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 concordance

< >
Scan Original
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="63" xlink:href="015/01/082.jpg"/>
            <p type="main">
              <s id="id001203">Propoſitio ſeptuageſima prima.</s>
            </p>
            <p type="main">
              <s id="id001204">Proportionem leuitatis ponderis per uirgam torcularem attra­
                <lb/>
              cti ad rectam ſuſpenſionem inuenire.</s>
            </p>
            <figure id="id.015.01.082.1.jpg" xlink:href="015/01/082/1.jpg" number="78"/>
            <p type="main">
              <s id="id001205">Sit torcularis uirga, cuius ſpiræ a b per circui­
                <lb/>
                <arrow.to.target n="marg252"/>
                <lb/>
              tum ſint centuplæ ad altitudinem a b, & axis d c
                <lb/>
                <arrow.to.target n="marg253"/>
                <lb/>
              ſemidiametro b c centupla, & quoniam per ſupe­
                <lb/>
              rius aſſumpta, qualis eſt proportio ſpatij ad ſpa­
                <lb/>
              tium, talis leuitatis ad
                <expan abbr="leuitatẽ">leuitatem</expan>
              ,
                <expan abbr="igit̃">igitur</expan>
              e pondus aſcen
                <lb/>
              dens per a b leuius quam per b
                <expan abbr="crectã">c rectam</expan>
              centuplo, et
                <lb/>
              ſimiliter cum circuitus b c, & d c ſint in eodem tem
                <lb/>
              pore, & circuitus d c, ſit centuplus ad ſpiralem b c
                <lb/>
              per demonſtrata ab Euclide, ergo e erit centuplo
                <lb/>
              leuius circum ductum per d quàm b, ſed per b circumductum cen­
                <lb/>
              tuplo leuius eſt, quàm per rectam, igitur e ponderat ſolum particu­
                <lb/>
              lam ex decem millibus recti ponderis.</s>
            </p>
            <p type="margin">
              <s id="id001206">
                <margin.target id="marg252"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              m.</s>
            </p>
            <p type="margin">
              <s id="id001207">
                <margin.target id="marg253"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              45.</s>
            </p>
            <p type="main">
              <s id="id001208">Propoſitio ſeptuageſima ſecunda.</s>
            </p>
            <p type="main">
              <s id="id001209">Proportionem ponderis ſphęræ pendentis ad aſcendentem per
                <lb/>
              accliue planum inuenire</s>
            </p>
            <figure id="id.015.01.082.2.jpg" xlink:href="015/01/082/2.jpg" number="79"/>
            <p type="main">
              <s id="id001210">Sit ſphæra æqualis ponderi g in pun­
                <lb/>
                <arrow.to.target n="marg254"/>
                <lb/>
              cto b, quæ debeat trahi ſuper b c accli­
                <lb/>
              ue planum b e ad perpendiculum pla­
                <lb/>
                <arrow.to.target n="marg255"/>
                <lb/>
              ni b f. </s>
              <s id="id001211">Quia ergo in b e mouetur a, qua­
                <lb/>
              uis modica ui per dicta ſuperius, erit per
                <lb/>
              communem animi ſententiam uis, quæ
                <lb/>
              mouebit a per e b nulla: per dicta uerò
                <lb/>
              a mouebitur ad f ſemper, a conſtanti ui
                <lb/>
              æquali g, & per b c a conſtanti ui æqua­
                <lb/>
              li k, ſicut per b d a conſtanti æquali h, ergo per ultimam petitio­
                <lb/>
              nem, cum termini ſeruent, quo ad partes eandem rationem ſin­
                <lb/>
              guli per ſe, & motus per b e ſit a nulla ui, erit proportio g ad k, ue­
                <lb/>
              lut proportio uis, quæ mouet per b f ad uim, quæ mouet per
                <lb/>
              b c, & uelut anguli per e b f recti ad angulum e b c, & ita uis,
                <lb/>
              quæ mouet a per b f, & eſt, ut dictum eſt, g ad uim, quæ mouet
                <lb/>
              per b d, & eſt h ex ſuppoſito, ut c b f ad e b d, igitur proportio dif­
                <lb/>
              ficultatis motus a per b d ad idem a per b c, eſt uelut h ad k, quod
                <lb/>
              erat demonſtrandum.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum