Clavius, Christoph, In Sphaeram Ioannis de Sacro Bosco commentarius

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            <s xml:id="echoid-s5476" xml:space="preserve">
              <pb o="116" file="152" n="153" rhead="Comment. in I. Cap. Sphæræ"/>
            rarum. </s>
            <s xml:id="echoid-s5477" xml:space="preserve">Vnde uidemus guttulas aquarum, ſi amittant figuram ſphæricam, cito
              <lb/>
            ac facile corrumpi, atque exiccari.</s>
            <s xml:id="echoid-s5478" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Ratio Ari-
            <lb/>
          ſtotelis pro
            <lb/>
          bans aquã
            <lb/>
          eſſe rotun
            <lb/>
          dam.</note>
          <p>
            <s xml:id="echoid-s5479" xml:space="preserve">
              <emph style="sc">Dvabvs</emph>
            his rationibus addere poſſumus aliam, quam etiam Ariſtoteles
              <lb/>
            affert lib. </s>
            <s xml:id="echoid-s5480" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5481" xml:space="preserve">de cœlo, hoc modo. </s>
            <s xml:id="echoid-s5482" xml:space="preserve">Aqua ſuapte natura confluit ad loca decli-
              <lb/>
            uiora, utexperiẽtia didicimus quotidianatigitur ro
              <lb/>
              <figure xlink:label="fig-152-01" xlink:href="fig-152-01a" number="46">
                <image file="152-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/152-01"/>
              </figure>
            tunda exiſtit. </s>
            <s xml:id="echoid-s5483" xml:space="preserve">Nam alias non conflueret ad loca de-
              <lb/>
            cliuiora. </s>
            <s xml:id="echoid-s5484" xml:space="preserve">Sit enim aquæ ſuperficies, ſi fieri poteſt,
              <lb/>
            plana, uel alterius figuræ non circularis, expanſa ſu-
              <lb/>
            per terrã per lineã A D B, & </s>
            <s xml:id="echoid-s5485" xml:space="preserve">ex centro mundi C, de-
              <lb/>
            ſcribatur circulus E G F; </s>
            <s xml:id="echoid-s5486" xml:space="preserve">& </s>
            <s xml:id="echoid-s5487" xml:space="preserve">ex C, educatur C D, per
              <lb/>
            pendicularis ad A B; </s>
            <s xml:id="echoid-s5488" xml:space="preserve">cõnectanturq́; </s>
            <s xml:id="echoid-s5489" xml:space="preserve">rectæ A C, B C:
              <lb/>
            </s>
            <s xml:id="echoid-s5490" xml:space="preserve">Et quoniã recta C D, minor eſt, quàm C A, vel C B,
              <lb/>
              <note position="left" xlink:label="note-152-02" xlink:href="note-152-02a" xml:space="preserve">19. primi.</note>
            erit punctum D, in loco decliuiori, hoc eſt, propin-
              <lb/>
            quius centro, quã punctum A, uel B. </s>
            <s xml:id="echoid-s5491" xml:space="preserve">A qua igitur nõ
              <lb/>
            impedita non confluet ad loca decliuiora. </s>
            <s xml:id="echoid-s5492" xml:space="preserve">Quod cũ
              <lb/>
            pugnet cum experientia, neceſſe eſt, ut pars aquæ media, nempe D, attollatut
              <lb/>
            ad punctũ G, & </s>
            <s xml:id="echoid-s5493" xml:space="preserve">partes aquæ iuxta A, & </s>
            <s xml:id="echoid-s5494" xml:space="preserve">B, deſidant, perueniantq́ue ad puncta E,
              <lb/>
            & </s>
            <s xml:id="echoid-s5495" xml:space="preserve">F, ut tota aqua habe at tumorem E G F, æqualiterq́; </s>
            <s xml:id="echoid-s5496" xml:space="preserve">diſtet à centro mundi.
              <lb/>
            </s>
            <s xml:id="echoid-s5497" xml:space="preserve">Hac enim ratione naturaliter quieſcet collibrata. </s>
            <s xml:id="echoid-s5498" xml:space="preserve">Ex qua quidem ratione pro-
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            babitur, nullam aliam figurã poſle habere aquã præter ſphæricam: </s>
            <s xml:id="echoid-s5499" xml:space="preserve">nã alias ſem
              <lb/>
            per haberet aliquas partes remotiores aterræ centro, (Sp hærica enim tantum
              <lb/>
            figura æqualiter undique propinquat centro) & </s>
            <s xml:id="echoid-s5500" xml:space="preserve">ex conſequenti non deflueret
              <lb/>
            ad loca decliuiora, quod pugnat cum natura aquæ. </s>
            <s xml:id="echoid-s5501" xml:space="preserve">Immoex hac ratione effi-
              <lb/>
            citur, quemlibet liquorem in aliquo uaſe contentum habere tumorem aliquẽ,
              <lb/>
            ſeu circuferentiam, cuius centrum idem eſt, quod centrum mundi.</s>
            <s xml:id="echoid-s5502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5503" xml:space="preserve">
              <emph style="sc">Sed</emph>
            omnium elegantiſſima eſt demonſtratio Archimedis in lib. </s>
            <s xml:id="echoid-s5504" xml:space="preserve">1. </s>
            <s xml:id="echoid-s5505" xml:space="preserve">de ijs.
