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="id003331">
                <pb pagenum="188 [=194]" xlink:href="015/01/213.jpg"/>
              in k per arcus æquales, & ducantur arcus h l & k m. </s>
              <s id="id003332">Quia n m & n l
                <lb/>
              ſunt minores quarta circuli, & maiores ſunt f e & fl, & angulus an­
                <lb/>
              gulo non minor, patet propoſitum. </s>
              <s id="id003333">Ita ergo motus, ut appropin­
                <lb/>
              quant
                <expan abbr="pũctis">punctis</expan>
              medijs ſunt uelociores, & in æquali
                <expan abbr="diſtãtia">diſtantia</expan>
              æquales.</s>
            </p>
            <p type="main">
              <s id="id003334">Et hoc inuentum fuit Ludouici Ferrarij, cuius meminimus in Ar
                <lb/>
              te magna, & nos ei ſubtexuimus ex noſtra inuentione, cuius ille de­
                <lb/>
              monſtrationem inuenire nequiuit.</s>
            </p>
            <p type="main">
              <s id="id003335">Propoſitio centeſima ſeptuageſima quarta.</s>
            </p>
            <p type="main">
              <s id="id003336">Progreſſus & regreſſus tam ſine latitudine, quàm cum latitudi­
                <lb/>
              ne in planetis per ſolos concentricos circulos æqualiter motos de­
                <lb/>
              monſtrare.
                <lb/>
                <arrow.to.target n="marg617"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003337">
                <margin.target id="marg617"/>
              C
                <emph type="italics"/>
              o
                <emph.end type="italics"/>
              ^{m}.</s>
            </p>
            <p type="main">
              <s id="id003338">Sit eclyptica a b c d, & arcus regreſſus b c in partes
                <lb/>
                <figure id="id.015.01.213.1.jpg" xlink:href="015/01/213/1.jpg" number="208"/>
                <lb/>
              quatuor æquales diuiſus, & deſcribantur circuli duo b
                <lb/>
              h & e k ſuper e & f, & ſupponatur orbis ſuperior ſub
                <lb/>
              eclyptica tamen, cuius polus in f, qui circumagatur in du
                <lb/>
              plo temporis retroceſſus planetæ, & in diſtantia circuli
                <lb/>
              e k ſub puncto e eclypticæ, polus alterius orbis concen­
                <lb/>
              trici inferioris, qui circumagatur in tempore retro ceſſus
                <lb/>
              planetæ, & planeta ſit in puncto 6, liquet ergo quòd pla
                <lb/>
              neta ille in uno circuitu e k circuli permeabit b c & re­
                <lb/>
              meabit, & ſemper erit ſub ipſa eclyptica. </s>
              <s id="id003339">Sed enim eclyptica habet
                <lb/>
              rationem rectæ lineæ, ut quiuis circulus maximus. </s>
              <s id="id003340">Et ſi quis relu­
                <lb/>
              ctetur fingamus rectam ſubtenſam arcui b c, & aliam poſtmodum
                <lb/>
              æquidiſtantem in eadem ſuperficie, & in orbe inferiore, & tunc pa­
                <lb/>
              tebit liquidò propoſitum. </s>
              <s id="id003341">Sed ſi uelim latitudinem deſcribam, ma­
                <lb/>
              ximam latitudinem à puncto b, & ducam circulum magnum per
                <lb/>
              punctum illud: reliqua ut prius, ad unguem: nihil enim refert quod
                <lb/>
              ad demonſtrationem præcedentis attinet, ſeu a d ponatur eclypti­
                <lb/>
              ca, ſeu alius circulus magnus.</s>
            </p>
            <p type="main">
              <s id="id003342">
                <arrow.to.target n="marg618"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003343">
                <margin.target id="marg618"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 1.</s>
            </p>
            <p type="main">
              <s id="id003344">Ex hoc patet cauſa cur retroceſſus in initio, & in fine ſint exigui,
                <lb/>
              in medio ſint magni imò maximi, & quomodo perpetuò uarietur
                <lb/>
              latitudo in tempore retro ceſſus, & ratio omnium, & ſimiliter de in­
                <lb/>
              crementis & uelocitate motus.</s>
            </p>
            <p type="main">
              <s id="id003345">
                <arrow.to.target n="marg619"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003346">
                <margin.target id="marg619"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              ^{m}. 2.</s>
            </p>
            <p type="main">
              <s id="id003347">Ex hoc ſequitur, quod cum erratica fuerit in centro ſeu polo f, &
                <lb/>
              tunc mouetur uelociſsímè, quòd tamen erit in oppoſito ſolis, &
                <lb/>
              tunc etiam ibi erit ipſe polus, quare alter erit cum ipſo ſole.</s>
            </p>
            <p type="main">
              <s id="id003348">
                <arrow.to.target n="marg620"/>
              </s>
            </p>
            <p type="margin">
              <s id="id003349">
                <margin.target id="marg620"/>
              C
                <emph type="italics"/>
              or
                <emph.end type="italics"/>
              _{m}. 3.</s>
            </p>
            <p type="main">
              <s id="id003350">Et quia dum motus eſt uelociſsimi ſecundum ordinem ſigno­
                <lb/>
              rum, tunc erratica ſuperior eſt ſoli iuncta, eſtque in polo, oportet ut
                <lb/>
              polus f moueatur ſecundum ordinem ſignorum, adeò ut cum ſol
                <lb/>
              peruenerit ad illius oppoſitum, orbis ſuperior dimidium perfecerit </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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