Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
[51. V.]
[52. DEMONSTRATIO SECVNDAE PARTIS.]
[53. COMMENTARIVS.]
[54. DEMONSTRATIO TERTIAE PARTIS.]
[55. COMMENTARIVS.]
[56. DEMONSTRATIO QVARTAE PARTIS.]
[57. DEMONSTRATIO QVINT AE PARTIS.]
[58. FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.]
[59. FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.]
[60. CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.]
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DE IIS QVAE VEH. IN AQVA.
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            m productam per pendicularem eſſe ad ipſam e f, quam
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            quidem ſecet in n.</s>
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              <emph style="sc">D_vcatvr_</emph>
            enim à puncto g linea g o ad rectos angulos ipſi
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            e f, diametrum in o ſecans: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus ab eodem puncto ducatur g p
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            ad diametrum perpendicularis: </s>
            <s xml:space="preserve">ſecet autem ipſa diameter producta
              <lb/>
            lineã e f in q. </s>
            <s xml:space="preserve">erit p b ipſi b q æqualis, ex trigeſimaquinta primi co
              <lb/>
            nicorum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g p pro-
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              <anchor type="figure" xlink:label="fig-0035-01a" xlink:href="fig-0035-01"/>
            portionalis ĩter q p, p o
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            quare quadratũ g p re-
              <lb/>
              <anchor type="note" xlink:label="note-0035-02a" xlink:href="note-0035-02"/>
            ctangulo o p q æquale
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            erit: </s>
            <s xml:space="preserve">ſed etiã æquale est
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            rectangulo cõtento ipſa
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            p b, & </s>
            <s xml:space="preserve">linea, iuxta quã
              <lb/>
            poſſunt, quæ à ſectione
              <lb/>
            ad diametrũ ordinatim
              <lb/>
            ducuntur, ex undecima
              <lb/>
            primi conicorum. </s>
            <s xml:space="preserve">ergo
              <lb/>
              <anchor type="note" xlink:label="note-0035-03a" xlink:href="note-0035-03"/>
            quæ est proportio q p
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            ad p b eadem est lineæ,
              <lb/>
            iuxta quã poſſunt, quæ
              <lb/>
            à ſectione ducũtur ad ip
              <lb/>
            ſam p o: </s>
            <s xml:space="preserve">est autem q p
              <lb/>
            dupla p b: </s>
            <s xml:space="preserve">cũ ſint p b,
              <lb/>
            b q æquales, ut dictum
              <lb/>
            est. </s>
            <s xml:space="preserve">Linea igitur iuxta
              <lb/>
            quam poſſunt, quæ à ſe-
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            ctione ducuntur ipſi-
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            us p o dupla erit: </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            propterea p o æqualis
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            ei, quæ uſque ad axem,
              <lb/>
            uidelicet ipſi k h: </s>
            <s xml:space="preserve">ſed eſt p g æqualis k m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">angulus o p g angu-
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            lo h k m; </s>
            <s xml:space="preserve">quòd uterque rectus. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">o g ipſi h m est œqualis:
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            </s>
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              <anchor type="note" xlink:label="note-0035-05a" xlink:href="note-0035-05"/>
            & </s>
            <s xml:space="preserve">angulus p o g angulo _k_ h m. </s>
            <s xml:space="preserve">æquidistantes igitur ſunt o g, h n:
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              <anchor type="note" xlink:label="note-0035-06a" xlink:href="note-0035-06"/>
            </s>
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