Cardano, Girolamo, De subtilitate, 1663

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            <pb pagenum="369" xlink:href="016/01/018.jpg"/>
            <p type="margin">
              <s id="s.000508">
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              Quomodo
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              pondera fa­
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              cile mouean­
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              tur.</s>
            </p>
            <figure id="id.016.01.018.1.jpg" xlink:href="016/01/018/1.jpg" number="15"/>
            <p type="main">
              <s id="s.000509">Adiecimus hoc, quia pleraque inſtrumen­
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              ta hauriendis aquis idonea, hominum aut
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              iumentorum viribus aguntur. </s>
              <s id="s.000510">Sed etſi ipſa­
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              rum aquarum rapido impetu agitentur ma­
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              chinæ, rurſus addita manubriis pondera fa­
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              ciliorum efficiunt motum. </s>
              <s id="s.000511">Licet itaque ſolo
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              impetu aquarum defluentium, aquas ipſas in
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              ſuprema loca impellere, atque ægros humi­
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              lioribus aquis irrigare. </s>
              <s id="s.000512">Sed hoc tantùm in
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              his quæ decurrunt, & impetum labendo ha­
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              bent. </s>
              <s id="s.000513">Aptetur enim à latere vno Cteſibica,
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              aut Brambilica, aut alterius generis machi­
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              na: nam ( vt dixi ) innumeri poſſunt eſſe
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              modi earum, quanquam hæ omnibus aliis,
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              coclea excepta, ſint elegantiores: & ( vtiam
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              docuimus ) alternus manubrij motus rota
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              cum pinnis agitata perficiatur, ſic fiet vt
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              ſpontè aqua ſeipſam ſurſum impellat: nam­
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              que ars contra ſua inſtituta eam facere co­
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              git. </s>
              <s id="s.000514">Quod exemplum nonnullæ ciuitates quæ
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              editioribus à flumine locis poſitæ ſunt, ſe­
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              quuntur.
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              </s>
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            <p type="margin">
              <s id="s.000515">
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              Quomodo
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              aqua
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              impellat ſur­
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              ſum.</s>
            </p>
            <p type="margin">
              <s id="s.000516">
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              De libra &
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              illius ratio­
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              ne.</s>
            </p>
            <p type="main">
              <s id="s.000517">Poſt hæc videndum eſt de ponderibus
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              quæ in libra conſtituuntur. </s>
              <s id="s.000518">Sit igitur libra,
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              cuius trutina ſit appenſa in A, & finis vbi
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              iunguntur latera lancis B, & lanx CD, &
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              manifeſtum eſt quòd CD mouetur circa B,
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              velut centrum quoddam, quia CD non po­
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              teſt ſeparari ab ipſo B: & ſit angulus ABC,
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              & ABD rectus. </s>
              <s id="s.000519">Dico quòd pondus in C
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              conſtitutum erit grauius, quàm ſi lanx collo­
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              cetur in quocunque alio loco, vt puto quòd
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              conſtitueretur lanx in F. </s>
              <s id="s.000520">Vt autem cognoſ­
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              camus quòd C ſit grauius in eo ſitu, quam
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              in F, neceſſarium eſt vt in æquali tempore
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              moueatur per maius ſpatium verſus cen­
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              trum. </s>
              <s id="s.000521">Videmus enim grauiora pari ratione
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              in reliquis, velociùs ad centrum ferri. </s>
              <s id="s.000522">Quòd
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              autem hoc contingat magis pondere & li­
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              bra in C collocata quàm in F, oſtendo dua­
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              bus rationibus. </s>
              <s id="s.000523">Prima, quòd ſi in aliquo
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              tempore moueatur ex C in E, & ſit arcus
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              CE æqualis FG, quod tardius deſcendet ex
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              F in G, quàm ex C in E, & ita erit leuiùs
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              in F, quàm in C. Secundò, quòd poſito
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              quòd in æquali ſpatio temporis moueretur
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              ex C in E, ex & F in G, adhuc per arcum
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              CE æqualem FG, magis appropinquaret
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              centro quàm per motum factum in arcu
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              FG. </s>
              <s id="s.000524">Ideò ergo duplici ratione magis gra­
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              uabit pondus lance poſita ad perpendicu­
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              lum cum trutina, quàm in quoque alio
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              loco. </s>
            </p>
            <p type="main">
              <s id="s.000525">Primùm igitur ſic declaratur. </s>
              <s id="s.000526">Manife­
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              ſtum eſt in ſtateris, & in his, qui pondera
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              eleuant, quòd quantò magis pondus à tru­
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              tina, eò magis graue videtur: ſed pondus
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              in G diſtat à trutina quantitate BC lineæ,
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              & in F quantitate FP, ſed CB eſt maior FP,
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              ex decimaquinta, tertij elementorum Eu­
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              clidis: igitur lance poſita in C, grauius pon­
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              dus videbitur quàm in F, quod erat primum.
