Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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          <p>
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              <pb file="0032" n="32" rhead="ARCHIMEDIS"/>
            ceatinclinata. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere ipſam; </s>
            <s xml:space="preserve">ſed
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            rectam reſtitui. </s>
            <s xml:space="preserve">Itaque ſecta ipſa plano per axem, recto ad
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            planum, quod eſt in ſuperficie humidi, portionis ſectio ſit
              <lb/>
            a p o l rectanguli coni ſectio: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis
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            diameter n o: </s>
            <s xml:space="preserve">ſuperficiei autem humidi ſectio ſit i s. </s>
            <s xml:space="preserve">Si
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            igitur portio non eſt recta; </s>
            <s xml:space="preserve">non utique erit a l ipſi i s æ-
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            quidiſtans. </s>
            <s xml:space="preserve">quare n o cum i s non faciet angulos rectos.
              <lb/>
            </s>
            <s xml:space="preserve">ducatur crgo k ω contingens ſectionem coni in p [quæ
              <lb/>
              <anchor type="note" xlink:label="note-0032-01a" xlink:href="note-0032-01"/>
            ipſi i s æquidiſtet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à puncto p ad i s ducatur p f æquidi
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            ſtans ipſi o n, quæ erit ſectionis i p o s diameter, & </s>
            <s xml:space="preserve">axis por
              <lb/>
              <anchor type="note" xlink:label="note-0032-02a" xlink:href="note-0032-02"/>
            tionis in humido demerſæ. </s>
            <s xml:space="preserve">ſumantur deinde centra graui
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            tatum: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſolidæ magnitudinis a p o l grauitatis centrũ
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              <anchor type="note" xlink:label="note-0032-03a" xlink:href="note-0032-03"/>
            r; </s>
            <s xml:space="preserve">ipſius uero i p o s centrum ſit b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta b r produca-
              <lb/>
              <anchor type="note" xlink:label="note-0032-04a" xlink:href="note-0032-04"/>
            tur ad g, quod ſit centrum grauitatis reliquæ figuræ i s l a.
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            </s>
            <s xml:space="preserve">Quoniam igitur n o ipſius quidem r o ſeſquialtera eſt; </s>
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            eius autẽ, quæ uſque ad axẽ minor, quam ſeſquialtera; </s>
            <s xml:space="preserve">erit
              <lb/>
              <anchor type="note" xlink:label="note-0032-05a" xlink:href="note-0032-05"/>
            r o minor, quàm quæ uſque ad axem. </s>
            <s xml:space="preserve">Quare angulus r p ω
              <lb/>
              <anchor type="note" xlink:label="note-0032-06a" xlink:href="note-0032-06"/>
            acutus erit: </s>
            <s xml:space="preserve">cum enim linea, quæ uſque ad axem maior ſit
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            ipſa r o; </s>
            <s xml:space="preserve">quæ à puncto r ad k ω perpendicularis ducitur,
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            uidelicet r t, cũ
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              <anchor type="figure" xlink:label="fig-0032-01a" xlink:href="fig-0032-01"/>
            linea f p extra
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            ſectionem con
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            ueniet: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pro-
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            pterea inter p
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            & </s>
            <s xml:space="preserve">ω puncta ca-
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            datneceſſe eſt.
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            </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">ſi per b g
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            ducantur lineæ
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            ipſi r t æquidi-
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            ſtantes; </s>
            <s xml:space="preserve">angu-
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            los rectos cum
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            ſuperficie humidi continebunt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quod in humido eſt ſur-
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              <anchor type="note" xlink:label="note-0032-07a" xlink:href="note-0032-07"/>
            ſum feretur ſecundum perpendicularem, quæ per b ducta
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            eſt, ipſi r t æquidiſtans: </s>
            <s xml:space="preserve">quod uero eſt extra humi dum ſe-</s>
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