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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          <div xml:id="echoid-div477" type="chapter" level="2" n="6">
            <div xml:id="echoid-div642" type="section" level="3" n="28">
              <div xml:id="echoid-div666" type="letter" level="4" n="8">
                <p>
                  <s xml:id="echoid-s4189" xml:space="preserve">
                    <pb o="346" rhead="IO. BABPT. BENED." n="358" file="0358" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/pageimg/0358"/>
                  deſcendat radius
                    <var>.b.d.K.s.f.</var>
                  ad
                    <reg norm="libitum" type="context">libitũ</reg>
                  hoc eſt rectè vel obliquè, cuius pars
                    <var>.b.d.</var>
                  in ipſo
                    <lb/>
                  aere exiſtat. </s>
                  <s xml:id="echoid-s4190" xml:space="preserve">Nunc manifeſtum erit partem
                    <var>.b.d.</var>
                  ipſius radij clariorem ſeu minus im
                    <lb/>
                    <reg norm="peditam" type="context">peditã</reg>
                  eſſe quam
                    <var>.d.K.</var>
                  quod ex eo etiam cognoſcere poſſumus quia
                    <var>.b.d.</var>
                  reflectitur à
                    <lb/>
                  puncto
                    <var>.d.</var>
                  ſuperficiei corporis a quei, quapropter minus luminoſa remanebit pars
                    <var>.d.
                      <lb/>
                    K.</var>
                  cum non tota claritas
                    <var>.b.d.</var>
                  deſcendat in corpore aqueo, ſed vna eius pars reflecta-
                    <lb/>
                  tur, reliqua verò tantummodò deſcendat, </s>
                  <s xml:id="echoid-s4191" xml:space="preserve">deinde pars
                    <var>.K.s.</var>
                  ex neceſſitate debilior
                    <lb/>
                  erit ipſa
                    <var>.d.K.</var>
                  eo quod ſuccedit poſt ipſam
                    <var>.d.K.</var>
                  propter hoc etiam, quia cum corpus
                    <lb/>
                  aqueum habeat aliquantulum opacitatis, radius
                    <var>.d.K.</var>
                  ab omni puncto ipſius ſpiſſitu-
                    <lb/>
                  dinis a quæ continuo reflectitur, quę quidem reflexio eſt illud lumen cęruleum, quod
                    <lb/>
                  in profunditate ipſius aquę nobis apparet. </s>
                  <s xml:id="echoid-s4192" xml:space="preserve">Cum igitur reflexio ipſa ſemper detra-
                    <lb/>
                  hat ab ipſo radio luminoſo, reſiduum verò ſit id quod penetrat, ideo
                    <var>.K.s.</var>
                  erit vna
                    <lb/>
                  pars tantummodò luminis ipſius
                    <var>.d.K</var>
                  : in
                    <var>.s.f.</var>
                  verò aliqua pars luminis ipſius
                    <var>.K.s.</var>
                  & ſic
                    <lb/>
                  continuò debilitatur radius, ita quod ad nihilum vſque deuenit, & vltra tale cor-
                    <lb/>
                  pus remanebit vmbra, quaſi ſi ipſum corpus eſſet perfectè opacum, cuius rei cauſa,
                    <lb/>
                  eſt illa continua reflexio, vt diximus, quæ continuò adimit aliquid ex ipſo radio,
                    <lb/>
                  nec permittit eum totum tranſire.</s>
                </p>
                <p>
                  <s xml:id="echoid-s4193" xml:space="preserve">Quapropter mirandum non eſt eos, qui margaritas quærunt in fundo maris nul-
                    <lb/>
                  lum ibi videre lumen. </s>
                  <s xml:id="echoid-s4194" xml:space="preserve">Nihilominus vmbra maris, quam dico nos poſſe videre in
                    <lb/>
                  ſuperficie corporis lunaris, ab alia etiam ratione prouenire poſſet. </s>
                  <s xml:id="echoid-s4195" xml:space="preserve">Imaginemur enim
                    <lb/>
                  aggregatum terrę,
                    <reg norm="marisque" type="simple">marisq́;</reg>
                  eſſe tantummodò aqueum, quod quidem eſſet perfectè
                    <lb/>
                  ſphæricum ratione centri grauitatis,
                    <reg norm="ſupponamusque" type="simple">ſupponamusq́;</reg>
                    <reg norm="ipsum" type="context">ipsũ</reg>
                  eſſe valde diaphanum, ita
                    <lb/>
                  quod radij ſolares ipſum penetraſſent. </s>
