Cardano, Girolamo, De subtilitate, 1663

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              <s id="s.010728">Et rurſus, dum è dextra in ſiniſtram tendis,
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              hoc aliud in ſepto:
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                <emph type="quote"/>
                <emph type="italics"/>
              Magnus veſtit honor, latus loquor hoc nationi.
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                <emph.end type="quote"/>
              </s>
            </p>
            <p type="main">
              <s id="s.010729">Simili curioſitate Plautus vſus eſt, in con­
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              ſcribendo nomine, argumenti fabulæ per
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              capita dictionum, quæ in initio argumenti
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              ipſius fabulæ poſita ſunt, literas primas col­
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              ligendo. </s>
              <s id="s.010730">Sed illa magis Comœdum decue­
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              runt, quàm ſi ex compoſito, hanc ratio­
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              nem totus ſe illi dedens iniſſet. </s>
              <s id="s.010731">Velut Hug­
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              baldus Gallus, monachus Eluomenſis, ex or­
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              dine beati Benedicti, qui centum triginta­
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              ſex carminibus, quorum ſingulæ dictiones
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              elemento C, initium ſumebant, Laudes Ca­
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              roli Calui Francorum Regis ſcripſit, quorum
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              initium eſt:
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                <emph type="quote"/>
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              Carmina clariſona caluis cantate camœnæ.
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                <emph.end type="quote"/>
              </s>
            </p>
            <p type="main">
              <s id="s.010732">Simili illud Placentij Porcij, qui Pu­
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              gnam porcorum trecentis penè carmini­
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              bus cecinit: quorum ſingulæ dictiones ex
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              P, littera initium ſumunt. </s>
              <s id="s.010733">Extat opus im­
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              preſſum non inelegans, apud me: cuius ini­
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              tium eſt:
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                <emph type="quote"/>
                <emph type="italics"/>
              Plandite porcelli, porcorum pigra propago.
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                <emph.end type="quote"/>
              </s>
            </p>
            <p type="main">
              <s id="s.010734">Sed ſi hæc coniunctam in ſe habe rent
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              aliquam vtilitatem, ſumma dignum laude
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              hominem arbitrarer: nunc verò tam operam
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              irridere licet, quàm etiam ingenium admi­
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              rari. </s>
              <s id="s.010735">Placere poteſt exemplum, copia horum
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              certè tædium parit. </s>
              <s id="s.010736">Hócque vnum fermè eſt
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              commune his, quorum nullus inter homines
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              vſus eſt. </s>
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            <p type="main">
              <s id="s.010737">Atque hæc penè ſimilia induſtriæ egregij
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              illius viri, qui cicere, cùm quemcunque
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              vellet locum feriret, ciceris modium ab A­
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              lexandro promeruit: magis auerſatus ina­
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              nem laborem, quàm induſtriam admira­
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              tus. </s>
              <s id="s.010738">Eiuſdem etiam, ſed aliquantò vtilio­
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              ris argumenti ſunt libri illi quatuor Geo­
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                <arrow.to.target n="marg1508"/>
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              metrici Procli in Euclidis elementa: nihil
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              enim nouum docent, ob idque ad artem non
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              ſpectant. </s>
              <s id="s.010739">Quia tamen varia eſt ſubtilitas il­
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              la, non vnius prorſus generis, vt in Rhabano
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              & Lullio, ideò non omninò vt inutiles abii­
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              ci, & ſperni debent. </s>
              <s id="s.010740">Nam & ipſius ſubtilita­
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              tis cùm plura fuerint exempla, ars quædam
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              etiam erit.
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                <arrow.to.target n="marg1509"/>
              </s>
            </p>
            <p type="margin">
              <s id="s.010741">
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              Procli libri
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              non ſpectant
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              ad artem
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                <expan abbr="Geometricã">Geometricam</expan>
              .</s>
            </p>
            <p type="margin">
              <s id="s.010742">
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              Quomodo
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              quæcunque
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              in elementis
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              Euclid. </s>
              <s id="s.010743">de­
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              monſtrata
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              ſunt, abſque
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              vlla propoſi­
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              ti vnius tan
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              tum circuli
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              mutatione
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              oſtendi poſ­
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              ſint.</s>
            </p>
            <p type="main">
              <s id="s.010744">Igitur conſimili argumento quale fuit
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              Procli, oſtentatione potius iuuenili, quàm
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              vtilitate manifeſta, tum ego, tum Ludo­
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              uicus Ferrarius paucis in diebus inuenimus,
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              quónam pacto quæcunque ab Euclide de­
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              monſtrantur, variata circini latitudine, à
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              nobis ſub quacunque latitudine illius à con­
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              tradicente propoſita inuariabilique, præ­
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              ter circulorum ſolam inſcriptionem ac cir­
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              cumſcriptionem, perfectè à nobis poſſent
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              oſtendi. </s>
              <s id="s.010745">Et quamvis dum hæc ſcriberemus,
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              Ludouicus ipſe hanc totam demonſtratio­
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              nem typis exceptam edidiſſet optimè, quia
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              tamen opus illud contentionis gratia ſcri­
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              ptum eſt, haud arbitror ſuperfuturum, cùm
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              nihil aliud fermè egregij contineat: & ſi
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              quædam ſint egregia, ſeorſum tamen poſi­
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              ta ſunt, & non vnius generis, ita poſtu­
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              lante materia: quo fit vt operæ pretium eſſe
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              duxerim, ne quandoque tam rarum ſubtili­
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              tatis exemplum periret, illud denuò hîc ſub
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              iicere. </s>
              <s id="s.010746">Sed quomodo? </s>
              <s id="s.010747">breuius demonſtratio­
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              nibus: ne abhorrentes à Geometricis tædio
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              capiantur. </s>
            </p>
            <p type="main">
              <s id="s.010748">Igitur primò, quarta primi Elemento­
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              rum, velut ab Euclide demonſtratur, cùm
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              nullius præcedentis alterius propoſitionis
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              auxilio indigeat, erit demonſtranda. </s>
              <s id="s.010749">Inde
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              quinta: nam quòd ad demonſtrationem at­
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              tinet, ſola quarta, quam primam vocabi­
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              mus, vt quintam ſecundam, indiget: quò
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              verò ad protrahendum lineas, circuli am­
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              plitudo nobis propoſita ſufficiet, cùm lineas
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              quantumlibet in directum producere liceat.
