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 ...

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="id001921">
                <pb pagenum="106" xlink:href="015/01/125.jpg"/>
              cilius ſit in anteriore parte propinquius comprehenſum calci, & ſi
                <lb/>
              craſsius, uel grauius propius cuſpidi. </s>
              <s id="id001922">Semper igitur ob hanc cau­
                <lb/>
              ſam mota ex medio grauitatis, ſeu uelo, ſeu ramo, ſeu manu uelo­
                <lb/>
              cius mouentur, quàm ex alijs partibus. </s>
              <s id="id001923">In remo etiam poteſt acce­
                <lb/>
              dere illud commodum, cuius meminit Ariſtoteles. </s>
              <s id="id001924">Propter hoc igi
                <lb/>
              tur, qui malum in naui collo carunt tantùm unum, in medio fermè
                <lb/>
              eum collocarunt, ut antiqui: & qui duos aut tres, maiorem craſsio­
                <lb/>
                <arrow.to.target n="marg396"/>
                <lb/>
              rem ſcilicet, & altiorem in medio conſtituerunt.</s>
            </p>
            <p type="margin">
              <s id="id001925">
                <margin.target id="marg392"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id001926">
                <margin.target id="marg393"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              86.</s>
            </p>
            <p type="margin">
              <s id="id001927">
                <margin.target id="marg394"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              10.
                <lb/>
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001928">
                <margin.target id="marg395"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              8.
                <emph type="italics"/>
              quin­
                <lb/>
              ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001929">
                <margin.target id="marg396"/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              82.</s>
            </p>
            <p type="main">
              <s id="id001930">Propoſitio centeſimaduodecima.</s>
            </p>
            <p type="main">
              <s id="id001931">Cur ex imo leuia longius ferantur declarare.</s>
            </p>
            <p type="main">
              <s id="id001932">Iam uerò
                <expan abbr="cõſideremus">conſideremus</expan>
              , quòd propoſitum eſt, non ſolum in com­
                <lb/>
                <arrow.to.target n="marg397"/>
                <lb/>
              paratione ad medium, ſed extremorum inuicem, miſſa enim ab imo
                <lb/>
              uelo cius feruntur, quàm à medio non ſolum manu, ſed ſcorpioni­
                <lb/>
              bus, & arcubus. </s>
              <s id="id001933">Videmus & hoc obſeruare pueros uirgam lon­
                <lb/>
              gius iacentes non ex medio, ſed imo apprehenſam, quoniam pars
                <lb/>
              ipſa anterior, & quæ manu apprehenſa eſt, uehementi impetu emit­
                <lb/>
              titur: & ut recipit impetum magis æqualem, longius fertur, nam
                <lb/>
              quod emittitur proportionem habet ad ſpatium. </s>
              <s id="id001934">Cum ergo appre
                <lb/>
              henſa in medio uirga ſolum medietate anteriore impetum recipiat
                <lb/>
              per ſe, ob id minus fertur: at impetus ſequitur proportionem, ut ui­
                <lb/>
              ſum eſt, quæ eſt circa medium ob leuitatem ponderis. </s>
              <s id="id001935">In leuibus
                <lb/>
              ergo maius ſpatium ſuperabunt emiſſa ex imo, quoniam propor­
                <lb/>
              tio ſpatij eadem eſt ad duplum, & ad dimidium. </s>
              <s id="id001936">igitur ex imo fer­
                <lb/>
              me duplum etiam ſpatij ſuperabit: non tamen omnino quia maio­
                <lb/>
              rem, ut dixi proportionem habet ad id, quod ex medio comprehen
                <lb/>
              ſum eſt. </s>
              <s id="id001937">At in leuibus non eſt neceſſarium, ut ex medio apprehen­
                <lb/>
              dantur, quoniam etiam cum incremento illo ponderis iam leuia
                <lb/>
              ſunt: plus ergo facit longitudo eius, quod eiaculatur, quàm impe­
                <lb/>
                <figure id="id.015.01.125.1.jpg" xlink:href="015/01/125/1.jpg" number="120"/>
                <lb/>
              tus, cuius demonſtratio eſt hæc. </s>
              <s id="id001938">Sit uirga
                <lb/>
              a b apprehenſa in medio ponderis unciæ
                <lb/>
              mediæ, & in a d, ut ſit d a palmus, & uigeſi­
                <lb/>
              ma pars totius a b, erit ergo reſiduum ad duplum, a d nonuplum,
                <lb/>
                <arrow.to.target n="marg398"/>
                <lb/>
              & a b tota unciarum quin que cum dimidia, ſi igitur grauetur, quia in
                <lb/>
              ſitu recto eſt mediæ unciæ, in æquidiſtanti terræ, quin que unciarum
                <lb/>
              cum dimidio, erit in ſitu dimidij recti unciarum trium. </s>
              <s id="id001939">Eſt igitur
                <lb/>
              proportio ſexcupla, ſi apprehendatur in medio, & ad æquidiſtan­
                <lb/>
              tem, ad apprehenſam in imo, & ad angulum medium: at emiſſa ex
                <lb/>
                <arrow.to.target n="marg399"/>
                <lb/>
              a d habet totum aërem a b circumdantem impulſum ex c b ſolum
                <lb/>
              dimidium reliqua pars ui trahitur, ergo proportio ſpatij a b, erit
                <lb/>
              ſexdecupla fermè ſpatio b c, quoniam eſt triplicata corporis ad cor
                <lb/>
              pus eius, quæ eſt longitudinis ad longitudinem, & quadruplicata </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>