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 ...
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="197" xlink:href="015/01/216.jpg"/>
            <p type="margin">
              <s id="id003376">
                <margin.target id="marg621"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003377">Propoſitio centeſima ſeptuageſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id003378">Rationem centri grauitatis declarare.</s>
            </p>
            <p type="main">
              <s id="id003379">Duplicem rationem
                <expan abbr="cẽtri">centri</expan>
              grauitatis inuenit Archimedes, unam
                <lb/>
                <arrow.to.target n="marg622"/>
                <lb/>
              ſuſpenſorum ponderum: alteram ſupernatantium aquæ, in qua­
                <lb/>
              rum utraque ſubtilitatis certè eſt quantum dignum eſt authore illo
                <lb/>
              ingenioſiſsimo, ſicut etiam in elica linea, fructus autem non pro ra­
                <lb/>
              tione laboris, neque enim ab ætate illa uſque nunc inuentus eſt quiſ­
                <lb/>
              quam, qui potuerit docere, nec ille idem quæ nam utilitas ex huiuſ­
                <lb/>
              modi contemplatione haberetur, propterea totum hoc una propo
                <lb/>
              ſitione concluſimus.</s>
            </p>
            <p type="margin">
              <s id="id003380">
                <margin.target id="marg622"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003381">Dico igitur quòd
                <expan abbr="cẽtrum">centrum</expan>
              grauitatis in appenſis æqualibus qua­
                <lb/>
              dratis aut quadrilateris parallelis eſt, ubi ſe interſecant duæ diame­
                <lb/>
              tri. </s>
              <s id="id003382">Et quod in triangulis eſt punctus in quo concurrant tres lineæ,
                <lb/>
              ductę ab angulis ad latera illa per æqualia ſecando. </s>
              <s id="id003383">In quadrilatero
                <lb/>
              autem trapezio centrum grauitatis eſt in puncto lineæ, quæ ſecat
                <lb/>
              ambo latera oppoſita per æqualia, ita ut proportio partis eius li­
                <lb/>
              neæ, quæ intercipitur à minore æquidiſtantium, ad partem quæ in­
                <lb/>
              tercipitur à maiore æquidiſtantium, ſit ueluti dupli maioris æqui­
                <lb/>
              diſtantium cum minore ad duplum minoris æquidiſtantium cum
                <lb/>
              maiore. </s>
              <s id="id003384">Cuiuſcunque portionis à recta linea, & rectanguli coni ſecti­
                <lb/>
              one comprehenſæ, centrum grauitatis diuidit diametrum portio­
                <lb/>
              nis, ita ut pars eius ad uerticem terminata, ſit ad partem eam ſexqui­
                <lb/>
              altera, quæ ad baſim portionis terminatur. </s>
              <s id="id003385">Cuiuslibet fruſti à ſecti­
                <lb/>
              one rectanguli coni ablati, centrum grauitatis eſt in linea recta, quę
                <lb/>
              fruſti exiſtit diametros: qua in quinque partes æquas diuiſa, cen­
                <lb/>
              trum in quinta eius media exiſtit, atque in eo eius puncto quo ipſa
                <lb/>
              quinta ſic diuiditur, ut portio eius propinquior minori baſi fru­
                <lb/>
              ſti ad reliquam eius portionem eam habeat proportionem, quam
                <lb/>
              habet ſolidum, cuius baſis ſit quadratum lineæ illius quæ fruſti ba­
                <lb/>
              ſis maior extiterit.. Altitudo ueró iſtis utriſque ſimul æqualis lineæ
                <lb/>
              quæ dupla ſit minoris baſis fruſti, & baſi maiori eiuſdem, ad ſoli­
                <lb/>
              dum quod baſim habeat quadratum baſis minoris fruſti, altitudi­
                <lb/>
              nem uero iſtis utriſque ſimul æqualem lineæ quæ dupla ſit maioris
                <lb/>
              baſis, & baſi minori. </s>
              <s id="id003386">Et hæc de prima, multa qúe alia pulchra de­
                <lb/>
              clarat Federicus Comandinus, in ſuo libro de Centro grauitatis, ut
                <lb/>
              pote. </s>
              <s id="id003387">Quod cuiuslibet portionis conoidis rectanguli axis à cen­
                <lb/>
              tro grauitatis ita diuiditur ut pars, quæ determinatur ad uerticem
                <lb/>
              reliquæ, quæ ad baſim terminatur dupla ſit, & longè ſubtiliora quę
                <lb/>
              quilibet uidere poterit apud illum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum