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
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
< >
page |< < of 291 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001889">
                <pb pagenum="104" xlink:href="015/01/123.jpg"/>
              per eſt in
                <expan abbr="eadẽ">eadem</expan>
              . </s>
              <s id="id001890">Ergo ſola inclinatio ad hoc ut
                <expan abbr="mediũ">medium</expan>
              grauis ſit in li­
                <lb/>
              nea
                <expan abbr="centrorũ">centrorum</expan>
              grauitatis & terræ, ſufficit. </s>
              <s id="id001891">Eſt ergo principium in ſe i­
                <lb/>
              pſo. </s>
              <s id="id001892">In appenſis ſimiliter. </s>
              <s id="id001893">Trutina enim, & finis iugi, & grauis
                <expan abbr="cen­trũ">cen­
                  <lb/>
                trum</expan>
              mundi
                <expan abbr="centrũ">centrum</expan>
              ſunt in
                <expan abbr="eadẽ">eadem</expan>
              linea, ut eſſe poſſunt, cum exigua illa
                <lb/>
              & ſola diſtantia intercedat. </s>
              <s id="id001894">& hoc eſt primum. </s>
              <s id="id001895">Quia ergo
                <expan abbr="iugũ">iugum</expan>
              eſt
                <lb/>
              ex materia ſolida, mouetur ratione, quæ dicta eſt, lances autem
                <lb/>
              oportet cum filis appenſi ſint, ut puncta f & h, uel l, & g k, uel g m
                <lb/>
              ſint in una linea cum centro terræ. </s>
              <s id="id001896">Et quia l magis diſtat a b f quam
                <lb/>
              h, & m a g magis, quam k, & oportet faciant eandem inclinatio­
                <lb/>
              nem, quia anguli trutinæ cum iugó ſunt ijdem, & linea cl eſt ma­
                <lb/>
              ior c h, & c m, quàm c k in quouis ſitu, ergo ſpatium, quod ambitur,
                <lb/>
              eſt maius ergo per d e monſtrata ſuperius l eſt grauius h etiam
                <lb/>
              præter uinculorum additionem, & m grauius k. </s>
              <s id="id001897">Quanto igi­
                <lb/>
              tur longiores ſunt funiculi à libræ extremitate ſeu iugi, tanto gra­
                <lb/>
              uius redditur pondus, quod tamen multi putant eſſe falſum: nec
                <lb/>
              aliquid referre, quòd ſit longum, aut breue ſuſtentaculum.</s>
            </p>
            <p type="main">
              <s id="id001898">Propoſitio centeſima decima.</s>
            </p>
            <p type="main">
              <s id="id001899">Si duæ ſphæræ ex eadem materia deſcendant in
                <expan abbr="aẽ">ae</expan>
                <lb/>
              re eodem temporis momento ad planum ueniunt.
                <lb/>
                <figure id="id.015.01.123.1.jpg" xlink:href="015/01/123/1.jpg" number="118"/>
                <lb/>
                <arrow.to.target n="marg391"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001900">
                <margin.target id="marg391"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id001901">Supponitur quod ex eodem loco. </s>
              <s id="id001902">Sermo enim
                <lb/>
              abſurda ſub interpretatione nunquam niſi ab inui­
                <lb/>
              dioſo, uel imperito intelligi debet. </s>
              <s id="id001903">Sit ergo a tripla
                <lb/>
              ad b, ſphærula ad ſphærulam ex plumbo ambæ fer­
                <lb/>
              ro uel lapide eiuſdem generis, dico, quòd inæquali
                <lb/>
              tempore peruenient ad planum c d. </s>
              <s id="id001904">Nam a propor­
                <lb/>
              tionem habet ad b, ut uiginti ſeptem ad unum. </s>
              <s id="id001905">pro­
                <lb/>
              portio autem ſpatij a ad ſpatium b nonupla eſt, &
                <lb/>
              proportio denſitatis aëris ad aërem eſt tripla, propterea quod den­
                <lb/>
              ſitas illa multiplicatur propter impetus magnitudinem. </s>
              <s id="id001906">nam ſi ro­
                <lb/>
              bur, ut decem percutiat baculo lato, ut quatuor ictus erit maior du­
                <lb/>
              plo, quàm ſit robur, ut quinque percutiat baculo, ut duo: propter
                <lb/>
              denſitatem ergo maiorem aëris in a, quam in b: & quoniam ſi ſub
                <lb/>
              maiore impetu mouetur
                <expan abbr="aẽr">aer</expan>
              ſub a, quam ſub b, igitur proportio
                <lb/>
              erit comparanda longitudini à centro a ad longitudinem a centro
                <lb/>
              b, quæ eſt tripla. </s>
              <s id="id001907">Si ergo ſubtripla eſt ratio motus b ad a, quod
                <lb/>
              ad medium attinet, tripla autem propter uelocitatem diſceſſus aë­
                <lb/>
              ris à medio grauitatis, quod eſt in ſuperficie e regione centri graui­
                <lb/>
              tatis in linea ad centrum mundi, ut dictum eſt in præcedenti: mani­
                <lb/>
              feſtum eſt, quod a, & b inæquali tempore peruenient ad ſubie­
                <lb/>
              ctum planum, & æquidiſtans centris eorum. </s>
              <s id="id001908">Similiter & in aqua: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum