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
381 369
382 370
383 371
384 372
385 373
386 374
387 375
388 376
389 377
390 378
391 379
392 380
393 381
394 382
395 383
396 384
397 385
398 386
399 387
400 388
401 389
402 390
403 391
404 392
405 393
406 394
407 395
408 396
409 397
410 398
< >
page |< < (399) 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">
                <quote>
                  <s xml:id="echoid-s4714" xml:space="preserve">
                    <pb o="399" rhead="EPISTOLAE." n="411" file="0411" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0411"/>
                  quamuis
                    <reg norm="perſpicuum" type="context">perſpicuũ</reg>
                  ſiue
                    <reg norm="tranſparens" type="context">tranſparẽs</reg>
                  ſit, nihilominus propter obſtaculum plumbi ſub
                    <lb/>
                  ipſo poſiti, efficit vt radij viſuales repercuſſi reuertantur. ita etiam quamuis aqua ſit
                    <lb/>
                  corpus tranſparens, nihilominus propter obſtaculum terræ opacæ, quæ ſubſidet in
                    <lb/>
                  fundo maris efficere poteſt obſcuras partes illas ſub aqua, illis hominibus qui in
                    <lb/>
                  ipſa aqua mèrguntur.</s>
                </quote>
                <p>
                  <s xml:id="echoid-s4715" xml:space="preserve">In hac ſecunda ratione decipitur Piccolhom. </s>
                  <s xml:id="echoid-s4716" xml:space="preserve">Primum quia ſi vſque ad imam par
                    <lb/>
                  tem maris, Solis radius ferri poſſet, ille qui ibi eſſet, attollens oculos ſurſum Solem
                    <lb/>
                  cerneret, </s>
                  <s xml:id="echoid-s4717" xml:space="preserve">deinde aſpiciendo ipſum fundum Maris, videret illum, ratione reflexio-
                    <lb/>
                  nis luminis ab ipſo fundo, & ex eadem ratione ſpeculi ab ipſo adducta, quæ contra
                    <lb/>
                  ipſum eſt.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4718" xml:space="preserve">Decipitur etiam cum dicatradios viſuales à ſpeculo ſeu plumbo repercuti, eo
                    <reg norm="quod" type="simple">ꝙ</reg>
                    <lb/>
                  non radij viſuales ſunt hi qui reflectuntur, ſed ſunt radij luminoſi primarij, ſeu ſecun
                    <lb/>
                  darij qui non ab oculis exeunt ſed à corpore lucido.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4719" xml:space="preserve">Scripſi etiam quod ſi verum eſſet proportionalitatem continuam
                    <reg norm="quantitatum" type="context">quãtitatum</reg>
                  ele-
                    <lb/>
                  mentorum ex proportione decupla conſtare, ignem pro maximo, terram verò pro
                    <lb/>
                  minimo terminorum ſumentes, totum aggregatum ex terra, aqua, aere, & igne, ita
                    <lb/>
                  eſſet maius terra, quemadmodum mille centum & vndecim ad vnum, vnde ſemidia
                    <lb/>
                  meter regionis elementaris eſſet quaſi aut paulo maior decuplo ſolum ſemidiame-
                    <lb/>
                  tro terræ, vnde inter conuexum ignis, & concauum minimi, ſeu inferioris orbis lu-
                    <lb/>
                  naris, relinqueretur quidam orbis vacuus ſpiſſitudinis vnius interualli plus quam vi-
                    <lb/>
                  ginti terræ ſemidiametrorum, quod ſpatium vacuum orbiculariter, maius exi-
                    <lb/>
                  ſteret ipſa totali regione elementari plus quam trigeſies millies, immo ſi ſemidia
                    <lb/>
                  meter dicti primi orbislunaris maior eſſet terreſtri vt trigintanouem ad unum,
                    <reg norm="dictus" type="simple">dictꝰ</reg>
                    <lb/>
                  orbis vacuus maior eſſet elementari regione plus quam .58208. ad vnum, proportio
                    <lb/>
                  nalitatem igitur continuam quæ ex decupla proportionalitate reſultat in elementis
                    <lb/>
                  eſſe putare eſt maximus error.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4720" xml:space="preserve">Subdit deinde Berga, hoc voluiſſe Platonem neceſſario requiri, vt extrema ele-
                    <lb/>
                  menta, nempeignis & terra cum duobus medijs aere, & aqua coniungerentur, cum in
                    <lb/>
                  corporibus ſolidis (quaſi Bergę ſint quædam corpora quæ ſolida non extent) poſſit
                    <lb/>
                  dari medium æquale in geometrica proportione.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4721" xml:space="preserve">Sed vbi Plato ad ſermonem de numero elementorum ſe confert, poſtquam ra-
                    <lb/>
                  tione creationis ignis, & terrę ſe propoſuiſſe putat, vt
                    <reg norm="idem" type="context">idẽ</reg>
                  de alijs duobus corporibus
                    <lb/>
                  medijs probet, comparatione proportionalitatis continuæ geometricæ in tribus ter-
                    <lb/>
                  minis, ratione rerum ſuperficialium primò, deinde in quatuor, ratione corporearum
                    <lb/>
                  vtitur, ita dicens.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s4722" xml:space="preserve">Vinculorum verò ideſt aptiſſimum atque pulcherrimum quod exſe, & ex ijs quę
                    <lb/>
                  aſtringunt, quam maximè vnum efficit,
                    <reg norm="&c." type="unresolved">&c.</reg>
                  </s>
                </quote>
                <p>
                  <s xml:id="echoid-s4723" xml:space="preserve">Quo in loco Plato inſerre vult de proportionalitate geometrica trium termino-
                    <lb/>
                  rum, in qua ijdem ita ſe habent, vt medius, primi,
                    <reg norm="vltimique" type="simple">vltimiq́;</reg>
                  vice fungatur, ita vt vtriuſ-
                    <lb/>
                  que ipſorum extremorum particeps fiat, cum productum quod à medio termino in
                    <lb/>
                  ſeipſo progignitur idem ſit ei quod ab extremis fuit, vnde medius, potentia idem eſt
                    <lb/>
                  quod productum ab extremis.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4724" xml:space="preserve">Subdit deinde Plato dicens.</s>
                </p>
                <quote>
                  <s xml:id="echoid-s4725" xml:space="preserve">Quando enim in tribus numeris, aut molibus, aut viribus, medium ita ſe habet
                    <lb/>
                  ad poſtremum vt primum ad medium,
                    <reg norm="viciſſimque" type="simple">viciſſimq́;</reg>
                  vt poſtremum cum medio, ita me-
                    <lb/>
                  dium cum primo congruit, </s>
                  <s xml:id="echoid-s4726" xml:space="preserve">tunc quod medium eſt, & primum fit &
                    <reg norm="poſtremum" type="context">poſtremũ</reg>
                  , po-
                    <lb/>
                  ſtremum quoque, & primum & media fiunt.</s>
                </quote>
              </div>
            </div>
          </div>
        </div>
      </text>
    </echo>
Impressum