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

Table of handwritten notes

< >
< >
page |< < (347) of 532 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div907" type="section" level="1" n="476">
          <p>
            <s xml:id="echoid-s11425" xml:space="preserve">
              <pb o="347" file="359" n="359" rhead=""/>
            modo aberrat, quod dicitur, a ſcopo. </s>
            <s xml:id="echoid-s11426" xml:space="preserve">Solum enim probat, vtrumque angu-
              <lb/>
            lum eodem genere quantitatis contineri, hoc eſt, vtrumque angulum pla-
              <lb/>
            num eſſe; </s>
            <s xml:id="echoid-s11427" xml:space="preserve">quod acutus angulus rectilineus, vel etiam rectus conſtare poſ-
              <lb/>
            ſit ex angulo contactus, & </s>
            <s xml:id="echoid-s11428" xml:space="preserve">alio angulo mixto: </s>
            <s xml:id="echoid-s11429" xml:space="preserve">quod neque ego, neque vllus
              <lb/>
            vnquam Geometra negauit. </s>
            <s xml:id="echoid-s11430" xml:space="preserve">Ego angulos illos eiuſdem eſſe generis nega-
              <lb/>
              <note position="right" xlink:label="note-359-01" xlink:href="note-359-01a" xml:space="preserve">Angulus
                <lb/>
              contactus,
                <lb/>
              & rectili-
                <lb/>
              neus curdi
                <lb/>
              cantur eſſe
                <lb/>
              diuerſi g@-
                <lb/>
              neris.</note>
            ui hac ſolum de cauſa, quòd angulus contactus quantumuis multiplicatus
              <lb/>
            angulum acutum rectilineum ſuperare nequeat, vt in ſcholio propof. </s>
            <s xml:id="echoid-s11431" xml:space="preserve">6.
              <lb/>
            </s>
            <s xml:id="echoid-s11432" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11433" xml:space="preserve">3. </s>
            <s xml:id="echoid-s11434" xml:space="preserve">euidenter oſtendi. </s>
            <s xml:id="echoid-s11435" xml:space="preserve">Hinc enim fit, vt alter ad alterum proportionem
              <lb/>
            non habeat, atque adeo quodammodo diuerſi generis ſint: </s>
            <s xml:id="echoid-s11436" xml:space="preserve">quemadmo-
              <lb/>
            dum eadẽ de cauſa linea recta finita, & </s>
            <s xml:id="echoid-s11437" xml:space="preserve">infinita non cenſentur eſſe eiuſdem
              <lb/>
            generis, cum altera ad alteram proportionem non habeat; </s>
            <s xml:id="echoid-s11438" xml:space="preserve">quamuis ſub
              <lb/>
            eodem genere magnitudinis; </s>
            <s xml:id="echoid-s11439" xml:space="preserve">nimirum ſub linea recta, comprehendantur. </s>
            <s xml:id="echoid-s11440" xml:space="preserve">
              <lb/>
            Hoc itaque feriat, vt collimaſſe videatur: </s>
            <s xml:id="echoid-s11441" xml:space="preserve">quamquam vt omnia faciat, col-
              <lb/>
            limabit nunquam; </s>
            <s xml:id="echoid-s11442" xml:space="preserve">ita longè abeſt, quod eſt propoſitum. </s>
            <s xml:id="echoid-s11443" xml:space="preserve">Magnitudines au-
              <lb/>
            tem, quarum altera multiplicata alteram ſuperare nequit, non cenſeri eiu-
              <lb/>
            ſdem generis, (quod ad proportionem attinet) licet ſub eodẽ genere quan
              <lb/>
            titatis, hoc eſt, ſub longitudine, aut latitudine, aut profunditate, aut nume-
              <lb/>
            ro, collocentur, liquido conſtat ex defin. </s>
            <s xml:id="echoid-s11444" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11445" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11446" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11447" xml:space="preserve">vbi Euclides ſatis perſpi-
              <lb/>
            cue explicat, cuiuſmodi debeant eſſe magnitudines eiuſdem generis, inter
              <lb/>
            quas proportio reperitur. </s>
            <s xml:id="echoid-s11448" xml:space="preserve">Quare viderint alij, Peletarius homo conſide
              <lb/>
            ratus quam cogitatè me incogitantem hominem appellarit; </s>
            <s xml:id="echoid-s11449" xml:space="preserve">quaſi non re-
              <lb/>
