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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          <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>
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