                  <s xml:id="echoid-s4196" xml:space="preserve">Tunc dico quod in ſuperficie corporis luna-
                    <lb/>
                  ris produceret vmbram. </s>
                  <s xml:id="echoid-s4197" xml:space="preserve">Pro cuius intelligentia cogitemus ſubſcriptam hic figuram
                    <lb/>
                    <var>b.h.q.a.e.</var>
                  eſſe ſphęram aliquam cryſtallinam, & ad partem
                    <var>.b.h.q.</var>
                  ſit radius lumino-
                    <lb/>
                  ſus ſolaris qui ipſam illuminet, cuius radij extremitates ſint
                    <var>.d.b.l.</var>
                  et
                    <var>.p.q.r.</var>
                  ſupponen-
                    <lb/>
                  do
                    <var>.d.l.</var>
                  et
                    <var>.p.r.</var>
                  terminos eſſe vnius plani ſecantis ipſum radium per axem, </s>
                  <s xml:id="echoid-s4198" xml:space="preserve">tunc vide-
                    <lb/>
                  bis ipſum radium
                    <var>.b.p.q.d.</var>
                    <reg norm="tranſeun- tem" type="context">tranſeũ-
                      <lb/>
                      <figure xlink:label="fig-0358-01" xlink:href="fig-0358-01a" number="392">
                        <image file="0358-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0358-01"/>
                      </figure>
                    tem</reg>
                  ipſam ſphæram, congregari ſeu
                    <lb/>
                    <reg norm="condenſari" type="context">condẽſari</reg>
                  , ob vniformem refractio-
                    <lb/>
                  nem, vſque ad punctum
                    <var>.o.</var>
                  deinde;
                    <lb/>
                  propter rectitudinem ipſius diffu-
                    <lb/>
                  ſionis, vltra punctum
                    <var>.o.</var>
                  ipſum dila-
                    <lb/>
                  tari, diſgregari, ſeu rarefieri,
                    <reg norm="quouſque" type="simple">quouſq;</reg>
                    <lb/>
                  nullius illuminationis actum habeat .
                    <lb/>
                  vt: exempli gratia
                    <var>.o.t.</var>
                  et
                    <var>.o.s.</var>
                  eius par
                    <lb/>
                  tes, ita quod interualla
                    <var>.c.o.b.</var>
                  et
                    <var>.u.</var>
                    <lb/>
                    <figure xlink:label="fig-0358-02" xlink:href="fig-0358-02a" number="393">
                      <image file="0358-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/163127KK/figures/0358-02"/>
                    </figure>
                    <var>o.q.</var>
                  relinquerentur priuata lumini-
                    <lb/>
                  bus, vnde vmbroſa remanerent. di-
                    <lb/>
                    <reg norm="ſtantiaque" type="simple">ſtantiaq́;</reg>
                  ab
                    <var>.o.</var>
                  ad ſuperficiem ſphęri
                    <lb/>
                  cam corporis
                    <var>.b.e.d.q.</var>
                  non ſolum
                    <reg norm="non" type="context">nõ</reg>
                    <lb/>
                  maior eſt diametro ipſius ſphæræ;
                    <lb/>
                  </s>
                  <s xml:id="echoid-s4199" xml:space="preserve">imo minor, vt à te ipſo experiri po-
                    <lb/>
                  tes. </s>
                  <s xml:id="echoid-s4200" xml:space="preserve">Poſito igitur aliquo obiecto
                    <lb/>
                  opaco in loco
                    <var>.K.o.g.</var>
                  eius ſuperficies
                    <lb/>
                  intercepta inter
                    <var>.K.</var>
                  et
                    <var>.g.</var>
                  adumbrata
                    <lb/>
                  erit, excepto puncto
                    <var>.o</var>
                  . </s>
                  <s xml:id="echoid-s4201" xml:space="preserve">Poſito dein
                    <lb/>
                  de ipſo obiecto in loco
                    <var>.n.y.x.m.</var>
                    <reg norm="eius" type="simple">eiꝰ</reg>
                    <lb/>
                  partes
                    <var>.y.n.</var>
                  et
                    <var>.x.m.</var>
                  remanebunt lu- </s>
                </p>
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