Theodosius <Bithynius>; Clavius, Christoph, Theodosii Tripolitae Sphaericorum libri tres

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            <s xml:id="echoid-s11684" xml:space="preserve">
              <pb o="353" file="365" n="365" rhead=""/>
            _& </s>
            <s xml:id="echoid-s11685" xml:space="preserve">circunferentia circunferentiæ circuli eiuſdem, & </s>
            <s xml:id="echoid-s11686" xml:space="preserve">anguli, qui à ſimili-_
              <lb/>
            _bus ſimiliter iacentibus lineis comprehenſi ſunt. </s>
            <s xml:id="echoid-s11687" xml:space="preserve">Horum autem dico, quòd_
              <lb/>
            _quæ æqualia data fuerint, ſibi inuicem congruũt._</s>
            <s xml:id="echoid-s11688" xml:space="preserve">] Nonne luce clarius ex his
              <lb/>
            colligitur, Proclum illos ſolum angulos contactus concedere æquales,
              <lb/>
            quorum rectæ lineæ, & </s>
            <s xml:id="echoid-s11689" xml:space="preserve">curuæ ſibi mutuò congruunt? </s>
            <s xml:id="echoid-s11690" xml:space="preserve">Temere igitur Pele-
              <lb/>
            tarius mihi obijcit angulum rectilineum & </s>
            <s xml:id="echoid-s11691" xml:space="preserve">circuilineum, triangulum & </s>
            <s xml:id="echoid-s11692" xml:space="preserve">
              <lb/>
            quadratum, atque alia huiuſmodi, de quibus eo loco ſermo non erat; </s>
            <s xml:id="echoid-s11693" xml:space="preserve">quip-
              <lb/>
            pe quæ non ſint eiuſdem ſpeciei, atque adeo æqualitatem tueantur, etiamſi
              <lb/>
            alterum alteri non congruat. </s>
            <s xml:id="echoid-s11694" xml:space="preserve">Vtiam vereri incipiam, ne Peletarius noſter
              <lb/>
            contentionis ſit cupidior, quàm veritatis.</s>
            <s xml:id="echoid-s11695" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11696" xml:space="preserve">POSTREMO, vt nihil intactum relinquat, me non modo Geo-
              <lb/>
            metriæ ignarum vocat, ſed etiam Logices: </s>
            <s xml:id="echoid-s11697" xml:space="preserve">propterea quòd lib. </s>
            <s xml:id="echoid-s11698" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11699" xml:space="preserve">dixi, non
              <lb/>
            recte à quibuſdam diuidi Proportionem rationalem in proportionẽ æqua-
              <lb/>
            litatis, atque inæqualitatis? </s>
            <s xml:id="echoid-s11700" xml:space="preserve">quòd multæ proportiones inæqualitatis ſint
              <lb/>
            etiam irrationales. </s>
            <s xml:id="echoid-s11701" xml:space="preserve">Ego vero (etſi non is ſum, qui mihi quicquã vllo in ge-
              <lb/>
            nere arrogem) tamen in hiſce ſtudijs, in quibus mediocriter verſatus ſum,
              <lb/>
            planè rudem non eſſe, præ me ſemper tuli. </s>
            <s xml:id="echoid-s11702" xml:space="preserve">Quantulum autem ſit id, quod
              <lb/>
            in vtroq; </s>
            <s xml:id="echoid-s11703" xml:space="preserve">poſſim, cæteri melius, qui vacant amore, & </s>
            <s xml:id="echoid-s11704" xml:space="preserve">odio, iudicabunt; </s>
            <s xml:id="echoid-s11705" xml:space="preserve">Pe-
              <lb/>
            letario quidem ipſi ita me adhuc reſpõdiſſe arbitror, vt iam minus fortaſſe
              <lb/>
            ignarus Geometriæ, ac Dialecticæ videar, quàm putarat. </s>
            <s xml:id="echoid-s11706" xml:space="preserve">Nunc, vt perſpi-
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            ciat, neq; </s>
            <s xml:id="echoid-s11707" xml:space="preserve">me pertinacem eſſe, neq; </s>
