, quo quadratum n o excedit quadratum m o ſit
              <lb/>
            quarta. </s>
            <s xml:space="preserve">ex his igitur magnitudinibus, primæ & </s>
            <s xml:space="preserve">ſecundæ ad ſecun-</s>
          </p>
        </div>
      </text>
    </echo>