Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
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FED. COMMANDINI
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            in linea e b punctũ g, it aut ſit g e æqualis e f. </s>
            <s xml:space="preserve">erit g por-
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            tionis a b c centrum. </s>
            <s xml:space="preserve">nam ſi hæ portiones, quæ æquales
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            & </s>
            <s xml:space="preserve">ſimiles ſunt, inter ſe ſe aptentur, ita ut b e cadat in d e,
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            & </s>
            <s xml:space="preserve">punctum b in d cadet, & </s>
            <s xml:space="preserve">g in f: </s>
            <s xml:space="preserve">figuris autem æquali-
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            bus, & </s>
            <s xml:space="preserve">ſimilibus inter ſe aptatis, centra quoque grauitatis
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            ipſarum inter ſe aptata erunt, ex quinta petitione Archi-
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            medis in libro de centro grauitatis planorum. </s>
            <s xml:space="preserve">Quare cum
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            portionis a d c centrum grauitatis ſit ſ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portionis
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            a b c centrum g: </s>
            <s xml:space="preserve">magnitudinis; </s>
            <s xml:space="preserve">quæ ex utriſque efficitur:
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            </s>
            <s xml:space="preserve">hoc eſt circuli uel ellipſis grauitatis centrum in medio li-
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            neæ f g, quod eſt e, conſiſtet, ex quarta propoſitione eiuſ-
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            dem libri Archimedis. </s>
            <s xml:space="preserve">ergo circuli, uel ellipſis centrum
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            grauitatis eſt idem, quod figuræ centrum. </s>
            <s xml:space="preserve">atque illud eſt,
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            quod demonſtrare oportebat.</s>
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            <figure xlink:label="fig-0123-02" xlink:href="fig-0123-02a">
              <image file="0123-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0123-02"/>
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            <s xml:space="preserve">Ex quibus ſequitur portionis circuli, uel ellip-
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            ſis, quæ dimidia maior ſit, centrum grauitatis in
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            diametro quoque ipſius conſiſtere.</s>
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          <figure>
            <image file="0124-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0124-01"/>
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            <s xml:space="preserve">Sit enim maior portio a b c, cu_i_us diameter b d, & </s>
            <s xml:space="preserve">com-
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            pleatur circulus, uel ellipſis, ut portio reliqua ſit a e c, dia</s>
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