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="id001103">
                <pb pagenum="59" xlink:href="015/01/078.jpg"/>
              in cono rectangulo uocat rectanguli coni ſectionem: ex qua cir­
                <lb/>
              cumacta fit conoidale, quia planam habet baſim. </s>
              <s id="id001104">Si ergo in ea­
                <lb/>
                <arrow.to.target n="marg218"/>
                <lb/>
              dem rectanguli coni ſectione à plano portiones æquales habentes
                <lb/>
              diametros abſcindantur, illæ portiones erunt æquales. </s>
              <s id="id001105">Et triangu­
                <lb/>
              li in eiſdem portionibus inſcripti æquales erunt. </s>
              <s id="id001106">Diametrum uo­
                <lb/>
              cat in
                <expan abbr="quacunqũe">quacunqune</expan>
              portione lineam, quæ omnes lineas baſi æquidi­
                <lb/>
              ſtantes per æqualia diuidit. </s>
              <s id="id001107">Omnis circuli cuius diameter eſt ma
                <lb/>
                <arrow.to.target n="marg219"/>
                <lb/>
              ior diameter ellipſis proportio ad ellipſim eſt uelut directè diame­
                <lb/>
              tri ellipſis ad diametrum tranſuerſam. </s>
              <s id="id001108">Ex quo patet quod pro­
                <lb/>
                <arrow.to.target n="marg220"/>
                <lb/>
              portio cuiuslibet circuli ad ellipſim eſt uelut quadrati ſuæ diame­
                <lb/>
              tri ad rectangulum recta, & tranſuerſa diametro ellipſis compre­
                <lb/>
              henſum. </s>
              <s id="id001109">Ex hoc rurſus ſequitur quod ellipſis ad ellipſim, ut re­
                <lb/>
                <arrow.to.target n="marg221"/>
                <lb/>
              ctanguli ex diametris unius ad rectangulum ex diametris alterius.</s>
            </p>
            <p type="margin">
              <s id="id001110">
                <margin.target id="marg209"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              14. & 15.
                <emph type="italics"/>
              duodeci mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              le.
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              ucl.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001111">
                <margin.target id="marg210"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              duodecimi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              le.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001112">
                <margin.target id="marg211"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              2.
                <emph type="italics"/>
              duodecimi
                <emph.end type="italics"/>
              , & 20.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001113">
                <margin.target id="marg212"/>
              8</s>
            </p>
            <p type="margin">
              <s id="id001114">
                <margin.target id="marg213"/>
              9</s>
            </p>
            <p type="margin">
              <s id="id001115">
                <margin.target id="marg214"/>
              10</s>
            </p>
            <p type="margin">
              <s id="id001116">
                <margin.target id="marg215"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              22.
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001117">
                <margin.target id="marg216"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              20.
                <emph type="italics"/>
              ſex ti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001118">
                <margin.target id="marg217"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              11.
                <emph type="italics"/>
              quinti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id001119">
                <margin.target id="marg218"/>
              11</s>
            </p>
            <p type="margin">
              <s id="id001120">
                <margin.target id="marg219"/>
              12</s>
            </p>
            <p type="margin">
              <s id="id001121">
                <margin.target id="marg220"/>
              13</s>
            </p>
            <p type="margin">
              <s id="id001122">
                <margin.target id="marg221"/>
              14</s>
            </p>
            <p type="main">
              <s id="id001123">Si conoides & ſphæroides ſecet plano æquidiſtanti axi fiet ſe­
                <lb/>
                <arrow.to.target n="marg222"/>
                <lb/>
              ctio conoidalis ſimilis ei à qua conoides ſeu ſphæroides deſcri­
                <lb/>
              ptum eſt. </s>
              <s id="id001124">Sin autem ſupra axem plano ad perpendiculum erecto
                <lb/>
