Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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              <pb o="42" file="0095" n="95" rhead="DE IIS QVAE VEH. IN AQVA."/>
            clinata, ut baſis humidum non contingat, ſectur plano per axem,
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            recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
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            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
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            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-
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            turq; </s>
            <s xml:id="echoid-s2492" xml:space="preserve">m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
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            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
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            dicularis. </s>
            <s xml:id="echoid-s2496" xml:space="preserve">Demonſtrandum eſt non manere portionem, ſed inclinari
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            ita, ut in uno puncto contingat ſuperficiem humidi. </s>
            <s xml:id="echoid-s2497" xml:space="preserve">ducatur enim p c
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            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
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            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
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            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
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            portio ad humi-
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              <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"/>
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            dum eam in gra-
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            uitate proportio
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            nem habeat, quá
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            quadratú p f ad
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            b d quadratum:
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            </s>
            <s xml:id="echoid-s2505" xml:space="preserve">atque eandem ha
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            beat portio ipſi-
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            us demerſa ad to
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            tam portionem; </s>
            <s xml:id="echoid-s2506" xml:space="preserve">
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            hoc eſt quadratú
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            m t ad quadratú
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              <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
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            tum m t quadra-
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            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
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            æqualis lmeæ p
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            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
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            m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
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            </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-
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            quitur ut a q, quæ ab extremitate ducitur, minorem acutum angulú
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            contineat cum diametro portionis, quàm ipſa i o. </s>
            <s xml:id="echoid-s2515" xml:space="preserve">Sed linea p φ li-
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            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>
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