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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ARCHIMEDIS
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          <head xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:space="preserve">Sint duæ portionis ſimiles, contentæ rectis lineis, & </s>
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              <lb/>
            rectangulorum conorum ſectionibus; </s>
            <s xml:space="preserve">a b c quidem ma-
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            ior, cuius diameter b d; </s>
            <s xml:space="preserve">e f c uero minor, cuius diameter
              <lb/>
            fg: </s>
            <s xml:space="preserve">aptenturq; </s>
            <s xml:space="preserve">inter ſeſe, ita ut maior minorem includat
              <lb/>
            & </s>
            <s xml:space="preserve">ſint earum baſes a c, e c in eadem recta linea, ut idẽ
              <lb/>
            punctum c ſit utriuſque terminus: </s>
            <s xml:space="preserve">ſumatur deinde in ſe
              <lb/>
            ctione a b c quodlibet punctum b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur h c. </s>
            <s xml:space="preserve">Di
              <lb/>
            co lineam h c ad partem ſui ipſius, quæ inter c, & </s>
            <s xml:space="preserve">ſe-
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            ctionem e f c interiicitur, eam proportionẽ habere, quam
              <lb/>
            habet a c ad c e.</s>
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          </p>
          <p style="it">
            <s xml:space="preserve">_
              <emph style="sc">Dvcatvr</emph>
            _ b c, quæ tranſibit per f. </s>
            <s xml:space="preserve">quoniam enim portiones
              <lb/>
            ſimiles ſunt, diametri cú baſibus æquales continent angulos. </s>
            <s xml:space="preserve">quare
              <lb/>
            æquidiſtant inter ſe ſe b d, f g: </s>
            <s xml:space="preserve">éſtq; </s>
            <s xml:space="preserve">b d ad a c, ut f g ad e c:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permu-
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              <anchor type="figure" xlink:label="fig-0074-01a" xlink:href="fig-0074-01"/>
            tando b d ad
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            f g, ut a c ad
              <lb/>
            c e: </s>
            <s xml:space="preserve">hoc eſt
              <lb/>
              <anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/>
            ut earum di-
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            midiæ d c ad
              <lb/>
            c g. </s>
            <s xml:space="preserve">ergo ex
              <lb/>
            antecedēti lé
              <lb/>
            mate ſequi-
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            tur lineá b c
              <lb/>
            per punctum
              <lb/>
            f tranſire.
              <lb/>
            </s>
            <s xml:space="preserve">Ducatur præ
              <lb/>
            terea à puncto h ad diametrum b d linea h K, æquidiſtans baſi
              <lb/>
            a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta k c, quæ diametrum f g ſecet in l; </s>
            <s xml:space="preserve">per l ducatur</s>
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