Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
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            ſimiliter demonſtrabitur totius priſmatis a _K_ grauitatis eſ
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            ſe centrum. </s>
            <s xml:id="echoid-s3539" xml:space="preserve">Simili ratione & </s>
            <s xml:id="echoid-s3540" xml:space="preserve">in aliis priſinatibus illud
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            idem ſacile demonſtrabitur. </s>
            <s xml:id="echoid-s3541" xml:space="preserve">Quo autem pacto in omni
              <lb/>
            figura rectilinea centrum grauitatis inueniatur, do cuimus
              <lb/>
            in commentariis in ſextam propoſitionem Archimedis de
              <lb/>
            quadratura parabolæ.</s>
            <s xml:id="echoid-s3542" xml:space="preserve"/>
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            <s xml:id="echoid-s3543" xml:space="preserve">Sit cylindrus, uel cylindri portio c e cuius axis a b: </s>
            <s xml:id="echoid-s3544" xml:space="preserve">ſece-
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            turq, plano per axem ducto; </s>
            <s xml:id="echoid-s3545" xml:space="preserve">quod ſectionem faciat paral-
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            lelo grammum c d e f: </s>
            <s xml:id="echoid-s3546" xml:space="preserve">& </s>
            <s xml:id="echoid-s3547" xml:space="preserve">diuiſis c f, d e bifariam in punctis
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              <figure xlink:label="fig-0139-01" xlink:href="fig-0139-01a" number="94">
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            g h, per ea ducatur planum baſi æquidiſtans. </s>
            <s xml:id="echoid-s3548" xml:space="preserve">erit ſectio g h
              <lb/>
            circulus, uel ellipſis, centrum habens in axe; </s>
            <s xml:id="echoid-s3549" xml:space="preserve">quod ſit K: </s>
            <s xml:id="echoid-s3550" xml:space="preserve">at-
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              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">4. huius.</note>
            que erunt ex iis, quæ demonſtrauimus, centra grauitatis
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            planorum oppoſitorum puncta a b: </s>
            <s xml:id="echoid-s3551" xml:space="preserve">& </s>
            <s xml:id="echoid-s3552" xml:space="preserve">plani g h ipſum _k_. </s>
            <s xml:id="echoid-s3553" xml:space="preserve">in
              <lb/>
            quo quidem plano eſt centrum grauitatis cylindri, uel cy-
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            lindri portionis. </s>
            <s xml:id="echoid-s3554" xml:space="preserve">Dico punctum K cylindri quoque, uel cy
              <lb/>
            lindri portionis grauitatis centrum eſſe. </s>
            <s xml:id="echoid-s3555" xml:space="preserve">Si enim fieri po-
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            teſt, ſitl centrum: </s>
            <s xml:id="echoid-s3556" xml:space="preserve">ducaturq; </s>
            <s xml:id="echoid-s3557" xml:space="preserve">k l, & </s>
            <s xml:id="echoid-s3558" xml:space="preserve">extra figuram in m pro-
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            ducatur. </s>
            <s xml:id="echoid-s3559" xml:space="preserve">quam uero proportionem habet linea m K ad _k_ </s>
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