Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
[31. LEMMAI.]
[32. LEMMA II.]
[33. LEMMA III.]
[34. LEMMA IIII.]
[35. PROPOSITIO VII.]
[36. PROPOSITIO VIII.]
[37. COMMENTARIVS.]
[38. PROPOSITIO IX.]
[39. COMMENTARIVS.]
[40. PROPOSITIO X.]
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ARCHIMEDIS
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            <s xml:space="preserve">
              <pb file="0018" n="18" rhead="ARCHIMEDIS"/>
            extet ex humidi ſuperficie. </s>
            <s xml:space="preserve">conſiſtat autem humidum, ma
              <lb/>
            neatq;</s>
            <s xml:space="preserve">: & </s>
            <s xml:space="preserve">intelligatur aliquod planum ductum per centrũ
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            terræ, per humidum, & </s>
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              <lb/>
              <anchor type="figure" xlink:label="fig-0018-01a" xlink:href="fig-0018-01"/>
            per magnitudinem ſoli-
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            dam: </s>
            <s xml:space="preserve">à quo ſuperficies
              <lb/>
            quidem humidi ſecetur
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            ſecundum circunferen-
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            tiam a b c; </s>
            <s xml:space="preserve">ſolida autem
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            magnitudo ſecundum fi
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            guram, in qua r: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cen-
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            trum terræ ſit K. </s>
            <s xml:space="preserve">Intelli
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            gatur etiam quædam py
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            ramis comprehendens
              <lb/>
            figuram r, ſicuti prius, quæ pũctum K pro uertice habeat:
              <lb/>
            </s>
            <s xml:space="preserve">fecenturq; </s>
            <s xml:space="preserve">ipſius plana à ſuperficie plani a b c ſecundum
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            a K K b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſumatur pyramis alia æ qualis, & </s>
            <s xml:space="preserve">ſimilis ſuperio
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            ri, cuius plana ſecentur à plano a b c, ſecundum b K K c: </s>
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              <lb/>
            deinde alterius ſphæræ ſuperficies quædam deſcribatur in
              <lb/>
            humido circa centrum K, ſub ſolida magnitudine: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſece-
              <lb/>
            tur ab eodem plano ſecundum x o p: </s>
            <s xml:space="preserve">poſtremo intelliga-
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            tur alia magnitudo h in poſteriori pyramide, quæ ex humi
              <lb/>
            do conſtet, & </s>
            <s xml:space="preserve">ſolidæ magnitudini r ſit æ qualis. </s>
            <s xml:space="preserve">partes igi-
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            tur humidi, & </s>
            <s xml:space="preserve">quæ in prima pyramide continetur ſuperfi-
              <lb/>
            cie x o; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ in ſecunda ſuperficie o p continetur, æquali
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            ter iacent, & </s>
            <s xml:space="preserve">continuatæ inter ſe ſe; </s>
            <s xml:space="preserve">non tamen ſimiliter
              <lb/>
            premuntur: </s>
            <s xml:space="preserve">nam quæ eſt in prima pyramide premitur ma
              <lb/>
            gnitudine ſolida r, & </s>
            <s xml:space="preserve">humido cõtinente ipſam, quod eſt in
              <lb/>
            loco pyramidis a b o x: </s>
            <s xml:space="preserve">quæ uero in altera pyramide pre-
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            mitur ſolida magnitudineh, & </s>
            <s xml:space="preserve">humido ipſam continente
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            in loco pyramidis p o b c. </s>
            <s xml:space="preserve">At grauitas ſolidæ magnitudi-
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            nis r, minor eſt grauitate humidi, in quo h: </s>
            <s xml:space="preserve">quoniam ma-
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            gnitudo ſolida mole quidem æqualis, & </s>
            <s xml:space="preserve">humido leuior po
              <lb/>
            nitur: </s>
            <s xml:space="preserve">grauitas autem humidi continentis magnitudines
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            r h eſt æqualis; </s>
            <s xml:space="preserve">cum pyramides æquales ſint. </s>
            <s xml:space="preserve">magis ergo</s>
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