Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Page concordance

< >
Scan Original
131 10
132
133 11
134
135 12
136
137 13
138
139 14
140
141 15
142
143 15
144 16
145 17
146
147 18
148
149 19
150
151 20
152
153 21
154
155 22
156
157 23
158
159 24
160
< >
page |< < (16) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div65" type="section" level="1" n="27">
          <p>
            <s xml:id="echoid-s902" 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:id="echoid-s903" 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:id="echoid-s904" xml:space="preserve">ex quo eſſicitur, ut p f non ſit minor
              <lb/>
              <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">C</note>
            ipſa o m; </s>
            <s xml:id="echoid-s905" xml:space="preserve">neque p b ipſa o h. </s>
            <s xml:id="echoid-s906" xml:space="preserve">quæ ergo ab h ducitur ad
              <lb/>
              <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">D</note>
            rectos angulos ipſi n o, coibit cum b p inter p & </s>
            <s xml:id="echoid-s907" xml:space="preserve">b. </s>
            <s xml:id="echoid-s908" xml:space="preserve">co-
              <lb/>
            eatin t. </s>
            <s xml:id="echoid-s909" xml:space="preserve">& </s>
            <s xml:id="echoid-s910" xml:space="preserve">quoniam in rectanguli coniſectione p f eſt æqui
              <lb/>
            diſtans diametro n o; </s>
            <s xml:id="echoid-s911" xml:space="preserve">h t autem ad diametrum perpẽ-
              <lb/>
            dicularis: </s>
            <s xml:id="echoid-s912" xml:space="preserve">& </s>
            <s xml:id="echoid-s913" xml:space="preserve">r h æqualis ei, quæ uſque ad axem: </s>
            <s xml:id="echoid-s914" xml:space="preserve">conſtat r t
              <lb/>
            productam ſacere angulos rectos cum ipſa k p ω. </s>
            <s xml:id="echoid-s915" xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:id="echoid-s916" xml:space="preserve">cum is. </s>
            <s xml:id="echoid-s917" xml:space="preserve">ergo rt perpendicularis eſt ad ſuperſiciem hu
              <lb/>
            midi. </s>
            <s xml:id="echoid-s918" xml:space="preserve">et ſi per b g puncta ducantur æquidiſtantes ipſirt,
              <lb/>
            ad ſuperſiciem humidi perpendicular es erunt. </s>
            <s xml:id="echoid-s919" xml:space="preserve">portio igi
              <lb/>
            tur, qnæ eſt extra humidum, deorſum in humidum feretur
              <lb/>
            ſecundum perpendicularem per b ductam; </s>
            <s xml:id="echoid-s920" xml:space="preserve">quæ uero in-
              <lb/>
            tra humidum ſecundum perpendicularem per g ſurſum
              <lb/>
            feretur: </s>
            <s xml:id="echoid-s921" xml:space="preserve">& </s>
            <s xml:id="echoid-s922" 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:id="echoid-s923" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div67" type="section" level="1" n="28">
          <head xml:id="echoid-head33" xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:id="echoid-s924" xml:space="preserve">_Quare non maiorem proportionem habet tota portio_
              <lb/>
              <note position="right" xlink:label="note-0043-03" xlink:href="note-0043-03a" xml:space="preserve">A</note>
            _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:id="echoid-s925" 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:id="echoid-s926" xml:space="preserve">In
              <lb/>
            telligatur portio, quæ extra bumidum, magnitudo prima: </s>
            <s xml:id="echoid-s927" xml:space="preserve">quæ in bu
              <lb/>
            mido demerſa est, ſecunda: </s>
            <s xml:id="echoid-s928" xml:space="preserve">tertia autem magnitudo ſit quadratum
              <lb/>
            mo: </s>
            <s xml:id="echoid-s929" xml:space="preserve">& </s>
            <s xml:id="echoid-s930" xml:space="preserve">exceſſus, quo quadratum n o excedit quadratum m o ſit
              <lb/>
            quarta. </s>
            <s xml:id="echoid-s931" xml:space="preserve">ex his igitur magnitudinibus, primæ & </s>
            <s xml:id="echoid-s932" xml:space="preserve">ſecundæ ad </s>
          </p>
        </div>
      </text>
    </echo>
Impressum