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              </s>
              <s id="s.010750">Inde tertia erit nobis, quæ ſeptima & quar­
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              ta, qua octaua: nam etſi ab Euclide ex ſe­
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              ptima demonſtretur, tamen & ſine abſur­
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              do ſic poterit demonſtrari. </s>
              <s id="s.010751">Collocato alte­
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              ro trigono ex aduerſo ſuper baſim, lineáque
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              à vertice ad verticem recta ducta: nam con­
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              ſtat, vt etiam à Proclo oſtenditur in tertio
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              libro ex ſecunda, & animi communi ſen­
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              tentia, trigonos habere angulos ſupremos,
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              & latera illos continentia æqualia, igitur
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              ex prima erunt æquales, transferre autem
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              trigonos licet, cùm Euclides in quarta ſua
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              Propoſitione id admittat. </s>
              <s id="s.010752">Quarta nobis erit
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              nona Euclidis in primo libro: nam de il­
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              lo intelligo, donec alterius libri mentio­
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              nem adiecero. </s>
              <s id="s.010753">Igitur factis lineis angu­
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              lum continentibus æqualibus iuxta circini
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              latitudinem propoſitum, circulos duos ſe­
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              cundum datam latitudinem factis centris
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              terminis linearum deſcribam, ſecantes ſe
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              in angulo propoſito & ex aduerſo, ad quam
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              ſectionem è centris circulorum ductis li­
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              neis, inde è ſectione ad ſectionem ex ter­
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              tia harum, & circuli diffinitione illicò pa­
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              tet propoſitum. </s>
              <s id="s.010754">Quòd ſi quis adeò peruer­
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              ſus ſit, vt ne admittat circulos alibi ſe
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              ſecare, quàm in angulo, ducta linea in­
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              ter fines angulum continentium recta, to­
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              ties vtrunque circulos repetemus, donec
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              ſe tandem, aut ſecent, aut contingant. </s>
              <s id="s.010755">Per
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                <arrow.to.target n="marg1511"/>
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              ſecundam & primam harum aſſequemur,
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              tandémque per tertiam propoſitum angu­
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              lum, ducta ex angulo, ad aduerſam circulo­
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              rum ſectionem recta, bifariàm. </s>
              <s id="s.010756">ſecari. </s>
              <s id="s.010757">Quin­
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              tam ſtatuemus decimam Euclidis, per præ­
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              cedentis modum, vim ac figuram demon­
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              ſtratam. </s>
            </p>
            <p type="margin">
              <s id="s.010758">
                <margin.target id="marg1510"/>
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              Primi Eucl.
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              </s>
              <s id="s.010759">noſtræ.
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              </s>
              <s id="s.010760">4 1
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              5 2
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              7 3
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              8 4
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              </s>
            </p>
            <p type="margin">
              <s id="s.010761">
                <margin.target id="marg1511"/>
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              Eucl. </s>
              <s id="s.010762">noſtræ.
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              </s>
              <s id="s.010763">10 6
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              11 7
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              </s>
            </p>
            <p type="main">
              <s id="s.010764">Sexta erit vndecima illius: hinc inde ex
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              puncto dato, quantum eſt circuli latitudo
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              capiemus: vtraque verò per quintam diui­
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              ſa bifariàm, erunt partes quæ ad punctum
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              iungentur dimidium latitudinis circini, am­
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              bæque iunctæ ipſa latitudo, vnde extremis
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              illius lineæ pro centris poſitis, vbi circuli
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              ſe interſecabunt, linea ducta ad punctum
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              datum, ex tertia harum perpendicularis erit.
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              </s>
              <s id="s.010765">Inde decimamtertiam, decimamquartam, &
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              decimamquintam Euclidis, ſeptimam, octa­
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                <arrow.to.target n="marg1512"/>
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              uam, & nonam harum ſtatuemus, cùm nullis
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              aliis, niſi demonſtratis, iam hîc indigeant. </s>
            </p>
            <p type="margin">
              <s id="s.010766">
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              13 8
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              14 9
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              15 10
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              Pars tertia.
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              </s>
              <s id="s.010767">11.
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              </s>
            </p>
            <p type="main">
              <s id="s.010768">
                <emph type="center"/>
              PARS TERTIÆ DECIMÆ.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.010769">Decima propoſitio erit hæc: Propoſitis
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              duabus lineis inæqualibus ſe tangentibus,
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              de maiore quantum æquale ſit minori abſ­
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              cindere: eſtque hæc pars tertiæ Euclidis: at </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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