Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE IIS QVAE VEH. IN AQVA.
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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,
              <lb/>
            recto ad ſuperficiem humidi, ut ſectio ſit a m o l rectanguli coni ſe-
              <lb/>
            ctio: </s>
            <s xml:space="preserve">ſuperficiei humidi ſectio ſit i o: </s>
            <s xml:space="preserve">axis portionis, & </s>
            <s xml:space="preserve">ſectionis
              <lb/>
            diameter b d; </s>
            <s xml:space="preserve">quæ in eaſdem, quas diximus, partes ſecetur: </s>
            <s xml:space="preserve">duca-
              <lb/>
            turq; </s>
            <s xml:space="preserve">m n quidem ipſi i o æquidiſtans, ut in puncto m ſectionem
              <lb/>
            cótingat: </s>
            <s xml:space="preserve">mt uero æquidiſtans ipſi b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">m s ad eandem perpen
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            dicularis. </s>
            <s xml:space="preserve">Demonſtrandum eſt non manere portionem, ſed inclinari
              <lb/>
            ita, ut in uno puncto contingat ſuperficiem humidi. </s>
            <s xml:space="preserve">ducatur enim p c
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            ad ipſam b d perpendicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta a f uſque ad ſectionem
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            producatur in q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per p ducatur p φ ipſi a q æquidiſtans. </s>
            <s xml:space="preserve">erunt
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            iam ex ijs, quæ demonſtrauimus a f, f q inter ſe ſe æquales. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum
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            portio ad humi-
              <lb/>
              <anchor type="figure" xlink:label="fig-0095-01a" xlink:href="fig-0095-01"/>
            dum eam in gra-
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            uitate proportio
              <lb/>
            nem habeat, quá
              <lb/>
            quadratú p f ad
              <lb/>
            b d quadratum:
              <lb/>
            </s>
            <s xml:space="preserve">atque eandem ha
              <lb/>
            beat portio ipſi-
              <lb/>
            us demerſa ad to
              <lb/>
            tam portionem; </s>
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              <lb/>
            hoc eſt quadratú
              <lb/>
            m t ad quadratú
              <lb/>
              <anchor type="note" xlink:label="note-0095-01a" xlink:href="note-0095-01"/>
            b d: </s>
            <s xml:space="preserve">erit quadra
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            tum m t quadra-
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            to p f æquale: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            idcirco linea m t
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            æqualis lmeæ p
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            f. </s>
            <s xml:space="preserve">Itaque quoniam in portionibus æqualibus, & </s>
            <s xml:space="preserve">ſimilibus a p q l, a
              <lb/>
            m o l ductæ ſunt lineæ a q, i o, quæ æquales portiones abſcindunt;
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            </s>
            <s xml:space="preserve">illa quidem ab extremitate baſis; </s>
            <s xml:space="preserve">hæc uero non ab extremitate: </s>
            <s 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:space="preserve">Sed linea p φ li-
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            neæ a q æquidiſtat, & </s>
            <s xml:space="preserve">m n ipſi i o. </s>
            <s xml:space="preserve">angulus igitur ad φ angulo ad n</s>
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