            cte intellexerim, quæ magnitudines ſint eiuſdẽ generis, quæ non ſint. </s>
            <s xml:id="echoid-s11450" xml:space="preserve">Nun-
              <lb/>
            quam enim dixi (id quod mihi affinxit, vt carperet) duarum magnitudi-
              <lb/>
            num, quæ ſub diuerſis quãtitatis generibus collocantur, quales ſunt linea,
              <lb/>
            ſuperficies, corpus, ac numerus, alterutram ita poſſe multiplicari, vt alte-
              <lb/>
            ram ſuperet: </s>
            <s xml:id="echoid-s11451" xml:space="preserve">In quo, nẽmine reluctante, fruſtra ſeſe fatigat, vt doceat, id
              <lb/>
            fieri non poſſe; </s>
            <s xml:id="echoid-s11452" xml:space="preserve">ſed de illis duntaxat magnitudinibus ſum locutus, quæ cum
              <lb/>
            in eodem genere quantitatis verſentur, diuerſi tamen generis cenſeri poſ-
              <lb/>
            ſunt: </s>
            <s xml:id="echoid-s11453" xml:space="preserve">quales ſunt ſuperficies rectilinea & </s>
            <s xml:id="echoid-s11454" xml:space="preserve">curuilinea, ſiue mixta: </s>
            <s xml:id="echoid-s11455" xml:space="preserve">Itemque li
              <lb/>
            nea recta, & </s>
            <s xml:id="echoid-s11456" xml:space="preserve">curua. </s>
            <s xml:id="echoid-s11457" xml:space="preserve">Hæ etenim ita differre inter ſe videntur, vt Ariſtote-
              <lb/>
            les liquido affirmarit, vnam alteri æqualem eſſe non poſſe: </s>
            <s xml:id="echoid-s11458" xml:space="preserve">quod tamen (pa
              <lb/>
            ce Ariftotelis dictum ſit) verum vſquequaque non eſt; </s>
            <s xml:id="echoid-s11459" xml:space="preserve">cum Archimedes
              <lb/>
            in lib. </s>
            <s xml:id="echoid-s11460" xml:space="preserve">de lineis ſpiralibus demonſtrauerit, quænam linea recta æqualis poſ
              <lb/>
            ſit eſſe circunferentiæ cuiuſuis circuli dati. </s>
            <s xml:id="echoid-s11461" xml:space="preserve">Non igitur negare poterit Pele
              <lb/>
            tarius, aut quiſquam alius, ab Euclide defin. </s>
            <s xml:id="echoid-s11462" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11463" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11464" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11465" xml:space="preserve">aliquas quantitates
              <lb/>
            a proportionis definitione excludi, diuerſique propterea eſſe quodammo-
              <lb/>
            do generis, quod ad proportionem attinet, licet in eodem magnitudinis
              <lb/>
            genere ponantur: </s>
            <s xml:id="echoid-s11466" xml:space="preserve">quales ſunt angulus contactus, & </s>
            <s xml:id="echoid-s11467" xml:space="preserve">angulus rectilineus; </s>
            <s xml:id="echoid-s11468" xml:space="preserve">Li
              <lb/>
            nea item recta finita, & </s>
            <s xml:id="echoid-s11469" xml:space="preserve">infinita: </s>
            <s xml:id="echoid-s11470" xml:space="preserve">Multas item magnitudines comprehendi
              <lb/>
            in eadem definitione proportionis, quas plerique excludebant; </s>
            <s xml:id="echoid-s11471" xml:space="preserve">cuiuſmo-
              <lb/>
            di ſunt curuilinea ſuperficies, & </s>
            <s xml:id="echoid-s11472" xml:space="preserve">rectilinea; </s>
            <s xml:id="echoid-s11473" xml:space="preserve">necnon linea circularis, & </s>
            <s xml:id="echoid-s11474" xml:space="preserve">re-
              <lb/>
            cta, vt paulo ante diximus, latiuſque in defin. </s>
            <s xml:id="echoid-s11475" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11476" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11477" xml:space="preserve">5. </s>
            <s xml:id="echoid-s11478" xml:space="preserve">expoſuimus. </s>
            <s xml:id="echoid-s11479" xml:space="preserve">Verum
              <lb/>
            Peletarius, ne opinionem illam ſuam, quam de angulo contactus ſemel im-
              <lb/>
            biberat, deſerere cogeretur, noluit hanc expoſitionem quintæ defin. </s>
            <s xml:id="echoid-s11480" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s11481" xml:space="preserve">5.</s>
            <s xml:id="echoid-s11482" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum