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 CENTRO GRAVIT. SOLID.
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              <pb o="14" file="0139" n="139" rhead="DE CENTRO GRAVIT. SOLID."/>
            ſimiliter demonſtrabitur totius priſmatis a _K_ grauitatis eſ
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            ſe centrum. </s>
            <s xml:space="preserve">Simili ratione & </s>
            <s xml:space="preserve">in aliis priſinatibus illud
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            idem ſacile demonſtrabitur. </s>
            <s xml:space="preserve">Quo autem pacto in omni
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            figura rectilinea centrum grauitatis inueniatur, do cuimus
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            in commentariis in ſextam propoſitionem Archimedis de
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            quadratura parabolæ.</s>
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            <figure xlink:label="fig-0138-01" xlink:href="fig-0138-01a">
              <image file="0138-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0138-01"/>
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            <s xml:space="preserve">Sit cylindrus, uel cylindri portio c e cuius axis a b: </s>
            <s xml:space="preserve">ſece-
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            turq, plano per axem ducto; </s>
            <s xml:space="preserve">quod ſectionem faciat paral-
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            lelo grammum c d e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">diuiſis c f, d e bifariam in punctis
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              <anchor type="figure" xlink:label="fig-0139-01a" xlink:href="fig-0139-01"/>
            g h, per ea ducatur planum baſi æquidiſtans. </s>
            <s xml:space="preserve">erit ſectio g h
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            circulus, uel ellipſis, centrum habens in axe; </s>
            <s xml:space="preserve">quod ſit K: </s>
            <s xml:space="preserve">at-
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              <anchor type="note" xlink:label="note-0139-01a" xlink:href="note-0139-01"/>
            que erunt ex iis, quæ demonſtrauimus, centra grauitatis
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            planorum oppoſitorum puncta a b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">plani g h ipſum _k_. </s>
            <s xml:space="preserve">in
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            quo quidem plano eſt centrum grauitatis cylindri, uel cy-
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            lindri portionis. </s>
            <s xml:space="preserve">Dico punctum K cylindri quoque, uel cy
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            lindri portionis grauitatis centrum eſſe. </s>
            <s xml:space="preserve">Si enim fieri po-
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            teſt, ſitl centrum: </s>
            <s xml:space="preserve">ducaturq; </s>
            <s xml:space="preserve">k l, & </s>
            <s xml:space="preserve">extra figuram in m pro-
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            ducatur. </s>
            <s xml:space="preserve">quam uero proportionem habet linea m K ad _k_ l</s>
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