Cardano, Geronimo, Opvs novvm de proportionibvs nvmerorvm, motvvm, pondervm, sonorvm, aliarvmqv'e rervm mensurandarum, non solùm geometrico more stabilitum, sed etiam uarijs experimentis & observationibus rerum in natura, solerti demonstratione illustratum, ad multiplices usus accommodatum, & in V libros digestum. Praeterea Artis Magnae, sive de regvlis algebraicis, liber vnvs abstrvsissimvs & inexhaustus planetotius Ariothmeticae thesaurus ... Item De Aliza Regvla Liber, hoc est, algebraicae logisticae suae, numeros recondita numerandi subtilitate, secundum Geometricas quantitates inquirentis ...

List of thumbnails

< >
131
131 		132
132
133
133 		134
134
135
135 		136
136
137
137 		138
138
139
139 		140
140
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id003746">
                <pb pagenum="222" xlink:href="015/01/241.jpg"/>
              c d quantum a b per primum ſuppoſitum. </s>
              <s id="id003747">Sed quoniam proposi­
                <lb/>
              to circulo alio non circa idem centrum, utpote k l reuoluetur &
                <lb/>
              perueniet ad h ex demonſtratis. </s>
              <s id="id003748">
                <expan abbr="Reſpondet̃">Reſpondetur</expan>
              ad hoc, quod idem eſt,
                <lb/>
              quia unus circulus tantum per ſe mouetur circa centrum, reliqui
                <lb/>
              omnes non perſe circa centrum, ſed ab alio circulo primo mouen­
                <lb/>
              tur, ideò nihil refert ſeu ſint circa idem centrum ſeu circa aliud, hoc
                <lb/>
              enim fortuitum eſt. </s>
              <s id="id003749">Ideo ad argumentum reſpondent cauilloſam
                <lb/>
              eſſe
                <expan abbr="hãc">hanc</expan>
              diſputationem, cum ſupponat idem ambobus circulis per
                <lb/>
              ſe centrum eſſe. </s>
              <s id="id003750">Sed non eſt perſe, uerùm per
                <expan abbr="accidẽs">accidens</expan>
              . </s>
              <s id="id003751">At tamen de­
                <lb/>
              miror de huiuſmodi ſolutione. </s>
              <s id="id003752">Primum quod ipſemet. </s>
              <s id="id003753">Ariſtoteles
                <lb/>
              de hoc nos docuit in primo Poſteriorum dicens. </s>
              <s id="id003754">Non eſt igitur ex
                <lb/>
              uno in aliud genus
                <expan abbr="tranſcẽdentem">tranſcendentem</expan>
              demonſtrare, ut Geometricum
                <lb/>
              Arithmetica. </s>
              <s id="id003755">Et
                <expan abbr="Auerroẽs">Auerroens</expan>
              in Commento magno inquit, ea uerba
                <lb/>
              exponens. </s>
              <s id="id003756">Fieri non poteſt, ut demonſtratio transferatur de
                <lb/>
              arte in artem. </s>
              <s id="id003757">Et ibidem docet, quod neque ut ambæ præmiſ­
                <lb/>
              ſæ ſint communes, neque etiam maior tantum, ſicut exponebat Al­
                <lb/>
              pharabices. </s>
              <s id="id003758">Verùm dicit, ſolum licet in artibus, quæ ſunt in com­
                <lb/>
              paratione generis ad ſpeciem, ut ſit concluſio ueluti phyſica ma­
                <lb/>
              ior propoſitio, in ſubiecta ſcientia ueluti medicina. </s>
              <s id="id003759">Vnde
                <expan abbr="cõcludit">concludit</expan>
                <lb/>
              Philoſophus. </s>
              <s id="id003760">Propter hoc Geometrię non licet demonſtrare quod
                <lb/>
              contrariorum una eſt ſcientia: ſed neque quod duo cubi cubus, neque
                <lb/>
              alij ſcientiæ quod alterius: niſi in his quæ ita inter ſe habent ut alte­
                <lb/>
              ra ſub altera ſit, ueluti perſpectiua ad Geometricam, & harmonica
                <lb/>
              ad
                <expan abbr="Arithmeticã">Arithmeticam</expan>
              . </s>
              <s id="id003761">Et poſt docet quod etiam non licet demonſtrare ex
                <lb/>
              communibus: hæc igitur ratio eſt ex alienis genere atque communi­
                <lb/>
              bus. </s>
              <s id="id003762">Quid, quòd non ſoluit difficultatem quę mathematica tota eſt
                <lb/>
              & innititur manifeſtis principijs. </s>
              <s id="id003763">Debuit enim oſten dere quomo­
                <lb/>
              do tardius moueatur circulus maior ipſo minore: hoc enim eſt ne­
                <lb/>
              ceſſe ſi eodem tempore debent æqualia ſpatia pertranſire. </s>
              <s id="id003764">Accipia­
                <lb/>
              mus ergo quod manifeſtum eſt, ſcilicet uectionem eſſe hanc in qua
                <lb/>
              e centrum perpetuò per æquidiſtantem lineam fertur in m, nullum
                <lb/>
              autem circulum progreſſus centri eſſe cauſam niſi ut rota mouet
                <lb/>
              currum & currus axem, reuolutio ergo notæ efficit ut ſpatium c g
                <lb/>
              pertranſeat nota, & ideo motus ille circularis non eſt, quia circula­
                <lb/>
              ris motus fit manente centro, ſed eſt circulus progrediens uelut &
                <lb/>
              punctum e: at in circulo, hoc eſt diſcrimen quòd puncta, uariantur
                <lb/>
              centrum autem non. </s>
              <s id="id003765">Dico ergo ut melius intelligas quòd talis mo­
                <lb/>
              tus eſt uelut famulorum fabrorum qui rotam circunducant
                <expan abbr="domũ">domum</expan>
                <lb/>
              impellentes, talis enim motus, eſt rectus, & eſt impulſionis non au­
                <lb/>
              tem circularis. </s>
              <s id="id003766">Et ideò omnia puncta æqualiter mouentur, & per
                <lb/>
              æquale ſpatium, accidit autem ut hic motus fiat circunuertendo, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum