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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              <pb file="0156" n="156" rhead="FED. COMMANDINI"/>
            mus: </s>
            <s xml:space="preserve">erit utique grauitatis centrum pyramidis punctum
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            g: </s>
            <s xml:space="preserve">in quo ſcilicet ipſi axes conueniunt.</s>
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        <div type="section" level="1" n="83">
          <head xml:space="preserve">THEOREMA XIIII. PROPOSITIO XVIII.</head>
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              <emph style="sc">Si</emph>
            ſolidum parallelepipedum ſecetur plano
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            baſibus æquidiſtante; </s>
            <s xml:space="preserve">erit ſolidum ad ſolidum,
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            ſicut altitudo ad altitudinem, uel ſicut axisad
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            axem.</s>
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          <p>
            <s xml:space="preserve">Sit ſolidum parallelepipe
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              <anchor type="figure" xlink:label="fig-0156-01a" xlink:href="fig-0156-01"/>
            dum a b c d e f g h, cuius axis
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            k 1: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">plano baſibus
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            æquidiſtante, quod faciat
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            fectionem m n o p; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axi in
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            puncto q occurrat. </s>
            <s xml:space="preserve">Dico
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            ſolidum g m ad ſolidum m c
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            eam proportionem habere,
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            quam altitudo ſolidi g m ha-
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            betad ſolidi m c altitudi-
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            nem; </s>
            <s xml:space="preserve">uel quam axis k q ad
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            axem q l. </s>
            <s xml:space="preserve">Sienim axis K l ad
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            baſis planum ſit perpendicu
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            laris, & </s>
            <s xml:space="preserve">linea g c, quæ ex quin
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            ta huius ipſi k l æquidiſtat,
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            perpendicularis erit ad idẽ
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            planum, & </s>
            <s xml:space="preserve">ſolidi altitudi-
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            nem dimetietur. </s>
            <s xml:space="preserve">Itaqueſo-
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              <anchor type="note" xlink:label="note-0156-01a" xlink:href="note-0156-01"/>
            lidum g m ad ſolidum m c
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            eam proportionem habet,
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            quam parallelogrammũ g n
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            ad parallelogrammum n c,
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            hoc eſt quam linea g o, quæ
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              <anchor type="note" xlink:label="note-0156-02a" xlink:href="note-0156-02"/>
            </s>
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