Benedetti, Giovanni Battista de, Io. Baptistae Benedicti ... Diversarvm specvlationvm mathematicarum, et physicarum liber : quarum seriem sequens pagina indicabit ; [annotated and critiqued by Guidobaldo Del Monte]

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EPISTOLAE.
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                <pb o="401" rhead="EPISTOLAE." n="413" file="0413" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0413"/>
                <p>
                  <s xml:id="echoid-s4744" xml:space="preserve">Volens inferre, quod quemadmodum inter duos numeros ſolidos, & inuicem
                    <lb/>
                  ſimiles,
                    <reg norm="vnus" type="simple">vnꝰ</reg>
                    <reg norm="tantum" type="context context">tãtũ</reg>
                  medius proportionalis intercedere
                    <reg norm="non" type="context">nõ</reg>
                  poteſt, ſed duo neceſſariò re
                    <lb/>
                  quiruntur (vt exijs quæ Euclid .8. lib. 16. 17. 18. et .19. propoſitione proponit viden­
                    <lb/>
                  tur) ita
                    <reg norm="dictante" type="context">dictãte</reg>
                  ratione inter igneum,
                    <reg norm="terreumque" type="simple">terreumq́;</reg>
                  corpus duo corpora interiecta
                    <reg norm="eſsent" type="context">eſsẽt</reg>
                  ,
                    <lb/>
                  non ratione proportionalitatis continuæ in quantitate
                    <reg norm="eorundem" type="context">eorũdem</reg>
                  corporum, ſed pro
                    <lb/>
                  pter ſimilitudinem connexionis, cum productum ex duobus medijs proportionali-
                    <lb/>
                  bus æquale ſit producto ab extremis, & idem reſpectus, quem primum ipſorum qua
                    <lb/>
                  tuor ad ſecundum habet, ſecundi ad tertium extet, vnde ſecundum primo ſimile
                    <lb/>
                  euadit, & contra, reſpectus qui eſt quarti ad tertium, ſit etiam tertij ad ſecundum, vn-
                    <lb/>
                  de ipſum tertium, ratione vltimi ſubit, & eius imaginem induit, & hanc ob cauſam
                    <lb/>
                  ſic ſcribit Plato.</s>
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                <quote>
                  <s xml:id="echoid-s4745" xml:space="preserve">Propterea ex huiuſmodi rebus numero quaternario concluſis, mundi corpus con
                    <lb/>
                  flatum eſt, ea connexum comparatione qua dixi. </s>
                  <s xml:id="echoid-s4746" xml:space="preserve">Ex quo ſeipſum amicitia concor-
                    <lb/>
                  di complectitur,
                    <reg norm="&c." type="unresolved">&c.</reg>
                  </s>
                </quote>
                <p>
                  <s xml:id="echoid-s4747" xml:space="preserve">Vbi Platonem, elementa maiora,
                    <reg norm="minoranue" type="context">minorãue</reg>
                  in proportionalitate continua, nec
                    <lb/>
                  geometrica, nec alterius cuiuſuis generis eſſe noluiſſe, clarè perſpicitur, ſed huiuſmo
                    <lb/>
                  di ſimilitudine, in eo quod media elementa cum extremis conueniunt eſt vſus, quæ
                    <lb/>
                  quidem conuenientia, nullibi maior, quam in proportionalitate continua geome-
                    <lb/>
                  trica reperitur. </s>
                  <s xml:id="echoid-s4748" xml:space="preserve">Sed etiam ſi Plato de huiuſmodi corporea elementorum magnitu-
                    <lb/>
                  dine ſeipſum intelligi voluiſſet, ſi ſemidiameter regionis elementaris ex ęquo vt .39
                    <lb/>
                  ad vnum, reſpectu ſemidiametri terræ fuiſſet, aqua, ipſam terram, magis quam tri-
                    <lb/>
                  geſies, & octies, non ſolum decies, & aer quoque eandem magis quam .1500. &
                    <lb/>
                  ignis magis quam .55000. partibus magnitudine ſuperaret.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4749" xml:space="preserve">Subſtantia vero rerum quas ſcripſeram circa finem illius conſiderationis talis fuit.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4750" xml:space="preserve">Nunc autem tempus eſſe videtur, vt ego etiam, ne tantum deſtruxiſſe, ſed etiam
                    <lb/>
                  conſtruxiſſe videar aliquid pro veritate diſſeram.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4751" xml:space="preserve">Non eſt igitur dubium, ſolidæ doctrinæ viris, quin præſtantiſſimus Piccolo. ſe-
                    <lb/>
                  cutus ſit tutam viam ad explorandum, quod terra maior ſit quam aqua, metiendo
                    <lb/>
                  vtriuſque horum corporum ſuperficiem detectam. </s>
                  <s xml:id="echoid-s4752" xml:space="preserve">Omittamus autem compenſa-
                    <lb/>
                  tionem illam curuitatis, & concauitatis vallium, & montium,
                    <reg norm="&c." type="unresolved">&c.</reg>
                  quam ipſe Piccolo.
                    <lb/>
                  propè finem ſexti cap. vellet dare fluminibus, ſtagnis, fontibus, & eiuſmodi aquis.
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4753" xml:space="preserve">eo enim in loco labitur Piccolo. vbi non conſiderat, quod eiuſmodi obliquis ſuper-
                    <lb/>
                  ficiebus non reſpondent anguli ſolidi centri ſphæræ, qui reſpiciunt eorum baſim ad
                    <lb/>
                  rectos angulos. </s>
                  <s xml:id="echoid-s4754" xml:space="preserve">Sed poſtquam Piccolo. comperit ſuperficiem terrę detectam, eſſe
                    <lb/>
                  maiorem apparente ſuperficie ſphærica aquæ, proculdubio poterat concludere ter-
                    <lb/>
                  ram eſſe maiorem aqua, ſicuti fecit,
                    <reg norm="etiam" type="context">etiã</reg>
                  ſi aqua profunda eſſet pyramidaliter
                    <reg norm="vſque" type="simple">vſq;</reg>
                    <lb/>
                  ad mundi centrum, ideſt .3500. milliaria, ſupponendo tantum eſſe huius globi ſemi
                    <lb/>
                  diametrum.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4755" xml:space="preserve">Verum quia poſſet aliquis dubitare circa diligentiam Piccolo. in hiſcæ duabus ſu
                    <lb/>
                  perficiebus dimetiendis, viſum eſt mihi non alienum ſequi aliam viam pro hac veri
                    <lb/>
                  tate probanda, ſupponendo verum eſſe, quod non vnus ſolus metitus fuerit, ſed mul
                    <lb/>
                  ti, ideſt ſupponendo
                    <reg norm="verum" type="context">verũ</reg>
                  eſſe quod maris profunditas menſurari poſſit, & præterea,
                    <lb/>
                  quod non modo ipſius maris maxima profunditas non perueniat ad quingentos paſ
                    <lb/>
                  ſus, ſicuti refert Piccolo. in fine ſui tractatus, & mihi aſſeruerunt Hiſpani multi, &
                    <lb/>
                  Luſitani præſtantiſſimi nautæ, tum Venetijs, tum Parmæ, in Aula Sereniſſimæ quon
                    <lb/>
                  dam Principis, inter quos, Venetijs fuit Illuſtris Rodericus Guzmanus, Dominus
                    <lb/>
                  Franciſcus Lopes, Dominus Garzias de Seuilia,
                    <reg norm="multique" type="simple">multiq́;</reg>
                  alij. </s>
                  <s xml:id="echoid-s4756" xml:space="preserve">Parmæ autem varij </s>
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