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              </s>
              <s id="s.000527">Ex hac etiam demonſtratione manifeſtum
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              eſt, libram quantò magis diſcendit verſus
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              C ex A, tantò grauiùs pondus reddere, & eò
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              velociùs moueri: at ex C verſus Q, contra­
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              ria ratione pondus reddi leuius, & motum
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              ſegniorem, quod & experimentum docet.
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              </s>
              <s id="s.000528">Secundum verò ſic demonſtratur. </s>
              <s id="s.000529">Quia enim
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              CE eſt æqualis FG, ſumatur CH æqualis
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              CE, eritque æqualis CH ipſi FG, quare re­
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              cta ſubtenſa CH, æqualis rectæ ſubtenſæ
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              FG. </s>
              <s id="s.000530">Igitur ex octaua primi elementorum
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              angulus BFG, æqualis erit angulo BCH. </s>
              <s id="s.000531">Igi­
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              tur ductis ad perpendiculum rectis FL &
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              HK, minor eſt angulus FGL. qui & ipſe
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              eſſet pars coæqualis BFG, ex quinta primi
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              elementorum, angulo KCH. </s>
              <s id="s.000532">Igitur latus
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              HK, maius latere FL: nam rectæ FG & HC
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              æquales fuerunt, & trigoni orthogonij ſeu
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              rectanguli: igitur BN maior OF, & ideo
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              BM maior OP. </s>
              <s id="s.000533">Dum igitur libra mouetur ex
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              C in E pondus deſcendit per BM lineam, ſeu
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              propinquius centro redditur quàm eſſet in
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              C, & dum mouetur per ſpatium arcus FG,
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              deſcenditque per OP, & BM, maior eſt OP.
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              </s>
              <s id="s.000534">Igitur ſuppoſito etiam quod in æquali tem­
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              pore tranſiret ex C in K, & ex F in G, adhuc
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              velociùs deſcendit ex C, quam ex F. </s>
              <s id="s.000535">Igitur
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              grauius eſt in C, quàm in F. </s>
              <s id="s.000536">Ex hoc autem
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              demonſtratur quod dicit Philoſophus, quòd
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              ſi æqualia ſint pondera in F & R, libra ta­
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              men ſpontè redit ad ſitum CD, vbi trutina
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              ſit AB. </s>
              <s id="s.000537">Nec hoc demonſtrat Iordanus, nec
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              intellexit. </s>
              <s id="s.000538">Similiter cur trutina QB poſita,
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              atque infrà libram ipſam, velut accidit con­
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              uerſa libra, vt manu trutinam teneas ſuper­
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              incumbente libra pondus quod iam deſcen­
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              derat tractum ad R, vbi æquale aliud ad
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              conſtitutum in F, vel lances omninò vacuæ
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              ſint, non ſolùm non reuertuntur ad ſitum
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              CD, ſeu perpendiculi, imò magis R deſcen­
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              dit verſus Q & F aſcendit verſus A. vt expe­
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              rimento patet. </s>
              <s id="s.000539">Hoc etiam Iordanus non de­
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              monſtrauit. </s>
              <s id="s.000540">Ariſtoteles dicit hoc contingere,
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              quum trutina eſt ſupra libram, quia angu­
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              lus QBF metæ, maior eſt angulo QBR, Et ſi­
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              militer quum trutina fuerit QB, erit meta
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              AB, & tunc angulus RBA, maior erit angu­
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              lo FBA, ſed maior angulus reddit grauius
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              pondus: igitur dum trutina ſuperius eſt F,
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              erit grauius R, ideo F trahet libram verſus
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              C, & dum fuerit inferius R, erit grauius
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              quàm F, ideo trahet libram verſus
                <expan abbr="q.">que</expan>
              Quòd ſi
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              quis obiiciat, igitur pondus in F, erit gra­
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              uius quàm in C, trutina in A appenſa cuius
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              tamen oppoſitum iam eſt demonſtratum.
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              </s>
              <s id="s.000541">Reſpondemus, quòd latior angulus à meta,
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              facit pondus grauius, quum rectæ fuerint </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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