            <s xml:id="echoid-s11708" xml:space="preserve">illa, quæ exagitat, à Dialecticorũ præ-
              <lb/>
            ceptis abhorrere, libẽter ei concedo, diuiſionẽ illam, quam à me reprehen
              <lb/>
            ſam criminatur, probã eſſe, ita tamen, ſi in quolibet diuiſionis membro Di-
              <lb/>
            uiſum intelligatur: </s>
            <s xml:id="echoid-s11709" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s11710" xml:space="preserve">vero hoc vnquã negaui, cum alibi ſimiles diuiſio-
              <lb/>
            nes vſurpem. </s>
            <s xml:id="echoid-s11711" xml:space="preserve">Solũ id eo loci contẽdi, rectius meo iudicio, diuidi Propor-
              <lb/>
            tionem in vniuerſum duplici diuiſione, priori quidem in proportionem ra
              <lb/>
            tionalem, & </s>
            <s xml:id="echoid-s11712" xml:space="preserve">irrationalem; </s>
            <s xml:id="echoid-s11713" xml:space="preserve">poſteriori vero in proportionẽ æqualitatis, atq;
              <lb/>
            </s>
            <s xml:id="echoid-s11714" xml:space="preserve">inæqualitatis, (quod veriſsimum eſſe, neminem negaturum cenſeo, qui
              <lb/>
            rem diligentius expenderit) cum tam priora duo membra diuidẽtia, quam
              <lb/>
            poſteriora totum Diuiſum (vt Logici loquuntur) exhauriant: </s>
            <s xml:id="echoid-s11715" xml:space="preserve">quam ſi
              <lb/>
            prius membrum prioris diuiſionis, hoc eſt, proportio rationalis, ſecetur in
              <lb/>
            proportionem æqualitatis, & </s>
            <s xml:id="echoid-s11716" xml:space="preserve">inæqualitatis, cum hæc membra diuidentia
              <lb/>
            latius pateant, quam Diuiſum, niſi in illis Diuiſum intelligatur. </s>
            <s xml:id="echoid-s11717" xml:space="preserve">Atque eò
              <lb/>
            magis duplex illa diuiſio mihi probatur, quòd non deſint, qui primum par-
              <lb/>
            tiantur Proportionem in proportioneẽ æqualitatis, & </s>
            <s xml:id="echoid-s11718" xml:space="preserve">inæqualitatis; </s>
            <s xml:id="echoid-s11719" xml:space="preserve">poſte-
              <lb/>
            riorem deinde hanc in proportionem rationalem, & </s>
            <s xml:id="echoid-s11720" xml:space="preserve">irrationalem: </s>
            <s xml:id="echoid-s11721" xml:space="preserve">contra-
              <lb/>
            rio ſcilicet modo, quàm priores. </s>
            <s xml:id="echoid-s11722" xml:space="preserve">Vt igitur hanc controuerſiam dirimerem,
              <lb/>
            ac dubitationem, vtri rectius faciant, priores ne an poſteriores, tollerem,
              <lb/>
            ſt atui duabus diuiſionibus ſecandam eſſe Proportionem, quarum vtraque
              <lb/>
            abſolutiſsima eſt, ac perfectiſsima. </s>
            <s xml:id="echoid-s11723" xml:space="preserve">Non aliter arbitror, omnes magis eſſe
              <lb/>
            probaturos, ſi corpus duplici diuiſione ſecetur, primum quidem in viuens,
              <lb/>
            & </s>
            <s xml:id="echoid-s11724" xml:space="preserve">non viuens; </s>
            <s xml:id="echoid-s11725" xml:space="preserve">deinde vero in album, nigrum, ac mixto colore affectum: </s>
            <s xml:id="echoid-s11726" xml:space="preserve">
              <lb/>
            quam ſi corpus viuens diuidatur in album, nigrum, ac mixto colore affe-
              <lb/>
            ctum; </s>
            <s xml:id="echoid-s11727" xml:space="preserve">ob cauſam iam dictam: </s>
            <s xml:id="echoid-s11728" xml:space="preserve">licet hęc ſubdiuiſio bona ſit, ſi Diuiſum </s>
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