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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            culi, uel ellipſes c d, e ſ a b ad circulum, uel ellipſim a b. </s>
            <s xml:id="echoid-s4456" xml:space="preserve">In-
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            telligatur pyramis q baſim habens æqualem tribus rectan
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            gulis a b, e f, c d; </s>
            <s xml:id="echoid-s4457" xml:space="preserve">& </s>
            <s xml:id="echoid-s4458" xml:space="preserve">altitudinem eãdem, quam fruſtum a d.
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            <s xml:id="echoid-s4459" xml:space="preserve">intelligatur etiam conus, uel coni portio q, eadem altitudi
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            ne, cuius baſis ſit tribus circulis, uel tribus ellipſibus a b,
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            e f, c d æqualis. </s>
            <s xml:id="echoid-s4460" xml:space="preserve">poſtremo intelligatur pyramis a l b, cuius
              <lb/>
            baſis ſit rectangulum m n o p, & </s>
            <s xml:id="echoid-s4461" xml:space="preserve">altitudo eadem, quæ fru-
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            ſti: </s>
            <s xml:id="echoid-s4462" xml:space="preserve">itemq, intelligatur conus, uel coni portio a l b, cuius
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            baſis circulus, uel ellipſis circa diametrum a b, & </s>
            <s xml:id="echoid-s4463" xml:space="preserve">eadem al
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            titudo. </s>
            <s xml:id="echoid-s4464" xml:space="preserve">ut igitur rectangula a b, e f, c d ad rectangulum a b,
              <lb/>
              <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">6. 11. duo
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              decimi</note>
            ita pyramis q ad pyramidem a l b; </s>
            <s xml:id="echoid-s4465" xml:space="preserve">& </s>
            <s xml:id="echoid-s4466" xml:space="preserve">ut circuli, uel ellip-
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            ſes a b, e f, c d ad a b circulum, uel ellipſim, ita conus, uel co
              <lb/>
            ni portio q ad conum, uel coni portionem a l b. </s>
            <s xml:id="echoid-s4467" xml:space="preserve">conus
              <lb/>
            igitur, uel coni portio q ad conum, uel coni portionem
              <lb/>
            a l b eſt, ut pyramis q ad pyramidem a l b. </s>
            <s xml:id="echoid-s4468" xml:space="preserve">ſed pyramis
              <lb/>
            a l b ad pyramidem a g b eſt, ut altitudo ad altitudinem, ex
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            20. </s>
            <s xml:id="echoid-s4469" xml:space="preserve">huius: </s>
            <s xml:id="echoid-s4470" xml:space="preserve">& </s>
            <s xml:id="echoid-s4471" xml:space="preserve">ita eſt conus, uel coni portio al b ad conum,
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            uel coni portionem a g b ex 14. </s>
            <s xml:id="echoid-s4472" xml:space="preserve">duodecimi elementorum,
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            & </s>
            <s xml:id="echoid-s4473" xml:space="preserve">ex iis, quæ nos demonſtrauimus in commentariis in un-
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            decimam de conoidibus, & </s>
            <s xml:id="echoid-s4474" xml:space="preserve">ſphæroidibus, propoſitione
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            quarta. </s>
            <s xml:id="echoid-s4475" xml:space="preserve">pyramis autem a g b ad pyramidem c g d propor-
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            tionem habet compoſitam ex proportione baſium & </s>
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            portione altitudinum, ex uigeſima prima huius: </s>
            <s xml:id="echoid-s4477" xml:space="preserve">& </s>
            <s xml:id="echoid-s4478" xml:space="preserve">ſimili-
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            ter conus, uel coni portio a g b a d conum, uel coni portio-
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            nem c g d proportionem habet compoſitã ex eiſdem pro-
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            portionibus, per ea, quæ in dictis commentariis demon-
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            ſtrauimus, propoſitione quinta, & </s>
            <s xml:id="echoid-s4479" xml:space="preserve">ſexta: </s>
            <s xml:id="echoid-s4480" xml:space="preserve">altitudo enim in
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            utriſque eadem eſt, & </s>
            <s xml:id="echoid-s4481" xml:space="preserve">baſes inter ſe ſe eandem habent pro-
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            portionem. </s>
            <s xml:id="echoid-s4482" xml:space="preserve">ergo ut pyramis a g b ad pyramidem c g d, ita
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            eſt conus, uel coni portio a g b ad a g d conum, uel coni
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            portionem: </s>
            <s xml:id="echoid-s4483" xml:space="preserve">& </s>
            <s xml:id="echoid-s4484" xml:space="preserve">per conuerſionẽ rationis, ut pyramis a g b
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            ad fruſtū à pyramide abſciſſum, ita conus uel coni portio
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            a g b ad fruſtum a d. </s>
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