              ſectio circulus erit. </s>
              <s id="id001125">Et ſi ſecentur obliquè fiet ellipſis, modo omnia
                <lb/>
              latera comprehendat. </s>
              <s id="id001126">Omnis portio conoidalis rectanguli, quam
                <lb/>
                <arrow.to.target n="marg223"/>
                <lb/>
              planum ſecat, ſexquialtera eſt, cono qui baſim & axem eandem ha­
                <lb/>
              bet. </s>
              <s id="id001127">Ex quo patet, quod ſi portio conoidalis rectanguli & ſphæ­
                <lb/>
                <arrow.to.target n="marg224"/>
                <lb/>
              ræ medietas eandem baſim habeant & axem eundem, medietas
                <lb/>
              ſphæræ ſexquitertia erit conoidali portioni. </s>
              <s id="id001128">Et ſi eiuſdem rectan
                <lb/>
                <arrow.to.target n="marg225"/>
                <lb/>
              guli conoidalis portiones abſcin dantur erit portionum propor­
                <lb/>
              tio uelut quadratorum axium. </s>
              <s id="id001129">Cuiuslibet ſphæroidis pars pla­
                <lb/>
                <arrow.to.target n="marg226"/>
                <lb/>
              no per centrum abſciſſa dupla eſt cono baſim & axem eadem ha­
                <lb/>
              benti. </s>
              <s id="id001130">Si autem non ſuper centrum erit proportio earum ad co­
                <lb/>
                <arrow.to.target n="marg227"/>
                <lb/>
              num baſim, & axem eandem habentem uelut coniunctæ ex axe al­
                <lb/>
              terius partis & dimidio axis ſphæroidis ad axem alterius partis.</s>
            </p>
            <p type="margin">
              <s id="id001131">
                <margin.target id="marg222"/>
              15</s>
            </p>
            <p type="margin">
              <s id="id001132">
                <margin.target id="marg223"/>
              16</s>
            </p>
            <p type="margin">
              <s id="id001133">
                <margin.target id="marg224"/>
              17</s>
            </p>
            <p type="margin">
              <s id="id001134">
                <margin.target id="marg225"/>
              18</s>
            </p>
            <p type="margin">
              <s id="id001135">
                <margin.target id="marg226"/>
              19</s>
            </p>
            <p type="margin">
              <s id="id001136">
                <margin.target id="marg227"/>
              20</s>
            </p>
            <p type="main">
              <s id="id001137">Demum proportio partis conoidis obtuſi anguli plano abſciſ­
                <lb/>
                <arrow.to.target n="marg228"/>
                <lb/>
              ſæ ad conum, baſim & axem eadem habentem eſt ueluti lineæ, com
                <lb/>
              poſitæ ex axe portionis & triplo adiectæ ad compoſitum ex axe
                <lb/>
              portionis & duplo eiuſdem adiectæ. </s>
              <s id="id001138">Adiectam uocat hyperbolis
                <lb/>
              tranſuerſam. </s>
              <s id="id001139">Omnis cylindrus cono triplus eſt habenti eandem
                <lb/>
                <arrow.to.target n="marg229"/>
                <lb/>
              baſim & altitudinem. </s>
              <s id="id001140">Omnes cylindri coni ſphæræ ſunt in pro­
                <lb/>
                <arrow.to.target n="marg230"/>
                <lb/>
              portione corporum ſimilium planis ſuperficiebus contentarum.</s>
            </p>
            <p type="margin">
              <s id="id001141">
                <margin.target id="marg228"/>
              21</s>
            </p>
            <p type="margin">
              <s id="id001142">
                <margin.target id="marg229"/>
              22</s>
            </p>
            <p type="margin">
              <s id="id001143">
                <margin.target id="marg230"/>
              23</s>
            </p>
            <p type="main">
              <s id="id001144">Propoſitio ſexageſima nona, collectorum ex quatuor libris
                <lb/>
              Apollonij Pergei &
                <expan abbr="q.">que</expan>
              Sereni.</s>
            </p>
            <p type="main">
              <s id="id001145">Si fuerit linea bifariam diuiſa, eique in longum alia addita, & rur­
                <lb/>
                <arrow.to.target n="marg231"/>
                <lb/>
              ſus alia detracta, fueritque totius cum addita ad eam, quæ addita eſt
                <lb/>
              ueluti reſidui ad detractam erit lineæ com­
                <lb/>
                <figure id="id.015.01.078.1.jpg" xlink:href="015/01/078/1.jpg" number="75"/>
                <lb/>
              poſitæ ex addita, & dimidia ad dimidiam </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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