              <lb/>
            </s>
            <s xml:id="echoid-s5506" xml:space="preserve">
              <note position="left" xlink:label="note-152-03" xlink:href="note-152-03a" xml:space="preserve">Archime-
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              dis demon
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              ſtratio pro-
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              bans omne
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              liquorem
                <lb/>
              ſphæricam
                <lb/>
              figuram ha
                <lb/>
              bere.</note>
            quæ uehuntur in aqua, qua demonſtrat, non ſolum Oceanum, & </s>
            <s xml:id="echoid-s5507" xml:space="preserve">alia maria, ve
              <lb/>
            rũ etiam quemlibet humorem conſiſtentem, ac manentem, ſigurã habere ſphæ
              <lb/>
            ricam, cuius centrum ſit idem, quod centrum mundi, ad quod omnia grauia fe
              <lb/>
            funtur ſuapte natura. </s>
            <s xml:id="echoid-s5508" xml:space="preserve">Aſſ
              <unsure/>
            umit autem primum, humidieam eſſe naturam, ut par
              <lb/>
            tibus ipſius æqualiter iacentibus, & </s>
            <s xml:id="echoid-s5509" xml:space="preserve">continuatis interſeſe, minus preſſa a ma-
              <lb/>
            gis preſſa expellatur. </s>
            <s xml:id="echoid-s5510" xml:space="preserve">Vnamquam que uero partẽ eius premi humido ſupra ip-
              <lb/>
            ſam exiſtente ad perpendiculũ, ſi humidũ ſit deſcendens in aliquo, aut ab alio
              <lb/>
            aliquo preſſum. </s>
            <s xml:id="echoid-s5511" xml:space="preserve">Id quod experientia verũ eſſe didicimus: </s>
            <s xml:id="echoid-s5512" xml:space="preserve">quandocunque enim
              <lb/>
            liquorẽ aliqua in parte premimus uel manu, uel alio ſuperfuſo humore, cedũt
              <lb/>
            aliæ partes circunſtantes, atq; </s>
            <s xml:id="echoid-s5513" xml:space="preserve">expelluntur. </s>
            <s xml:id="echoid-s5514" xml:space="preserve">Deinde demonſtrat, ſi ſuperficies
              <lb/>
            aliqua plano ſecetur per idem ſemper punctum, ſitq́ ſectio circuli circunferem-
              <lb/>
            tia centrum habens punctum illud, per quod plano ſecatur, ſuperficiem illam
              <lb/>
            eſſe ſphæ icam, cuius centrum idem illud punctum ſit. </s>
            <s xml:id="echoid-s5515" xml:space="preserve">Demonſtratio huius rei
              <lb/>
            eruſmodi eſt. </s>
            <s xml:id="echoid-s5516" xml:space="preserve">Secetur ſuperficies aliqua plano per A, punctum ducto, ſitq́ue ſe-
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            ctio ſemper circuli circun ferentia centrum habens punctum A. </s>
            <s xml:id="echoid-s5517" xml:space="preserve">Dico eam ſu-
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            perficiem eſſe ſphæricam, cuius centrum A, hoc eſt, omnes lineas à puncto A,
              <lb/>
            ad illam ſuperficiem ductas inter ſe eſſe æquales. </s>
            <s xml:id="echoid-s5518" xml:space="preserve">Ducantur enim ex A, ad ſu-
              <lb/>
            perficiem duæ lineæ rectæ utcunque A B, A C, ut in prima figura: </s>
            <s xml:id="echoid-s5519" xml:space="preserve">per quas,
              <lb/>
            cum ſint in eodem plano, ducatur planum faciens in ſuperficie propoſita li-
              <lb/>
              <note position="left" xlink:label="note-152-04" xlink:href="note-152-04a" xml:space="preserve">2. vndec.</note>
            neam B C, quæ ex hypotheſi circunferentia circuli erit. </s>
            <s xml:id="echoid-s5520" xml:space="preserve">Recta igitur A C,
              <lb/>
            rectæ A B, per defin. </s>
            <s xml:id="echoid-s5521" xml:space="preserve">circuli, æqualis erit. </s>
            <s xml:id="echoid-s5522" xml:space="preserve">Eadem ratione oſtendemus, omnes
              <lb/>
            alias lineas rectas a puncto A, ad ſuperficiem propoſitam ductas rectæ A </s>
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