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]

Page concordance

< >
Scan Original
361 349
362 350
363 351
364 352
365 353
366 354
367 355
368 356
369 357
370 358
371 359
372 360
373 361
374 362
375 363
376 364
377 365
378 366
379 367
380 368
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
< >
page |< < (401) of 445 > >|
    <echo version="1.0">
      <text type="book" xml:lang="la">
        <div xml:id="echoid-div7" type="body" level="1" n="1">
          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div756" type="section" level="3" n="43">
              <div xml:id="echoid-div756" type="letter" level="4" n="1">
                <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>
                </p>
                <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>
                </p>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum