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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          <p>
            <s xml:space="preserve">
              <pb file="0092" n="92" rhead="ARCHIMEDIS"/>
            quia o g ipſius g x eſt dupla. </s>
            <s xml:space="preserve">Sit p h dupla h t: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iun-
              <lb/>
            cta h κ ad ω producatur. </s>
            <s xml:space="preserve">erit totius quidem portionis cen
              <lb/>
            trum grauitatis k; </s>
            <s xml:space="preserve">partis eius, quæ intra humidum h; </s>
            <s xml:space="preserve">eius
              <lb/>
            uero, quæ extra humidum in linea κ ω, quod ſit ω. </s>
            <s xml:space="preserve">Itaque
              <lb/>
            demonſtrabitur
              <lb/>
              <anchor type="figure" xlink:label="fig-0092-01a" xlink:href="fig-0092-01"/>
            ſimiliter & </s>
            <s xml:space="preserve">k z ad
              <lb/>
            humidi ſuperſi-
              <lb/>
            ciem perpẽdicu-
              <lb/>
            laris, & </s>
            <s xml:space="preserve">quæ per
              <lb/>
            puncta h ω æqui-
              <lb/>
            diſtantes ipſi κ z
              <lb/>
            ducuntur. </s>
            <s xml:space="preserve">quare
              <lb/>
            nõ manebit por
              <lb/>
            tio, ſed inclinabi
              <lb/>
            tur, donec baſis
              <lb/>
            ipſius in uno pũ
              <lb/>
            cto contingat ſu
              <lb/>
            perficiem humi-
              <lb/>
            di: </s>
            <s xml:space="preserve">atque ita con
              <lb/>
            ſiſtet. </s>
            <s xml:space="preserve">nam in por
              <lb/>
            tionibus æquali-
              <lb/>
            bus a o q l, a p m l, ductæ erunt ab extremitatibus baſium
              <lb/>
            a q, a m, quæ æquales portiones abſcindunt: </s>
            <s xml:space="preserve">etenim a o q
              <lb/>
            ipſi a p m, utin ſuperioribus æqualis demonſtrabitur. </s>
            <s xml:space="preserve">ergo
              <lb/>
              <anchor type="note" xlink:label="note-0092-01a" xlink:href="note-0092-01"/>
            æquales faciunt acutos angulos a q, a m cum diametris ba
              <lb/>
            ſium: </s>
            <s xml:space="preserve">quòd anguli ad χ & </s>
            <s xml:space="preserve">n æquales ſint. </s>
            <s xml:space="preserve">quare ſi ducta
              <lb/>
            h k ad ω producatur, erit totius portionis grauitatis cen-
              <lb/>
            trum k; </s>
            <s xml:space="preserve">partis eius, quæ in humido h; </s>
            <s xml:space="preserve">at eius, quæ extra
              <lb/>
            humidum in linea h κ; </s>
            <s xml:space="preserve">quod ſit ω: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">h k ad humidi ſuper-
              <lb/>
            ficiem perpendicularis. </s>
            <s xml:space="preserve">per eaſdem igitur rectas lineas,
              <lb/>
            quod quidem in humido eſt, ſurſum, & </s>
            <s xml:space="preserve">quod extra humi-
              <lb/>
            dum deorſum feretur. </s>
            <s xml:space="preserve">quare manebit portio, cuius baſis
              <lb/>
            humidi ſuperficiem in uno puncto continget: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis cum
              <lb/>
            ipſa angulum faciet æqualem angulo χ. </s>
            <s xml:space="preserve">Similiter demon-
              <lb/>
              <anchor type="note" xlink:label="note-0092-02a" xlink:href="note-0092-02"/>
            </s>
          </p>
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