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="id002201">
                <pb pagenum="113 [=123]" xlink:href="015/01/142.jpg"/>
              ſunt æquidiſtantes per octauum contemptum, erunt per dicta tri­
                <lb/>
              anguli ſimiles, igitur proportio l m gnomonis ad l n umbram
                <lb/>
              ut k h gnomonis ad k d umbram, ſed k h, ad k d, ut c e umbræ ad c d
                <lb/>
              gnomonem: igitur proportio l m gnomonis ad l n
                <expan abbr="umbrã">umbram</expan>
              , ut um­
                <lb/>
              bræ c e ad c d gnomonem, quod fuit demonſtrandum.</s>
            </p>
            <p type="margin">
              <s id="id002202">
                <margin.target id="marg427"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              15.
                <emph type="italics"/>
              pri
                <lb/>
              mi
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002203">
                <margin.target id="marg428"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              4.
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002204">Ex hoc primùm patet & pręcedenti, quod cognita proportione
                <lb/>
                <arrow.to.target n="marg429"/>
                <lb/>
              umbrę uerſę ad gnomonem cognoſcitur ſinus ſolis, & arcus altitu­
                <lb/>
              dinis in circulo magno, & eſt altitudo ab horizontis parte, quæ
                <lb/>
              proximior eſt loco ſolis, ut demonſtratum à nobis in Geometricis.</s>
            </p>
            <p type="margin">
              <s id="id002205">
                <margin.target id="marg429"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id002206">Sequitur etiam, quòd cùm umbra fuerit æqualis gnomoni, ſeu
                <lb/>
                <arrow.to.target n="marg430"/>
                <lb/>
              recta, ſeu uerſa ſolis, uel Lunæ, uel ſtellæ, altitudo erit partium qua­
                <lb/>
              draginta quin que: nam anguli d & e, uel d & h erunt æquales: igitur
                <lb/>
              arcus f a medietas quartæ ideò partium xlv. </s>
              <s id="id002207">Et ſi gnomo fuerit ma­
                <lb/>
              ior umbra uerſa, uel minor recta, erit arcus f a minor xlv partibus, ſi
                <lb/>
              contrà maior. </s>
              <s id="id002208">Et hoc ubique terrarum. </s>
              <s id="id002209">Et ubi non poſsit tantundem
                <lb/>
              eleuari, ut quando ſol eſt ſub circulo capricorni, nunquam nobis
                <lb/>
                <arrow.to.target n="marg431"/>
                <lb/>
              gnomo æquabitur umbræ rectæ ſed ſemper erit minor, & ſemper
                <lb/>
                <arrow.to.target n="marg432"/>
                <lb/>
              maior umbra uerſa pari ratione.</s>
            </p>
            <p type="margin">
              <s id="id002210">
                <margin.target id="marg430"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="margin">
              <s id="id002211">
                <margin.target id="marg431"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              5.
                <emph type="italics"/>
              primi
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lement.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002212">
                <margin.target id="marg432"/>
              P
                <emph type="italics"/>
              er ult. </s>
              <s id="id002213">ſexti
                <emph.end type="italics"/>
                <lb/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002214">Propoſitio centeſima uigeſima quinta.</s>
            </p>
            <p type="main">
              <s id="id002215">Proportionem dimetientis, & peripherię cuiuslibet circuli paral
                <lb/>
              leli æquinoctiali per cognitam partem magni circuli demonſtrare.</s>
            </p>
            <p type="main">
              <s id="id002216">Hæc erat tam clara, ut hic locum non mereretur: tam neceſſaria
                <lb/>
                <arrow.to.target n="marg433"/>
                <lb/>
              huic propoſito, ut non potuerit omitti. </s>
              <s id="id002217">Sit ergo Aequinoctij circu­
                <lb/>
              lus a b portio circuli magni nota, a c parallelus circulus, ęquinoctij
                <lb/>
              circulo c d, erit igitur ſinus c d notus. </s>
              <s id="id002218">Et ideò
                <expan abbr="quadratũ">quadratum</expan>
              c d notum,
                <lb/>
                <arrow.to.target n="marg434"/>
                <lb/>
              ergo & pars utraque b d d a nota. </s>
              <s id="id002219">Quare detracta a d ex d b relinqui­
                <lb/>
              tur d g æqualis f c diametro paralleli aſsignari. </s>
              <s id="id002220">Quare proportio
                <lb/>
                <arrow.to.target n="marg435"/>
                <lb/>
              a b ad e f nota ex obiter ſuprà demonſtratis, & pariter ambi­
                <lb/>
              tus circuli a b ad ambitum circuli c d, eſt enim ut dimetientis ad di­
                <lb/>
                <arrow.to.target n="marg436"/>
                <lb/>
              metientem.</s>
            </p>
            <p type="margin">
              <s id="id002221">
                <margin.target id="marg433"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="margin">
              <s id="id002222">
                <margin.target id="marg434"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              3.
                <emph type="italics"/>
              tertij,
                <emph.end type="italics"/>
                <lb/>
              & 8. & 17.
                <lb/>
                <emph type="italics"/>
              ſexti
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002223">
                <margin.target id="marg435"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              5.
                <emph type="italics"/>
              ſecun­
                <lb/>
              di
                <emph.end type="italics"/>
              E
                <emph type="italics"/>
              lem.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002224">
                <margin.target id="marg436"/>
              P
                <emph type="italics"/>
              er
                <emph.end type="italics"/>
              113.
                <lb/>
              P
                <emph type="italics"/>
              ropoſ.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s id="id002225">Propoſitio centeſima uigeſima ſexta.</s>
            </p>
            <p type="main">
              <s id="id002226">Circuli horarij naturam declarare.
                <lb/>
                <arrow.to.target n="marg437"/>
              </s>
            </p>
            <p type="margin">
              <s id="id002227">
                <margin.target id="marg437"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <figure id="id.015.01.142.1.jpg" xlink:href="015/01/142/1.jpg" number="133"/>
            <p type="main">
              <s id="id002228">Circulus horarius eſt circulus magnus
                <lb/>
              tranſiens per
                <expan abbr="ſolẽ">ſolem</expan>
              , aut lunam, aut quoduis
                <lb/>
              ſydus, de quo agitur, & per polos mundi,
                <lb/>
              ideò differt à circulo priore altitudinis So­
                <lb/>
              lis, quia ille ſtat ad perpendiculum ſuper
                <lb/>
              horizontem, niſi cum tangitur uice meridi­
                <lb/>
              ani, uterque tamen tranſit per
                <expan abbr="centrũ">centrum</expan>
              mundi,
                <lb/>
              ac ſolis. </s>
              <s id="id002229">Hic etiam ad ſimiles partes æqui­
                <lb/>
              noctij circulum, & omnes parallelos ſecat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>